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. 2021 Jun 2;81(6):488. doi: 10.1140/epjc/s10052-021-09200-x

Measurements of production cross sections of the Higgs boson in the four-lepton final state in proton–proton collisions at s=13TeV

CMS Collaboration288, A M Sirunyan 1, A Tumasyan 1, W Adam 2, J W Andrejkovic 2, T Bergauer 2, S Chatterjee 2, M Dragicevic 2, A Escalante Del Valle 2, R Frühwirth 2,195, M Jeitler 2,195, N Krammer 2, L Lechner 2, D Liko 2, I Mikulec 2, F M Pitters 2, J Schieck 2,195, R Schöfbeck 2, M Spanring 2, S Templ 2, W Waltenberger 2, C-E Wulz 2,195, V Chekhovsky 3, A Litomin 3, V Makarenko 3, M R Darwish 4,196, E A De Wolf 4, X Janssen 4, T Kello 4,197, A Lelek 4, H Rejeb Sfar 4, P Van Mechelen 4, S Van Putte 4, N Van Remortel 4, F Blekman 5, E S Bols 5, J D’Hondt 5, J De Clercq 5, M Delcourt 5, S Lowette 5, S Moortgat 5, A Morton 5, D Müller 5, A R Sahasransu 5, S Tavernier 5, W Van Doninck 5, P Van Mulders 5, D Beghin 6, B Bilin 6, B Clerbaux 6, G De Lentdecker 6, L Favart 6, A Grebenyuk 6, A K Kalsi 6, K Lee 6, I Makarenko 6, L Moureaux 6, L Pétré 6, A Popov 6, N Postiau 6, E Starling 6, L Thomas 6, C Vander Velde 6, P Vanlaer 6, D Vannerom 6, L Wezenbeek 6, T Cornelis 7, D Dobur 7, M Gruchala 7, G Mestdach 7, M Niedziela 7, C Roskas 7, K Skovpen 7, M Tytgat 7, W Verbeke 7, B Vermassen 7, M Vit 7, A Bethani 8, G Bruno 8, F Bury 8, C Caputo 8, P David 8, C Delaere 8, I S Donertas 8, A Giammanco 8, V Lemaitre 8, K Mondal 8, J Prisciandaro 8, A Taliercio 8, M Teklishyn 8, P Vischia 8, S Wertz 8, S Wuyckens 8, G A Alves 9, C Hensel 9, A Moraes 9, W L Aldá Júnior 10, M Barroso Ferreira Filho 10, H Brandao Malbouisson 10, W Carvalho 10, J Chinellato 10,198, E M Da Costa 10, G G Da Silveira 10,199, D De Jesus Damiao 10, S Fonseca De Souza 10, J Martins 10,200, D Matos Figueiredo 10, C Mora Herrera 10, K Mota Amarilo 10, L Mundim 10, H Nogima 10, P Rebello Teles 10, L J Sanchez Rosas 10, A Santoro 10, S M Silva Do Amaral 10, A Sznajder 10, M Thiel 10, F Torres Da Silva De Araujo 10, A Vilela Pereira 10, C A Bernardes 11, L Calligaris 11, T R Fernandez Perez Tomei 11, E M Gregores 11, D S Lemos 11, P G Mercadante 11, S F Novaes 11, Sandra S Padula 11, A Aleksandrov 12, G Antchev 12, I Atanasov 12, R Hadjiiska 12, P Iaydjiev 12, M Misheva 12, M Rodozov 12, M Shopova 12, G Sultanov 12, A Dimitrov 13, T Ivanov 13, L Litov 13, B Pavlov 13, P Petkov 13, A Petrov 13, T Cheng 14, W Fang 14,197, Q Guo 14, T Javaid 14,201, M Mittal 14, H Wang 14, L Yuan 14, M Ahmad 15, G Bauer 15, C Dozen 15,202, Z Hu 15, Y Wang 15, K Yi 15,203,204, E Chapon 16, G M Chen 16,201, H S Chen 16,201, M Chen 16, A Kapoor 16, D Leggat 16, H Liao 16, Z-A LIU 16,201, R Sharma 16, A Spiezia 16, J Tao 16, J Thomas-wilsker 16, J Wang 16, H Zhang 16, S Zhang 16,201, J Zhao 16, A Agapitos 17, Y Ban 17, C Chen 17, Q Huang 17, A Levin 17, Q Li 17, M Lu 17, X Lyu 17, Y Mao 17, S J Qian 17, D Wang 17, Q Wang 17, J Xiao 17, Z You 18, X Gao 19,197, H Okawa 19, M Xiao 20, C Avila 21, A Cabrera 21, C Florez 21, J Fraga 21, A Sarkar 21, M A Segura Delgado 21, J Jaramillo 22, J Mejia Guisao 22, F Ramirez 22, J D Ruiz Alvarez 22, C A Salazar González 22, N Vanegas Arbelaez 22, D Giljanovic 23, N Godinovic 23, D Lelas 23, I Puljak 23, Z Antunovic 24, M Kovac 24, T Sculac 24, V Brigljevic 25, D Ferencek 25, D Majumder 25, M Roguljic 25, A Starodumov 25,205, T Susa 25, A Attikis 26, E Erodotou 26, A Ioannou 26, G Kole 26, M Kolosova 26, S Konstantinou 26, J Mousa 26, C Nicolaou 26, F Ptochos 26, P A Razis 26, H Rykaczewski 26, H Saka 26, M Finger 27,206, M Finger Jr 27,206, A Kveton 27, J Tomsa 27, E Ayala 28, E Carrera Jarrin 29, S Abu Zeid 30,207, S Khalil 30,208, E Salama 30,207,209, M A Mahmoud 31, Y Mohammed 31, S Bhowmik 32, A Carvalho Antunes De Oliveira 32, R K Dewanjee 32, K Ehataht 32, M Kadastik 32, J Pata 32, M Raidal 32, C Veelken 32, P Eerola 33, L Forthomme 33, H Kirschenmann 33, K Osterberg 33, M Voutilainen 33, E Brücken 34, F Garcia 34, J Havukainen 34, V Karimäki 34, M S Kim 34, R Kinnunen 34, T Lampén 34, K Lassila-Perini 34, S Lehti 34, T Lindén 34, H Siikonen 34, E Tuominen 34, J Tuominiemi 34, P Luukka 35, H Petrow 35, T Tuuva 35, C Amendola 36, M Besancon 36, F Couderc 36, M Dejardin 36, D Denegri 36, J L Faure 36, F Ferri 36, S Ganjour 36, A Givernaud 36, P Gras 36, G Hamel de Monchenault 36, P Jarry 36, B Lenzi 36, E Locci 36, J Malcles 36, J Rander 36, A Rosowsky 36, M Ö Sahin 36, A Savoy-Navarro 36,210, M Titov 36, G B Yu 36, S Ahuja 37, F Beaudette 37, M Bonanomi 37, A Buchot Perraguin 37, P Busson 37, C Charlot 37, O Davignon 37, B Diab 37, G Falmagne 37, R Granier de Cassagnac 37, A Hakimi 37, I Kucher 37, A Lobanov 37, C Martin Perez 37, M Nguyen 37, C Ochando 37, P Paganini 37, J Rembser 37, R Salerno 37, J B Sauvan 37, Y Sirois 37, A Zabi 37, A Zghiche 37, J-L Agram 38,211, J Andrea 38, D Apparu 38, D Bloch 38, G Bourgatte 38, J-M Brom 38, E C Chabert 38, C Collard 38, D Darej 38, J-C Fontaine 38,211, U Goerlach 38, C Grimault 38, A-C Le Bihan 38, P Van Hove 38, E Asilar 39, S Beauceron 39, C Bernet 39, G Boudoul 39, C Camen 39, A Carle 39, N Chanon 39, D Contardo 39, P Depasse 39, H El Mamouni 39, J Fay 39, S Gascon 39, M Gouzevitch 39, B Ille 39, Sa Jain 39, I B Laktineh 39, H Lattaud 39, A Lesauvage 39, M Lethuillier 39, L Mirabito 39, K Shchablo 39, L Torterotot 39, G Touquet 39, M Vander Donckt 39, S Viret 39, A Khvedelidze 40,206, Z Tsamalaidze 40,206, L Feld 41, K Klein 41, M Lipinski 41, D Meuser 41, A Pauls 41, M P Rauch 41, J Schulz 41, M Teroerde 41, D Eliseev 42, M Erdmann 42, P Fackeldey 42, B Fischer 42, S Ghosh 42, T Hebbeker 42, K Hoepfner 42, H Keller 42, L Mastrolorenzo 42, M Merschmeyer 42, A Meyer 42, G Mocellin 42, S Mondal 42, S Mukherjee 42, D Noll 42, A Novak 42, T Pook 42, A Pozdnyakov 42, Y Rath 42, H Reithler 42, J Roemer 42, A Schmidt 42, S C Schuler 42, A Sharma 42, S Wiedenbeck 42, S Zaleski 42, C Dziwok 43, G Flügge 43, W Haj Ahmad 43,212, O Hlushchenko 43, T Kress 43, A Nowack 43, C Pistone 43, O Pooth 43, D Roy 43, H Sert 43, A Stahl 43,213, T Ziemons 43, H Aarup Petersen 44, M Aldaya Martin 44, P Asmuss 44, I Babounikau 44, S Baxter 44, O Behnke 44, A Bermúdez Martínez 44, A A Bin Anuar 44, K Borras 44,214, V Botta 44, D Brunner 44, A Campbell 44, A Cardini 44, P Connor 44, S Consuegra Rodríguez 44, V Danilov 44, M M Defranchis 44, L Didukh 44, D Domínguez Damiani 44, G Eckerlin 44, D Eckstein 44, L I Estevez Banos 44, E Gallo 44,215, A Geiser 44, A Giraldi 44, A Grohsjean 44, M Guthoff 44, A Harb 44, A Jafari 44,216, N Z Jomhari 44, H Jung 44, A Kasem 44,214, M Kasemann 44, H Kaveh 44, C Kleinwort 44, J Knolle 44, D Krücker 44, W Lange 44, T Lenz 44, J Lidrych 44, K Lipka 44, W Lohmann 44,217, T Madlener 44, R Mankel 44, I-A Melzer-Pellmann 44, J Metwally 44, A B Meyer 44, M Meyer 44, J Mnich 44, A Mussgiller 44, V Myronenko 44, Y Otarid 44, D Pérez Adán 44, S K Pflitsch 44, D Pitzl 44, A Raspereza 44, A Saggio 44, A Saibel 44, M Savitskyi 44, V Scheurer 44, C Schwanenberger 44, A Singh 44, R E Sosa Ricardo 44, N Tonon 44, O Turkot 44, A Vagnerini 44, M Van De Klundert 44, R Walsh 44, D Walter 44, Y Wen 44, K Wichmann 44, C Wissing 44, S Wuchterl 44, O Zenaiev 44, R Zlebcik 44, R Aggleton 45, S Bein 45, L Benato 45, A Benecke 45, K De Leo 45, T Dreyer 45, M Eich 45, F Feindt 45, A Fröhlich 45, C Garbers 45, E Garutti 45, P Gunnellini 45, J Haller 45, A Hinzmann 45, A Karavdina 45, G Kasieczka 45, R Klanner 45, R Kogler 45, V Kutzner 45, J Lange 45, T Lange 45, A Malara 45, A Nigamova 45, K J Pena Rodriguez 45, O Rieger 45, P Schleper 45, M Schröder 45, J Schwandt 45, D Schwarz 45, J Sonneveld 45, H Stadie 45, G Steinbrück 45, A Tews 45, B Vormwald 45, I Zoi 45, J Bechtel 46, T Berger 46, E Butz 46, R Caspart 46, T Chwalek 46, W De Boer 46, A Dierlamm 46, A Droll 46, K El Morabit 46, N Faltermann 46, K Flöh 46, M Giffels 46, J o Gosewisch 46, A Gottmann 46, F Hartmann 46,213, C Heidecker 46, U Husemann 46, I Katkov 46,218, P Keicher 46, R Koppenhöfer 46, S Maier 46, M Metzler 46, S Mitra 46, Th Müller 46, M Musich 46, M Neukum 46, G Quast 46, K Rabbertz 46, J Rauser 46, D Savoiu 46, D Schäfer 46, M Schnepf 46, D Seith 46, I Shvetsov 46, H J Simonis 46, R Ulrich 46, J Van Der Linden 46, R F Von Cube 46, M Wassmer 46, M Weber 46, S Wieland 46, R Wolf 46, S Wozniewski 46, S Wunsch 46, G Anagnostou 47, P Asenov 47, G Daskalakis 47, T Geralis 47, A Kyriakis 47, D Loukas 47, G Paspalaki 47, A Stakia 47, M Diamantopoulou 48, D Karasavvas 48, G Karathanasis 48, P Kontaxakis 48, C K Koraka 48, A Manousakis-katsikakis 48, A Panagiotou 48, I Papavergou 48, N Saoulidou 48, K Theofilatos 48, E Tziaferi 48, K Vellidis 48, E Vourliotis 48, G Bakas 49, K Kousouris 49, I Papakrivopoulos 49, G Tsipolitis 49, A Zacharopoulou 49, I Evangelou 50, C Foudas 50, P Gianneios 50, P Katsoulis 50, P Kokkas 50, N Manthos 50, I Papadopoulos 50, J Strologas 50, M Csanad 51, M M A Gadallah 51,219, S Lökös 51,220, P Major 51, K Mandal 51, A Mehta 51, G Pasztor 51, A J Rádl 51, O Surányi 51, GI Veres 51, M Bartók 52,221, G Bencze 52, C Hajdu 52, D Horvath 52,222, F Sikler 52, V Veszpremi 52, G Vesztergombi 52, S Czellar 53, J Karancsi 53,221, J Molnar 53, Z Szillasi 53, D Teyssier 53, P Raics 54, Z L Trocsanyi 54,223, B Ujvari 54, T Csorgo 55,224, F Nemes 55,224, T Novak 55, S Choudhury 56, J R Komaragiri 56, D Kumar 56, L Panwar 56, P C Tiwari 56, S Bahinipati 57,225, D Dash 57, C Kar 57, P Mal 57, T Mishra 57, V K Muraleedharan Nair Bindhu 57,226, A Nayak 57,226, P Saha 57, N Sur 57, S K Swain 57, S Bansal 58, S B Beri 58, V Bhatnagar 58, G Chaudhary 58, S Chauhan 58, N Dhingra 58,227, R Gupta 58, A Kaur 58, S Kaur 58, P Kumari 58, M Meena 58, K Sandeep 58, J B Singh 58, A K Virdi 58, A Ahmed 59, A Bhardwaj 59, B C Choudhary 59, R B Garg 59, M Gola 59, S Keshri 59, A Kumar 59, M Naimuddin 59, P Priyanka 59, K Ranjan 59, A Shah 59, M Bharti 60,228, R Bhattacharya 60, S Bhattacharya 60, D Bhowmik 60, S Dutta 60, S Ghosh 60, B Gomber 60,229, M Maity 60,230, S Nandan 60, P Palit 60, P K Rout 60, G Saha 60, B Sahu 60, S Sarkar 60, M Sharan 60, B Singh 60,228, S Thakur 60,228, P K Behera 61, S C Behera 61, P Kalbhor 61, A Muhammad 61, R Pradhan 61, P R Pujahari 61, A Sharma 61, A K Sikdar 61, D Dutta 62, V Jha 62, V Kumar 62, D K Mishra 62, K Naskar 62,231, P K Netrakanti 62, L M Pant 62, P Shukla 62, T Aziz 63, S Dugad 63, G B Mohanty 63, U Sarkar 63, S Banerjee 64, S Bhattacharya 64, R Chudasama 64, M Guchait 64, S Karmakar 64, S Kumar 64, G Majumder 64, K Mazumdar 64, S Mukherjee 64, D Roy 64, S Dube 65, B Kansal 65, S Pandey 65, A Rane 65, A Rastogi 65, S Sharma 65, H Bakhshiansohi 66,232, M Zeinali 66,233, S Chenarani 67,234, S M Etesami 67, M Khakzad 67, M Mohammadi Najafabadi 67, M Felcini 68, M Grunewald 68, M Abbrescia 69, R Aly 69,235, C Aruta 69, A Colaleo 69, D Creanza 69, N De Filippis 69, M De Palma 69, A Di Florio 69, A Di Pilato 69, W Elmetenawee 69, L Fiore 69, A Gelmi 69, M Gul 69, G Iaselli 69, M Ince 69, S Lezki 69, G Maggi 69, M Maggi 69, I Margjeka 69, V Mastrapasqua 69, J A Merlin 69, S My 69, S Nuzzo 69, A Pompili 69, G Pugliese 69, A Ranieri 69, G Selvaggi 69, L Silvestris 69, F M Simone 69, R Venditti 69, P Verwilligen 69, G Abbiendi 70, C Battilana 70, D Bonacorsi 70, L Borgonovi 70, S Braibant-Giacomelli 70, L Brigliadori 70, R Campanini 70, P Capiluppi 70, A Castro 70, F R Cavallo 70, C Ciocca 70, M Cuffiani 70, G M Dallavalle 70, T Diotalevi 70, F Fabbri 70, A Fanfani 70, E Fontanesi 70, P Giacomelli 70, L Giommi 70, C Grandi 70, L Guiducci 70, F Iemmi 70, S Lo Meo 70,236, S Marcellini 70, G Masetti 70, F L Navarria 70, A Perrotta 70, F Primavera 70, A M Rossi 70, T Rovelli 70, G P Siroli 70, N Tosi 70, S Albergo 71,71,237, S Costa 71,71,237, A Di Mattia 71, R Potenza 71, A Tricomi 71,71,237, C Tuve 71, G Barbagli 72, A Cassese 72, R Ceccarelli 72, V Ciulli 72, C Civinini 72, R D’Alessandro 72, F Fiori 72, E Focardi 72, G Latino 72, P Lenzi 72, M Lizzo 72, M Meschini 72, S Paoletti 72, R Seidita 72, G Sguazzoni 72, L Viliani 72, L Benussi 73, S Bianco 73, D Piccolo 73, M Bozzo 74, F Ferro 74, R Mulargia 74, E Robutti 74, S Tosi 74, A Benaglia 75, F Brivio 75, F Cetorelli 75, V Ciriolo 75,75,213, F De Guio 75, M E Dinardo 75, P Dini 75, S Gennai 75, A Ghezzi 75, P Govoni 75, L Guzzi 75, M Malberti 75, S Malvezzi 75, A Massironi 75, D Menasce 75, F Monti 75, L Moroni 75, M Paganoni 75, D Pedrini 75, S Ragazzi 75, N Redaelli 75, T Tabarelli de Fatis 75, D Valsecchi 75,75,213, D Zuolo 75, S Buontempo 76, N Cavallo 76, A De Iorio 76, F Fabozzi 76, A O M Iorio 76, L Lista 76, S Meola 76,76,213, P Paolucci 76,213, B Rossi 76, C Sciacca 76, P Azzi 77, N Bacchetta 77, D Bisello 77, P Bortignon 77, A Bragagnolo 77, R Carlin 77, P Checchia 77, P De Castro Manzano 77, T Dorigo 77, F Gasparini 77, U Gasparini 77, S Y Hoh 77, L Layer 77,238, M Margoni 77, A T Meneguzzo 77, M Presilla 77, P Ronchese 77, R Rossin 77, F Simonetto 77, G Strong 77, M Tosi 77, H Yarar 77, M Zanetti 77, P Zotto 77, A Zucchetta 77, G Zumerle 77, C Aime‘ 78, A Braghieri 78, S Calzaferri 78, D Fiorina 78, P Montagna 78, S P Ratti 78, V Re 78, M Ressegotti 78, C Riccardi 78, P Salvini 78, I Vai 78, P Vitulo 78, G M Bilei 79, D Ciangottini 79, L Fanò 79, P Lariccia 79, G Mantovani 79, V Mariani 79, M Menichelli 79, F Moscatelli 79, A Piccinelli 79, A Rossi 79, A Santocchia 79, D Spiga 79, T Tedeschi 79, P Azzurri 80, G Bagliesi 80, V Bertacchi 80, L Bianchini 80, T Boccali 80, E Bossini 80, R Castaldi 80, M A Ciocci 80, R Dell’Orso 80, M R Di Domenico 80, S Donato 80, A Giassi 80, M T Grippo 80, F Ligabue 80, E Manca 80, G Mandorli 80, A Messineo 80, F Palla 80, G Ramirez-Sanchez 80, A Rizzi 80, G Rolandi 80, S Roy Chowdhury 80, A Scribano 80, N Shafiei 80, P Spagnolo 80, R Tenchini 80, G Tonelli 80, N Turini 80, A Venturi 80, P G Verdini 80, F Cavallari 81, M Cipriani 81, D Del Re 81, E Di Marco 81, M Diemoz 81, E Longo 81, P Meridiani 81, G Organtini 81, F Pandolfi 81, R Paramatti 81, C Quaranta 81, S Rahatlou 81, C Rovelli 81, F Santanastasio 81, L Soffi 81, R Tramontano 81, N Amapane 82, R Arcidiacono 82, S Argiro 82, M Arneodo 82, N Bartosik 82, R Bellan 82, A Bellora 82, J Berenguer Antequera 82, C Biino 82, A Cappati 82, N Cartiglia 82, S Cometti 82, M Costa 82, R Covarelli 82, N Demaria 82, B Kiani 82, F Legger 82, C Mariotti 82, S Maselli 82, E Migliore 82, V Monaco 82, E Monteil 82, M Monteno 82, M M Obertino 82, G Ortona 82, L Pacher 82, N Pastrone 82, M Pelliccioni 82, G L Pinna Angioni 82, M Ruspa 82, R Salvatico 82, K Shchelina 82, F Siviero 82, V Sola 82, A Solano 82, D Soldi 82, A Staiano 82, M Tornago 82, D Trocino 82, S Belforte 83, V Candelise 83, M Casarsa 83, F Cossutti 83, A Da Rold 83, G Della Ricca 83, F Vazzoler 83, S Dogra 84, C Huh 84, B Kim 84, D H Kim 84, G N Kim 84, J Lee 84, S W Lee 84, C S Moon 84, Y D Oh 84, S I Pak 84, B C Radburn-Smith 84, S Sekmen 84, Y C Yang 84, H Kim 85, D H Moon 85, B Francois 86, T J Kim 86, J Park 86, S Cho 87, S Choi 87, Y Go 87, B Hong 87, K Lee 87, K S Lee 87, J Lim 87, J Park 87, S K Park 87, J Yoo 87, J Goh 88, A Gurtu 88, H S Kim 89, Y Kim 89, J Almond 90, J H Bhyun 90, J Choi 90, S Jeon 90, J Kim 90, J S Kim 90, S Ko 90, H Kwon 90, H Lee 90, S Lee 90, B H Oh 90, M Oh 90, S B Oh 90, H Seo 90, U K Yang 90, I Yoon 90, D Jeon 91, J H Kim 91, B Ko 91, J S H Lee 91, I C Park 91, Y Roh 91, D Song 91, IJ Watson 91, S Ha 92, H D Yoo 92, Y Choi 93, Y Jeong 93, H Lee 93, Y Lee 93, I Yu 93, T Beyrouthy 94, Y Maghrbi 94, V Veckalns 95,239, M Ambrozas 96, A Juodagalvis 96, A Rinkevicius 96, G Tamulaitis 96, A Vaitkevicius 96, W A T Wan Abdullah 97, M N Yusli 97, Z Zolkapli 97, J F Benitez 98, A Castaneda Hernandez 98, J A Murillo Quijada 98, L Valencia Palomo 98, G Ayala 99, H Castilla-Valdez 99, E De La Cruz-Burelo 99, I Heredia-De La Cruz 99,240, R Lopez-Fernandez 99, C A Mondragon Herrera 99, D A Perez Navarro 99, A Sanchez-Hernandez 99, S Carrillo Moreno 100, C Oropeza Barrera 100, M Ramirez-Garcia 100, F Vazquez Valencia 100, I Pedraza 101, H A Salazar Ibarguen 101, C Uribe Estrada 101, J Mijuskovic 102,241, N Raicevic 102, D Krofcheck 103, S Bheesette 104, P H Butler 104, A Ahmad 105, M I Asghar 105, A Awais 105, M I M Awan 105, H R Hoorani 105, W A Khan 105, S Qazi 105, M A Shah 105, M Shoaib 105, V Avati 106, L Grzanka 106, M Malawski 106, H Bialkowska 107, M Bluj 107, B Boimska 107, T Frueboes 107, M Górski 107, M Kazana 107, M Szleper 107, P Traczyk 107, P Zalewski 107, K Bunkowski 108, K Doroba 108, A Kalinowski 108, M Konecki 108, J Krolikowski 108, M Walczak 108, M Araujo 109, P Bargassa 109, D Bastos 109, A Boletti 109, P Faccioli 109, M Gallinaro 109, J Hollar 109, N Leonardo 109, T Niknejad 109, J Seixas 109, O Toldaiev 109, J Varela 109, S Afanasiev 110, D Budkouski 110, P Bunin 110, M Gavrilenko 110, I Golutvin 110, I Gorbunov 110, A Kamenev 110, V Karjavine 110, A Lanev 110, A Malakhov 110, V Matveev 110,242,243, V Palichik 110, V Perelygin 110, M Savina 110, D Seitova 110, V Shalaev 110, S Shmatov 110, S Shulha 110, V Smirnov 110, O Teryaev 110, N Voytishin 110, A Zarubin 110, I Zhizhin 110, G Gavrilov 111, V Golovtcov 111, Y Ivanov 111, V Kim 111,244, E Kuznetsova 111,245, V Murzin 111, V Oreshkin 111, I Smirnov 111, D Sosnov 111, V Sulimov 111, L Uvarov 111, S Volkov 111, A Vorobyev 111, Yu Andreev 112, A Dermenev 112, S Gninenko 112, N Golubev 112, A Karneyeu 112, M Kirsanov 112, N Krasnikov 112, A Pashenkov 112, G Pivovarov 112, D Tlisov 112, A Toropin 112, V Epshteyn 113, V Gavrilov 113, N Lychkovskaya 113, A Nikitenko 113,246, V Popov 113, G Safronov 113, A Spiridonov 113, A Stepennov 113, M Toms 113, E Vlasov 113, A Zhokin 113, T Aushev 114, R Chistov 115,247, M Danilov 115,248, A Oskin 115, P Parygin 115, S Polikarpov 115,248, V Andreev 116, M Azarkin 116, I Dremin 116, M Kirakosyan 116, A Terkulov 116, A Belyaev 117, E Boos 117, V Bunichev 117, M Dubinin 117,249, L Dudko 117, A Gribushin 117, V Klyukhin 117, O Kodolova 117, I Lokhtin 117, S Obraztsov 117, M Perfilov 117, S Petrushanko 117, V Savrin 117, V Blinov 118,250, T Dimova 118,250, L Kardapoltsev 118,250, I Ovtin 118,250, Y Skovpen 118,250, 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PMCID: PMC8550241  PMID: 34727143

Abstract

Production cross sections of the Higgs boson are measured in the HZZ4 (=e,μ) decay channel. A data sample of proton–proton collisions at a center-of-mass energy of 13TeV, collected by the CMS detector at the LHC and corresponding to an integrated luminosity of 137fb-1 is used. The signal strength modifier μ, defined as the ratio of the Higgs boson production rate in the 4 channel to the standard model (SM) expectation, is measured to be μ=0.94±0.07(stat)-0.08+0.09(syst) at a fixed value of mH=125.38GeV. The signal strength modifiers for the individual Higgs boson production modes are also reported. The inclusive fiducial cross section for the H4 process is measured to be 2.84-0.22+0.23(stat)-0.21+0.26(syst)fb, which is compatible with the SM prediction of 2.84±0.15fb for the same fiducial region. Differential cross sections as a function of the transverse momentum and rapidity of the Higgs boson, the number of associated jets, and the transverse momentum of the leading associated jet are measured. A new set of cross section measurements in mutually exclusive categories targeted to identify production mechanisms and kinematical features of the events is presented. The results are in agreement with the SM predictions.

Introduction

The discovery of the Higgs boson (H) in 2012 by the ATLAS and CMS collaborations [13] has been a major step towards the understanding of the electroweak symmetry breaking mechanism [49]. Further studies by the two experiments [1013] have shown that the properties of the new particle are consistent with the standard model (SM) expectations for the H boson.

The HZZ4 decay channel (=e,μ) has a large signal-to-background ratio thanks to a low background rate and the complete reconstruction of the final state decay products, capitalizing on the excellent lepton momentum resolution of the CMS detector. The measurements performed using this decay channel with the LHC Run 1 data set at center-of-mass energies of 7 and 8TeV, and the Run 2 data set at 13TeV include the determination of the mass, the spin and the parity of the H boson [1419], its width [2023], the inclusive and differential fiducial cross sections [18, 2428], and the tensor structure of the H boson interaction with a pair of neutral gauge bosons in both on-shell and off-shell regions [17, 19, 21, 29, 30].

This paper presents the measurement of production cross sections in granular kinematic regions of the H boson in the HZZ4 decay channel. A data sample of proton–proton (pp) collisions at a center-of-mass energy of s=13TeV, collected by the CMS detector at the LHC and corresponding to an integrated luminosity of 137fb-1 is used. The inclusive signal strength modifier, defined as the ratio of the H boson production rate in the 4 channel to the SM expectation, and signal strength modifiers for the individual H boson production modes are measured. The measurements of the inclusive and differential fiducial cross sections are also presented, and their compatibility with the SM predictions is tested. The present analysis is similar to that previously performed by the CMS Collaboration [18], but is based on a larger data sample.

In addition, measurements of the H boson cross sections within the simplified template cross section (STXS) framework [3133] are also presented. The main goals of the STXS framework are to increase the reinterpretability of the precision H boson measurements and to minimize the theory dependence. This is achieved by defining exclusive kinematic regions in the H boson production phase space. The results presented within the STXS framework nonetheless depend on the SM simulation used to model the experimental acceptance of the signal processes, which could be modified in beyond the SM (BSM) scenarios. These kinematic regions, referred to as bins, are defined in different stages corresponding to increasing degrees of granularity. This paper presents results in the STXS stage 0 where the bins correspond closely to the different H boson production mechanisms. Previous measurements of cross sections in stage 0 production bins in the H4 decay channel were already presented by the CMS Collaboration [18]. In the STXS framework, additional stages are defined by further splitting of the bins enhancing the sensitivity to possible signature of BSM physics at high transverse momentum of the H boson. Measurements of stage 0, stage 1, and stage 1.1 cross sections in the H4 decay channel were recently published by the ATLAS Collaboration [27]. The most recent refinement of STXS binning is referred to as STXS stage 1.2. This paper presents a first set of the cross section measurements in the STXS stage 1.2 bins in the H4 decay channel.

The paper is organized as follows. A brief introduction of the CMS detector is given in Sect. 2. The data, as well as the simulated signal and background samples, are described in Sect. 3. The event reconstruction and selection, the kinematic discriminants, and the categorization of the H boson candidate events are described in Sects. 45, and 6 , respectively. The background estimation is detailed in Sect. 7 while the signal modeling is described in Sect. 8. The experimental and theoretical systematic uncertainties are described in Sect. 9 and the results are presented in Sect. 10. Concluding remarks are given in Sect. 11.

The CMS detector

The central feature of the CMS apparatus is a superconducting solenoid of 6m internal diameter, providing a magnetic field of 3.8T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity η coverage provided by the barrel and endcap detectors. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid.

Events of interest are selected using a two-tiered trigger system. The first level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100kHz within a fixed latency of about 4μs [34]. The second level, known as the high-level trigger, consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around 1kHz before data storage [35].

The candidate vertex with the largest value of summed physics-object squared transverse momentum pT2 is taken to be the primary pp interaction vertex (PV). The physics objects are the jets, clustered using the jet finding algorithm [36, 37] with the tracks assigned to candidate vertices as inputs, and the associated missing transverse momentum, taken as the negative vector sum of the pT of those jets.

The electron momentum is estimated by combining the energy measurement in the ECAL with the momentum measurement in the tracker. The momentum resolution for electrons with pT45GeV from Zee decays ranges from 1.7% to 4.5%. It is generally better in the barrel region than in the endcaps, and also depends on the bremsstrahlung energy emitted by the electron as it traverses the material in front of the ECAL [38]. The ECAL consists of 75 848 lead tungstate crystals, which provide coverage of |η|<1.48 in the barrel region and 1.48<|η|<3.00 in the two endcap regions (EE). Preshower detectors consisting of two planes of silicon sensors interleaved with a total of 3X0 of lead are located in front of each EE detector.

Muons are measured in the pseudorapidity range |η|<2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive plate chambers. The single muon trigger efficiency exceeds 90% over the full η range, and the efficiency to reconstruct and identify muons is greater than 96%. Matching muons to tracks measured in the silicon tracker results in a relative transverse momentum resolution, for muons with pT up to 100GeV, of 1% in the barrel and 3% in the endcaps. The pT resolution in the barrel is better than 7% for muons with pT up to 1TeV [39].

A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [40].

Data and simulated samples

This analysis is based on the pp collision data collected by the CMS detector at the LHC in 2016, 2017, and 2018 with integrated luminosities of 35.9, 41.5, and 59.7fb-1, respectively [4143]. The collision events are selected by high-level trigger algorithms that require the presence of leptons passing loose identification and isolation requirements. The main triggers select either a pair of electrons or muons, or an electron and a muon. The minimal transverse momentum of the leading and subleading leptons changed throughout the years to account for the different data-taking conditions and is summarized in Table 1.

Table 1.

The minimal pT of the leading/subleading leptons for the main di-electron (e/e), di-muon (μ/μ), and electron-muon (e/μ, μ/e) high-level trigger algorithms used in the H4 analysis in 2016, 2017, and 2018

e/e (GeV) μ/μ (GeV) e/μ, μ/e (GeV)
2016 17/12 17/8 17/8, 8/23
2017 23/12 17/8 23/8, 12/23
2018 23/12 17/8 23/8, 12/23

To maximize the coverage of the H4 phase space, triggers requiring three leptons with relaxed transverse momenta thresholds and no isolation requirement are also used, as are isolated single-electron and single-muon triggers. The overall trigger efficiency for simulated signal events that pass the full event selection (described in Sect. 4) is larger than 99%. The trigger efficiency is derived from data using a sample of 4 events collected by the single-lepton triggers and a method based on the “tag and probe” technique. One of the four leptons is matched to a candidate reconstructed by the single-lepton trigger and the remaining three leptons in the event are used as probes. The probe leptons are combined in an attempt to reconstruct any of the triggers used in the analysis. The efficiency in data is found to be in agreement with the expectation from the simulation.

Monte Carlo (MC) simulation samples for the signals and the relevant background processes are used to evaluate the signal shape, estimate backgrounds, optimize the event selection, and evaluate the acceptance and systematic uncertainties. The SM H boson signals are simulated at next-to-leading order (NLO) in perturbative QCD (pQCD) with the powheg  2.0 [4446] generator for the five main production processes: gluon fusion (ggH) [47], vector boson fusion (VBF) [48], associated production with a vector boson (VH, where V is a W or a Z boson) [49], and associated production with a pair of top quarks (tt¯H) [50]. The ZH production occurs in two ways, qq¯ZH and a much smaller contribution from ggZH, which is simulated at leading order (LO) using jhugen 7.3.0 [5155]. In addition to the five main production processes, the contributions due to H boson production in association with a single top quark (tH) and either a quark (tHq) or a W boson (tHW) are simulated at LO using jhugen 7.0.2 and MadGraph 5_amc@nlo  2.2.2 [56], respectively. The associated production with a pair of bottom quarks (bb¯H) is simulated at LO with jhugen 7.0.2. In all cases, the decay of the H boson to four leptons is modeled with jhugen 7.0.2. The theoretical predictions used for the various production and decay modes can be found in Refs. [5779] and are summarized in Ref. [32].

The ZZ background contribution from quark-antiquark annihilation is simulated at NLO pQCD with powheg  2.0 [80], while the ggZZ process is generated at LO with mcfm  7.0.1 [81]. The WZ background and the triboson backgrounds ZZZ, WZZ, and WWZ are modeled at NLO using MadGraph 5_amc@nlo  2.4.2. The smaller tt¯Z, tt¯WW, and tt¯ZZ background processes are simulated at LO with MadGraph 5_amc@nlo  2.4.2. The events containing Z bosons with associated jets (Z+jets) are simulated at NLO with MadGraph 5_amc@nlo  2.4.2 and the tt¯ background is simulated at NNLO with powheg  2.0. The reducible background determination does not rely on the MC but is based on data, as described in Sect. 7.2.

All signal and background event generators are interfaced with pythia 8.230 [82] using the CUETP8M1 tune [83] for the 2016 data-taking period and the CP5 tune [84] for the 2017 and 2018 data-taking periods, to simulate the multi-parton interaction and hadronization effects. The NNPDF3.0 set of parton distribution functions (PDFs) is used [85]. The generated events are processed through a detailed simulation of the CMS detector based on Geant4 [86, 87] and are reconstructed with the same algorithms that are used for data. The simulated events include overlapping pp interactions (pileup) and have been reweighted so that the distribution of the number of interactions per LHC bunch crossing in simulation matches that observed in data.

Event reconstruction and selection

The particle-flow (PF) algorithm [88] aims to reconstruct and identify each individual particle (PF candidate) in an event, with an optimized combination of information from the various elements of the CMS detector. The energy of photons is obtained from the ECAL measurement. The energy of electrons is determined from a combination of the electron momentum at the PV as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track. The energy of muons is obtained from the curvature of the corresponding track. The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for the response function of the calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from the corresponding ECAL and HCAL energies.

The missing transverse momentum vector pTmiss is computed as the negative vector sum of the transverse momenta of all the PF candidates in an event, and its magnitude is denoted as pTmiss [89]. The pTmiss is modified to account for corrections to the energy scale of the reconstructed jets in the event.

Muons with pTμ>5GeV are reconstructed within the geometrical acceptance, corresponding to the region |ημ|<2.4, by combining information from the silicon tracker and the muon system [39]. The matching between the inner and outer tracks proceeds either outside-in, starting from a track in the muon system, or inside-out, starting from a track in the silicon tracker. Inner tracks that match segments in only one or two stations of the muon system are also considered because they may belong to very low-pT muons that do not have sufficient energy to penetrate the entire muon system. The muons are selected among the reconstructed muon track candidates by applying minimal requirements on the track in both the muon system and the inner tracker system, and taking into account the compatibility with small energy deposits in the calorimeters.

To discriminate between prompt muons from Z boson decay and those arising from electroweak (EW) decays of hadrons within jets, an isolation requirement of Iμ<0.35 is imposed, where the relative isolation is defined as

Iμ(pTcharged+max[0,pTneutral+pTγ-pTμ,PU])/pTμ. 1

In Eq. (1), pTcharged is the scalar sum of the transverse momenta of charged hadrons originating from the chosen PV of the event. The quantities pTneutral and pTγ are the scalar sums of the transverse momenta for neutral hadrons and photons, respectively. The isolation sums involved are all restricted to a volume bound by a cone of angular radius ΔR=0.3 around the muon direction at the PV, where the angular distance between two particles i and j is ΔR(i,j)=(ηi-ηj)2+(ϕi-ϕj)2. Since the isolation variable is particularly sensitive to energy deposits from pileup interactions, a pTμ,PU contribution is subtracted, defined as pTμ,PU0.5ipTi,PU, where i runs over the charged hadron PF candidates not originating from the PV, and the factor of 0.5 corrects for the different fraction of charged and neutral particles in the cone [90].

Electrons with pTe>7GeV are reconstructed within the geometrical acceptance, corresponding to the pseudorapidity region |ηe|<2.5 [38]. Electrons are identified using a multivariate discriminant which includes observables sensitive to the presence of bremsstrahlung along the electron trajectory, the geometrical and momentum–energy matching between the electron trajectory and the associated cluster in the ECAL, the shape of the electromagnetic shower in the ECAL, and variables that discriminate against electrons originating from photon conversions. Instead of an additional isolation requirement, similar to the one for muons, the electron multivariate discriminant also includes the isolation sums described above (pTcharged, pTneutral, and pTγ) but computed around the electron direction. The inclusion of isolation sums helps suppressing electrons originating from electroweak decays of hadrons within jets [91] and has a better performance than a simple requirement on the relative isolation observable. The package xgboost [92] is used for the training and optimization of the multivariate discriminant employed for electron identification and isolation. The training is performed with simulated events that are not used at any other stage of the analysis. Events are divided into six regions defined by two transverse momentum ranges (7–10 GeV and >10GeV) and three pseudorapidity regions: central barrel (|ηe|<0.8), outer barrel (0.8<|ηe|<1.479), and endcaps (1.479<|ηe|<2.5). Separate training is performed for the three different data-taking periods and selection requirements are determined such that the signal efficiency remains the same for all three periods.

The effect of the final-state radiation (FSR) from leptons is recovered as follows. Bremsstrahlung photons already associated to electrons in the reconstruction step are not considered in this procedure. Photons reconstructed by the PF algorithm within |ηγ|<2.4 are considered as FSR candidates if they satisfy the conditions pTγ>2GeV and Iγ<1.8, where the photon relative isolation Iγ is defined as for the muon in Eq. (1). Every such photon is associated to the closest selected lepton in the event. Photons that do not satisfy the requirements ΔR(γ,)/(pTγ)2<0.012GeV-2 and ΔR(γ,)<0.5 are discarded. The lowest-ΔR(γ,)/(pTγ)2 photon candidate of every lepton, if any, is retained. The photons thus identified are excluded from the isolation computation of the muons selected in the event.

In order to suppress muons from in-flight decays of hadrons and electrons from photon conversions, leptons are rejected if the ratio of their impact parameter in three dimensions, computed with respect to the PV position, to their uncertainty is greater or equal to four.

The momentum scale and resolution of electrons and muons are calibrated in bins of pT and η using the decay products of known dilepton resonances as described in Refs. [38, 39].

A “tag and probe” technique [93] based on samples of Z boson events in data and simulation is used to measure the efficiency of the reconstruction and selection for prompt electrons and muons in several bins of pT and η. The difference in the efficiencies measured in simulation and data is used to rescale the yields of selected events in the simulated samples.

For each event, hadronic jets are clustered from the reconstructed particles using the infrared- and collinear-safe anti-kT algorithm [36, 37] with a distance parameter of 0.4. The jet momentum is determined as the vectorial sum of all particle momenta in the jet, and is found from simulation to be within 5–10% of the true momentum over the whole pT spectrum and detector acceptance. Additional pp interactions within the same or nearby bunch crossings can contribute extra tracks and calorimetric energy depositions to the jet. To mitigate this effect, tracks identified as originating from pileup vertices are discarded and an offset correction is applied to correct for the remaining contributions. Jet energy corrections are derived from simulation to match that of particle level jets on average. In situ measurements of the momentum balance in dijet, photon + jet, Z+ jet, and multijet events are used to account for any residual differences in jet energy scale in data and simulation [94]. Jet energies in simulation are smeared to match the resolution in data. The jet energy resolution amounts typically to 16% at 30GeV, 8% at 100GeV, and 4% at 1TeV. Additional selection criteria are applied to remove jets potentially dominated by anomalous contributions from various subdetector components or reconstruction failures. To be considered in the analysis, jets must satisfy the conditions pTjet>30GeV and |ηjet|<4.7, and be separated from all selected lepton candidates and any selected FSR photons by ΔR(/γ,jet)>0.4. Jets are also required to pass the tight identification criteria and the tight working point of pileup jet identification described in Ref. [90].

For event categorization, jets are tagged as b jets using the DeepCSV algorithm [95], which combines information about impact parameter significance, secondary vertex, and jet kinematics. Data to simulation scale factors for the b tagging efficiency are applied as a function of jet pT, η, and flavor.

The event selection is designed to extract signal candidates from events containing at least four well-identified and isolated leptons, each originating from the PV and possibly accompanied by an FSR photon candidate. In what follows, unless otherwise stated, FSR photons are included in invariant mass computations.

First, Z candidates are formed with pairs of leptons of the same flavor and opposite-charge (e+e-, μ+μ-) that pass the requirement 12<m+-<120GeV. They are then combined into ZZ candidates, wherein we denote as Z1 the Z candidate with an invariant mass closest to the nominal Z boson mass [96], and as Z2 the other one. The flavors of the involved leptons define three mutually exclusive subchannels: 4e, 4μ, and 2e2μ.

To be considered for the analysis, ZZ candidates have to pass a set of kinematic requirements that improve the sensitivity to H boson decays. The Z1 invariant mass must be larger than 40GeV. All leptons must be separated in angular space by at least ΔR(i,j)>0.02. At least two leptons are required to have pT>10GeV and at least one is required to have pT>20GeV. In the 4μ and 4e subchannels, where an alternative ZaZb candidate can be built out of the same four leptons, we discard candidates with mZb<12GeV if Za is closer to the nominal Z boson mass than Z1 is. This rejects events that contain an on-shell Z and a low-mass dilepton resonance. To further suppress events with leptons originating from hadron decays in jet fragmentation or from the decay of low-mass resonances, all four opposite-charge lepton pairs that can be built with the four leptons (irrespective of flavor) are required to satisfy the condition m+->4GeV, where selected FSR photons are disregarded in the invariant mass computation. Finally, the four-lepton invariant mass m4 must be larger than 70GeV, which defines the mass range of interest for the subsequent steps of the analysis.

In events where more than one ZZ candidate passes the above selection, the candidate with the highest value of Dbkgkin (defined in Sect. 5) is retained, except if two candidates consist of the same four leptons, in which case the candidate with the Z1 mass closest to the nominal Z boson mass is retained.

Kinematic discriminants

The full kinematic information from each event using either the H boson decay products and/or the associated particles in the H boson production is extracted by means of matrix element calculations and is used to form several kinematic discriminants. These computations rely on the MELA package [5153, 55] and exploit the jhugen matrix elements for the signal and the mcfm matrix elements for the background. Both the H boson decay kinematics and the kinematics of the associated production of H+1jet, H+2 jets, VBF, ZH, and WH are explored. The full event kinematics is described by decay observables ΩH4 or observables describing the associated production ΩH+jj, which may or may not include the H4 decay kinematic information depending on the use case. The definition of these observables can be found in Refs. [5153].

Two types of kinematic discriminants are exploited in the H4 analysis. First we construct the three categorization discriminants in order to classify signal events into exclusive categories as defined in Sect. 6.2. Categorization discriminants are designed to increase the purity of the targeted production mechanism in a dedicated event category. In addition, we define another set of three kinematic discriminants that are taken as an observable in the two-dimensional likelihood fits carried out to extract the results, as described in Sect. 10. These kinematic discriminants are designed to separate the targeted H boson production mechanism from its dominant background.

Categorization discriminants are calculated following the prescription in Refs. [18, 21, 97]. The discriminants sensitive to the VBF signal topology with two associated jets, the VBF signal topology with one associated jet, and the VH (either ZH or WH) signal topology with two associated jets are:

D2jetVBF=1+PHjj(ΩH+jj|m4)PVBF(ΩH+jj|m4)-1D1jetVBF=1+PHj(ΩH+j|m4)dηjPVBF(ΩH+jj|m4)-1D2jetWH=1+PHjj(ΩH+jj|m4)PWH(ΩH+jj|m4)-1D2jetZH=1+PHjj(ΩH+jj|m4)PZH(ΩH+jj|m4)-1, 2

where PVBF, PHjj, PHj, and PVH are the probabilities for the VBF process, the ggH process in association with two jets (combination of gg/qg/qq parton collisions producing H+2 jets), the ggH process in association with one jet (H+1 jet), and the VH process, respectively. The quantity dηjPVBF is the integral of the two-jet VBF matrix element probability over the ηj values of the unobserved jet, with the constraint that the total transverse momentum of the H+2 jets system is zero. The discriminant D2jetVH, used for event categorization, is defined as the maximum value of the two discriminants, D2jetVH=max(D2jetZH,D2jetWH).

A set of three discriminants used in the likelihood fits is calculated as in Refs. [17, 18]. The discriminant sensitive to the gg/qq¯4 process exploits the kinematics of the four-lepton decay system. It is used in most of the event categories described in Sect. 6 to separate signal from background and is defined as:

Dbkgkin=1+Pbkgqq¯(ΩH4|m4)Psiggg(ΩH4|m4)-1, 3

where Psiggg is the probability for the signal and Pbkgqq¯ is the probability for the dominant qq¯4 background process, calculated using the LO matrix elements. In the VBF-2jet-tagged and VH-hadronic-tagged event categories (defined in Sect. 6.2), the background includes the QCD production of ZZ/Zγ/γγ4 in association with two jets, the EW background from the vector boson scattering (VBS), as well as the triboson (VVV) production process. We therefore use dedicated production-dependent discriminants based on the kinematics of the four-lepton decay and information from the associated jets (noted with VBF+ dec or VH+ dec), defined as:

DbkgVBF+dec=[1+cVBF(m4)[PbkgEW(ΩH+jj|m4)+PbkgQCD(ΩH+jj|m4)]PsigEW(ΩH+jj|m4)]-1 4
DbkgVH+dec=[1+cVH(m4)[PbkgEW(ΩH+jj|m4)+PbkgQCD(ΩH+jj|m4)]PsigEW(ΩH+jj|m4)]-1, 5

where PsigEW is the probability for the VBF and VH signal, PbkgEW is the probability for the VBS and VVV background processes, and PbkgQCD is the probability for ZZ/Zγ/γγ4 QCD production in association with two jets. The quantity cp(m4) for category p is the m4-dependent parameter that allows to change the relative normalization of the EW probabilities, separately for the VBF and VH topologies. For each slice of m4, the distributions of the signal and background discriminants are plotted, and the cp(m4) value is determined in such a way that the two distributions cross at 0.5. This procedure allows rescaling of the distributions for the linear-scale binning of the templates used in the likelihood fits described in Sect. 10.

Event categorization

In order to improve the sensitivity to the H boson production mechanisms, the selected events are classified into mutually exclusive categories based on the features of the reconstructed objects associated with the H4 candidates. Event categorization is organized in two steps with increasing granularity of the categories. First step is primarily designed to separate the ggH, VBF, VH, and tt¯H processes. There is little sensitivity to bb¯H or tH, even though these production modes are considered explicitly in the analysis. The reconstructed event categories from the first step are further subdivided (as discussed in Sect. 6.2) in order to study each production mechanism in more detail. This subdivision is carried out by matching the recommended binning of the framework of STXS described in the following section.

STXS production bins

The STXS framework has been adopted by the LHC experiments as a common framework for studies of the H boson. It has been developed to define fine-grained measurements of the H boson production modes in various kinematic regions, and to reduce the theoretical uncertainties that are folded into the measurements. It also allows for the use of advanced categorization techniques and provides a common scheme for combining measurements in different decay channels or by different experiments. The regions of phase space defined by this framework are referred to as production bins and are determined by using generator-level information for H bosons with rapidity |yH|<2.5. Generator-level jets are defined as anti-kT jets with a distance parameter of 0.4 and a pT threshold of 30GeV; no requirement is placed on the generator-level leptons.

The STXS framework has been designed to complement the Run I measurements of the production signal strength modifiers and fiducial differential cross sections of the H boson by combining their advantages. The sensitivity to theoretical uncertainties in the signal strength modifier results is suppressed by excluding dominant theoretical uncertainties causing production bin migration effects from the STXS measurements. They are included only when comparing the results with the theoretical predictions. In contrast to the fiducial differential cross section measurements, in the STXS framework measurements are optimized for sensitivity by means of event categories and matrix element discriminants. To account for the evolving experimental sensitivity, different stages of production bins with increasing granularity are developed.

The stage 0 production bins are called ggH, qqH, VH-lep, and ttH and are designed to closely match the main H boson production mechanisms. The qqH bin includes the EW production of the H boson in association with two quarks from either VBF or VH events with hadronic decays of the vector boson V. The VH-lep production bin includes VH events with leptonic decays of the vector boson V. The low rate bb¯H and tH production processes are considered together with the ggH and ttH production bins, respectively. In this analysis, a modified version of the stage 0 production bins is also studied, where instead of VH-lep and qqH bins we define the WH, ZH, and VBF bins that map the H boson production mechanisms without the splitting of the VH events in leptonic and hadronic decays.

Stage 1 of the STXS framework was designed by further splitting the bins from the stage 0, one of the main motives being the enhanced sensitivity to possible signatures of BSM physics. This is achieved by dividing stage 0 bins with additional requirements on generator-level quantities that include the transverse momentum of the H boson (pTH), the number of associated jets (Nj), the dijet invariant mass (mjj), the transverse momentum of the H boson and the leading jet (pTHj), and the transverse momentum of the H boson and the two leading jets (pTHjj). These bins were designed in order to maximize sensitivity to new physics while also taking into account the current experimental sensitivity limited mostly by the amount of collected data. The most recent set of bins defined in the STXS framework is referred to as stage 1.2. This paper presents a first set of cross section measurements in the H4 channel for the stage 1.2 of the STXS framework. However, several stage 1.2 production bins are merged as the full set of bins cannot be measured with the current data sample. The merging scheme results in 19 production bins; it is illustrated in Fig. 1 and discussed in more detail below.

Fig. 1.

Fig. 1

Binning of the gluon fusion production process, the electroweak production process (combines VBF and VH with hadronic V decay), the VH production process with leptonic V decay (combining WH, ZH, and gluon fusion ZH production), and the tt¯H production process in the merged stage 1.2 of the STXS framework used in the HZZ4 analysis

The ggH production process is split into events with pTH<200GeV and pTH>200GeV. The events with pTH>200GeV are placed into one single production bin called ggH/pT>200. The events with pTH<200GeV are split in events with zero, one, and two or more jets. The events with zero or one jets are split into the following production bins according to the H boson pT: ggH-0j/pT[0,10], ggH-0j/pT[10,200], ggH-1j/pT[0,60], ggH-1j/pT[60,120], and ggH-1j/pT[120,200]. The events with two or more jets are split according to the dijet invariant mass as follows. The events with mjj<350GeV are split into three production bins according to the H boson pT: ggH-2j/pT[0,60], ggH-2j/pT[60,120], and ggH-2j/pT[120,200]. The events with mjj>350GeV are all placed into one production bin ggH-2j/mjj>350, which merges four bins originally suggested in stage 1.2 of the STXS framework.

The merging scheme of the electroweak qqH production bins is as follows. The events with zero jets, one jet, or with two or more jets with mjj<60GeV or 120<mjj<350GeV correspond to production bins with insufficient statistics; they are all merged into one bin called qqH-rest. The events with two or more jets and 60<mjj<120GeV are placed in the qqH-2j/mjj[60,120] bin. The events with two or more jets and mjj>350GeV are split into events with pTH<200GeV and pTH>200GeV. The events with pTH>200GeV are placed into one single production bin called qqH-2j/pT>200. The events with pTH<200GeV and pTHjj<25GeV are split into two production bins, qqH-2j/mjj[350,700] and qqH-2j/mjj>700, and otherwise if pTHjj>25GeV are merged in a single bin called qqH-3j/mjj>350.

The three production processes qq¯WH, ggZH, and qq¯ZH are combined to build VH-lep reduced stage 1.2 production bins. Several proposed production bins are merged into just two bins according to the pT of the H boson: VH-lep/pTH[0,150] and VH-lep/pTH>150.

In stage 1.2 of the STXS framework the ttH stage 0 production bin is split in five different bins according to the pT of the H boson. Because of the very low expected yields all these bins are merged into a single bin that includes the tH production process as well.

Finally, in stage 1.2 the bb¯H production process, which has small cross section, is classified in the ggH-0j/pT[10,200] production bin.

The first measurement of STXS stage 1.2 cross sections was recently performed by the CMS Collaboration [98].

Reconstructed event categories

In order to be sensitive to different production bins, the ZZ candidates that pass the event selection described in Sect. 4 are classified into several dedicated reconstructed event categories. The category definitions are based on the multiplicity of jets, b-tagged jets, and additional leptons in the event. Additional leptons are not involved in the ZZ candidate selection but, if present, should satisfy the identification, vertex compatibility, and isolation requirements. Requirements on the categorization discriminants described in Sect. 5, the invariant mass of the two leading jets, and the transverse momentum of the ZZ candidate are also exploited.

The event categorization is carried out in two steps. In the first step, the ZZ candidates are split into seven initial categories to target the main H boson production mechanisms corresponding to the stage 0 production bins. The first step of the categorization closely follows the analysis strategy from the previous publication [18]. To ensure exclusive categories, an event is considered for the subsequent category only if it does not satisfy the requirements of the previous one.

In the first categorization step, the following criteria are applied:

  • The VBF-2jet-tagged category requires exactly 4 leptons. In addition there must be either 2 or 3 jets of which at most 1 is b-tagged, or at least 4 jets and no b-tagged jets. Finally, D2jetVBF>0.5 is required.

  • The VH-hadronic-tagged category requires exactly 4 leptons. In addition there must be 2 or 3 jets with no b-tagging requirements, or at least 4 jets and no b-tagged jets. Finally, D2jetVH>0.5 is required.

  • The VH-leptonic-tagged category requires no more than 3 jets and no b-tagged jets in the event, and exactly 1 additional lepton or 1 additional pair of opposite sign, same flavor leptons. This category also includes events with no jets and at least 1 additional lepton.

  • The tt¯H-hadronic-tagged category requires at least 4 jets, of which at least 1 is b-tagged, and no additional leptons.

  • The tt¯H-leptonic-tagged category requires at least 1 additional lepton in the event.

  • The VBF-1jet-tagged category requires exactly 4 leptons, exactly 1 jet and D1jetVBF>0.7.

  • The untagged category consists of the remaining events.

Reconstructed events are further subdivided in the second step of the categorization that is designed to closely match the merged stage 1.2 production bins described in the previous section. In the second categorization step, the untagged, VBF-2jet-tagged, VH-hadronic-tagged, and VH-leptonic-tagged categories are further split exploiting additional variables like the invariant mass of the two leading jets and the transverse momentum of the ZZ candidate. A total number of twenty-two reconstructed event categories is defined and details of the categorization are presented in Table 2.

Table 2.

Event categorization criteria of the H4 analysis targeting stage 1.2 STXS production bins. Events from the first step of the categorization are further classified based on the kinematical properties listed in the table. A dash indicates no requirement

Reconstructed event category 1st categorization step Number of jets Kinematical requirements (GeV) Targeted production bin
Untagged-0j-pT4[0,10] Untagged 0 0<pT4<10 ggH-0j/pT[0,10]
Untagged-0j-pT4[10,200] Untagged 0 10<pT4<200 ggH-0j/pT[10,200]
Untagged-1j-pT4[0,60] Untagged 1 0<pT4<60 ggH-1j/pT[0,60]
Untagged-1j-pT4[60,120] Untagged 1 60<pT4<120 ggH-1j/pT[60,120]
Untagged-1j-pT4[120,200] Untagged 1 120<pT4<200 ggH-1j/pT[120,200]
Untagged-2j-pT4[0,60] Untagged 2 0<pT4<60, mjj<350 ggH-2j/pT[0,60]
Untagged-2j-pT4[60,120] Untagged 2 60<pT4<120, mjj<350 ggH-2j/pT[60,120]
Untagged-2j-pT4[120,200] Untagged 2 120<pT4<200, mjj<350 ggH-2j/pT[120,200]
Untagged-pT4>200 Untagged pT4>200 ggH/pT>200
Untagged-2j-mjj>350 Untagged 2 mjj>350 ggH-2j/mjj>350
VBF-1jet-tagged VBF-1jet-tagged qqH-rest
VBF-2jet-tagged-mjj[350,700] VBF-2jet-tagged pT4<200, pT4jj<25, 350<mjj<700 qqH-2j/mjj[350,700]
VBF-2jet-tagged-mjj>700 VBF-2jet-tagged pT4<200, pT4jj<25, mjj>700 qqH-2j/mjj>700
VBF-3jet-tagged-mjj>350 VBF-2jet-tagged pT4<200, pT4jj>25, mjj>350 qqH-3j/mjj>350
VBF-2jet-tagged-pT4>200 VBF-2jet-tagged pT4>200, mjj>350 qqH-2j/pT>200
VBF-rest VBF-2jet-tagged mjj<350 qqH-rest
VH-hadronic-tagged-mjj[60,120] VH-hadronic-tagged 60<mjj<120 qqH-2j/mjj[60,120]
VH-rest VH-hadronic-tagged mjj<60 or mjj>120 qqH-rest
VH-leptonic-tagged-pT4[0,150] VH-leptonic-tagged pT4<150 VH-lep/pTH[0,150]
VH-leptonic-tagged-pT4>150 VH-leptonic-tagged pT4>150 VH-lep/pTH>150
tt¯H-leptonic-tagged tt¯H-leptonic-tagged ttH
tt¯H-hadronic-tagged tt¯H-hadronic-tagged ttH

Background estimation

Irreducible backgrounds

The irreducible background to the H boson signal in the 4 channel, which comes from the production of ZZ via qq¯ annihilation or gluon fusion, is estimated using simulation. The fully differential cross section for the qq¯ZZ process is computed at NNLO [99], and the NNLO/NLO K factor as a function of mZZ is applied to the powheg sample. This K factor varies from 1.0 to 1.2 and is 1.1 at mZZ=125GeV. Additional NLO electroweak corrections that depend on the initial state quark flavor and kinematics are also applied in the region mZZ>2mZ following the prescription in Ref. [100].

The production of ZZ via gluon fusion contributes at NNLO in pQCD. It has been shown that the soft collinear approximation is able to describe the cross section for this process and the interference term at NNLO [101]. Further calculations also show that the K factors are very similar at NLO for signal and background [102] and at NNLO for signal and interference terms [103]. Therefore, the same K factor is used for signal and background [104]. The NNLO K factor for the signal is obtained as a function of mZZ using the hnnlo v2 program [105107] by calculating the NNLO and LO ggH22 cross sections for the H boson decay width of 4.07Me and taking their ratios. The NNLO/LO K factor for ggZZ varies from 2.0 to 2.6 and is 2.27 at mZZ=125GeV; a systematic uncertainty of 10% is assigned to it when applied to the background process.

The triboson background processes ZZZ, WZZ, and WWZ, as well as tt¯Z, tt¯WW, and tt¯ZZ are also considered. These rare backgrounds are all estimated from simulation and are jointly referred to as the EW backgrounds.

Simulated samples are used to obtain shapes of the four-lepton invariant mass that are later used to build the likelihood function. For each irreducible background contribution, events are divided in three final states (4μ, 4e, and 2e2μ) and 22 event sub-categories defined in Sect. 6.1. To extract the shape of the m4 distribution, expected yields are fitted to empirical functional forms built from a third order Bernstein polynomial. In sub-categories with not enough statistics to perform a fit, the shape is extracted from the inclusive distribution in the corresponding final state.

Reducible backgrounds

Additional backgrounds to the H boson signal in the 4 channel arise from processes in which decays of heavy-flavor hadrons, in-flight decays of light mesons within jets, or (for electrons) charged hadrons overlapping with π0 decays are misidentified as leptons. The main processes leading to these backgrounds are Z+jets, tt¯+jets, Zγ+jets, WW+jets, and WZ+jets production. We denote these reducible backgrounds as ”Z+X” since they are dominated by the Z+jets process. The contribution from the reducible background is estimated with two independent methods, each with dedicated control regions in data. The control regions are defined by the presence of both a lepton pair satisfying all the requirements of a Z1 candidate and two additional opposite sign (OS) or same sign (SS) leptons; the two additional leptons satisfy identification requirements looser than those used in the analysis. These four leptons are then required to pass the analysis ZZ candidate selection. The event yield in the signal region is obtained by weighting the control region events by the lepton misidentification probability fe (fμ), defined as the fraction of non-signal electrons (muons) that are identified by the analysis selection criteria. A detailed description of both methods can be found in Ref. [18].

The lepton misidentification rates fe and fμ are measured as a function of pT and η by means of a sample that includes a Z1 candidate consisting of a pair of leptons, both passing the selection requirements used in the analysis, and exactly one additional lepton passing the relaxed selection. Furthermore, the pTmiss is required to be less than 25GeV in order to suppress contamination from WZ and tt¯ processes.

For the OS method, the mass of the Z1 candidate is required to satisfy the condition |Z1-mZ|<7GeV in order to reduce the contribution of (asymmetric) photon conversions, which is estimated separately. In the SS method, the contribution of photon conversions to the misidentification rate is estimated with dedicated samples.

The predicted yields of the reducible background from the two methods are in agreement within their uncertainties for each final state (4μ, 4e, and 2e2μ). The final yield used in the analysis is a weighted average of the two independent estimates. To extract the shape of the m4 distribution for the reducible background a maximum-likelihood fit is performed in each of the 22 event sub-categories defined in Sect. 6.1. For each sub-category, the expected ”Z+X” yields from the OS and SS methods are binned as a function of m4 and fitted to empirical functional forms built from Landau distributions [108]. In sub-categories with not enough statistics to perform a fit, the shape is extracted from the inclusive distribution in the corresponding final state.

The dominant systematic uncertainty on the reducible background estimation arises from the difference in the composition of the sample from which the misidentification rate is computed and that of the control regions. It is determined from the MC simulation and is found to be around 30%, depending on the final state. Additional sources of systematic uncertainty arise from the limited number of events in the control regions as well as in the region where the misidentification rates are computed.

Signal modeling

In order to generate an accurate signal model, the pT spectrum of the H boson, pTH, was tuned in the powheg simulation of the dominant gluon fusion production mode to better match the predictions from full phase space calculations implemented in the HRes generator [107, 109, 110].

In order to take advantage of the accuracy of the nnlops [111] simulation available for the ggH process, an event reweighting procedure is used. Events originating from the ggH process are subdivided into classes with 0, 1, 2, and 3 jets; the jets with pT>30GeV are clustered from all stable particles using the anti-kT algorithm with a distance parameter of 0.4, excluding the decay products of the H boson or associated vector bosons. The weights are obtained as the ratios of the pTH distributions from the nnlops and the powheg generators for each event class; the sum of the weights in each sample is normalized to the inclusive cross section.

The signal shape is parametrized by means of a double-sided Crystal Ball function [112] around mH125GeV. A Landau function is added in the total probability density function for the non-resonant part of the signal for the case of WH, ZH and tt¯H production modes. The signal shape is parametrized as a function of mH by performing a simultaneous fit of several mass points for all production modes in the 105 to 140GeV mass range. Each parameter of the double-sided Crystal Ball function has a linear dependence on mH, for a total of 12 free parameters. An examples of the fit is shown in Fig. 2.

Fig. 2.

Fig. 2

The shape of the parametric signal model for each year of simulated data, and for the sum of all years together. The black points represent weighted simulation events of the ggH production mechanism for mH=125GeV and the blue line the corresponding model. Also shown is the σCB value (half the width of the narrowest interval containing 68% of the invariant mass distribution) in the gray shaded area. The contribution of the signal model from each year of data-taking is illustrated with the dotted lines. The models are shown for the 4e (upper) and 4μ (lower) final states in the untagged event category

Systematic uncertainties

The systematic uncertainties are divided into experimental and theoretical. The main experimental uncertainties originate from the imperfect knowledge of the detector; the dominant sources are the uncertainties in the luminosity measurement, the lepton reconstruction and selection efficiency, the lepton and jet energy scale and resolution, the b tagging efficiency, and the reducible background estimate. The theoretical uncertainties account for the uncertainties in the modeling of the signal and background processes.

Both types of uncertainties can affect the signal selection, cause migrations between the event categories, and affect the signal or background shapes used in the fit. All the uncertainties affecting this analysis are modeled as nuisance parameters (NPs) that are profiled in the maximum likelihood fit described in Sect. 10.

In the combination of the three data-taking periods, all theoretical uncertainties are treated as correlated across these periods. The experimental uncertainties related to reconstruction and selection efficiency, the lepton energy scale and resolution, and the b-tagging efficiency are also considered correlated across data-taking periods. Luminosity uncertainty is treated as partially correlated. All other experimental uncertainties are treated as uncorrelated. Correlated sources of uncertainty are assigned the same NP and uncorrelated sources have a dedicated NP in the likelihood fit described in Sect. 10.

The dominant sources of uncertainties and their effect on the analysis are discussed in detail in the following subsections. The impact of a NP on a parameter of interest (POI) is defined as the shift induced on POI when NP is varied by a ±1 standard deviation from its post-fit value, with all other parameters profiled as usual. The relative impact of the dominant systematic uncertainties on some of the measurements discussed in Sect. 10 is illustrated in Fig. 3.

Fig. 3.

Fig. 3

The impact of the dominant systematic uncertainties (in percent) on the inclusive signal strength μ and stage 0 production mode cross section described in Sect. 10. Impacts from different NPs are combined assuming no correlation. Only dominant experimental sources are presented: integrated luminosity uncertainty (Lumi.), lepton reconstruction and selection efficiency, scale and resolution (Leptons), jet energy scale and resolution (Jet), b-tagging efficiency (B-tag), and reducible background estimation uncertainty (Red. bkg). Only dominant theoretical sources are presented: ggH, VBF, and VH cross section theoretical uncertainty scheme (THU), renormalization and factorization scale (QCD), choice of the PDF set (PDF), the branching fraction of H4 (B), modeling of hadronization and the underlying event (Hadr), and background modeling (Bkg. mod.). The THU uncertainty is not considered in the stage 0 cross section measurements. The uncertainties are rounded to the nearest 0.5%

Experimental uncertainties

The integrated luminosities of the 2016, 2017, and 2018 data-taking periods are individually known with uncertainties in the 2.3–2.5% range [4143], while the total Run 2 (2016–2018) integrated luminosity has an uncertainty of 1.8%, the improvement in precision reflecting the (uncorrelated) time evolution of some systematic effects. The experimental uncertainty on the integrated luminosity measurement affects all final states, both signal and background. Another experimental uncertainty common to all final states is the uncertainty in the lepton reconstruction and selection efficiency. Here selection efficiency includes all the steps from trigger to impact parameter significance and finally identification and isolation requirements. The uncertainty ranges from 1 to 2.3% in the 4μ channel and from 11 to 15.5% in the 4e channel. While for muon efficiency measurements in the low pTμ regions we rely on low mass di-muon resonances, the electron efficiency measurement relies solely on the Z boson resonance, resulting in a higher uncertainty in the low pTe region.

Lepton momentum scale and resolution uncertainties are estimated from dedicated studies on the Z+- mass distribution in data and simulation. Events are classified according to the pT and η of one of the two leptons, determined randomly, and integrated over the other. The dilepton mass distributions are then fit by a Breit–Wigner parameterization convolved with the double-sided Crystal Ball function described in Sect. 8. The scale uncertainty is found to be 0.04% in the 4μ channel and 0.3% in the 4e channel, while the resolution uncertainty is 20% for both channels. In both cases full correlation between the leptons in the event is assumed. Both scale and resolution uncertainties alter the signal shape by allowing the corresponding parameters of the double-sided Crystal Ball function to vary. The impact is found to be non-negligible only in the case of fiducial cross section measurements.

The effects of the jet energy corrections are studied in a similar manner. While jet energy scale and smearing do not alter signal selection efficiency, they cause event migrations between the categories. They can also alter the shape of the discriminants, but the effect on the shape is negligible. The uncertainty in the jet energy scale ranges from 1% in the high jet pT range and increases up to 5% in the low jet pT range. The uncertainty in jet energy resolution ranges from 1 to 2%. A detailed description of the determination of the jet energy scale and smearing uncertainties can be found in [113]. The effect on the analysis is studied in detail by propagating the uncertainties and estimating the effect on event migration in each of the 22 sub-categories. Their impact on the inclusive measurements is found to be negligible. However, the impact is significant in measurements of the VBF and VH production modes and differential cross section measurements as a function of jet kinematics, where it is one of the leading sources of uncertainty.

The uncertainty in the b-tagging efficiency is found to be 1% in the high jet pT range and increases up to 3% in the low jet pT range. The impact from the category migration is found to be negligible in all categories.

Finally, experimental uncertainties in the reducible background estimation, described in Sect. 7.2, originating from the background composition and misidentification rate uncertainties vary between 30 and 45% depending on the final state and category. However, the impact of this uncertainty on the measurements is found to be negligible.

Other sources of experimental uncertainties are also studied but their impact is negligible compared to the sources described above.

Theoretical uncertainties

Theoretical uncertainties that affect both the signal and background estimation include those related to the renormalization and factorization scales, and the choice of the PDF set. The uncertainty from the renormalization and factorization scales is determined by varying these scales between 0.5 and 2 times their nominal value, while keeping their ratio between 0.5 and 2. The uncertainty due to the PDF set is determined following the PDF4LHC recommendations by taking the root mean square of the variation of the results when using different replicas of the default NNPDF set [114, 115]. The uncertainties just described have an effect both on the signal and background yields, as well as on the migration of events between the categories. An additional 10% uncertainty in the K factor used for the ggZZ prediction is applied as described in Sect. 7.1. A systematic uncertainty of 2% [32] in the branching fraction of H4 only affects the signal yield.

Theoretical uncertainties that affect the predictions of the STXS production bins are described in Ref. [32]. From here on we will refer to these uncertainties as the theoretical uncertainty scheme (THU).

The THU for the ggH process includes 10 NPs, which account for uncertainties in the cross section prediction for exclusive jet bins (including the migration between the 0 and 1-jet, as well as between the 1 and 2-jet bins), the 2 jet and 3 jet VBF phase space, migrations around the pTH bin boundaries at 10, 60, and 120GeV, and the uncertainty in the pTH distribution due to missing higher order finite top quark mass corrections.

In the THU uncertainties for VBF and VH production, additional sources are introduced to account for the uncertainty in the modeling of the pTH, mjj and pTHjj distributions, as well as that of the number of jets in the event. A total of 6 NPs account for the migrations of events across the mjj boundaries at 60, 120, 350, 700, 1000, and 1500GeV. Two additional NPs account for migrations across the pTH=200GeV and pTHjj=25GeV bin boundaries. Finally, a single source is introduced to account for migrations between the zero and one jet, as well as the the two or more jet bins. In each case, the uncertainty is computed by varying the renormalization and factorization scales and recalculating the fractional breakdown of the qqH STXS stage 1.2 cross sections.

A set of THU uncertainties is considered as NPs in the likelihood fit when signal strength modifiers, rather than STXS, are measured. In the STXS framework, THU uncertainties only enter at the interpretation step and are thus applied only to the SM cross section predictions.

Additional theoretical effects that only cause migration of signal and background events between categories originate from the modeling of the hadronization and the underlying event. The underlying event modeling uncertainty is determined by varying initial- and final-state radiation scales between 0.25 and 4 times their nominal value. The effects of the modeling of hadronization are determined by simulating additional events with the variation of the nominal pythia tune described in Sect. 3.

Results

The reconstructed four-lepton invariant mass distribution is shown in Fig. 4 for the 4e, 4μ and 2e2μ events together, and is compared with the expectations for signal and background processes. The error bars on the data points correspond to the intervals at 68% confidence level (CL) [116]. The observed distribution agrees with the expectation within the statistical uncertainties over the whole spectrum.

Fig. 4.

Fig. 4

Four-lepton mass distribution, m4, up to 500GeV with 4GeV bin size (upper) and in the low-mass range with 2GeV bin size (lower). Points with error bars represent the data and stacked histograms represent the expected distributions for the signal and background processes. The SM Higgs boson signal with mH=125GeV, denoted as H(125), the ZZ and rare electroweak backgrounds are normalized to the SM expectation, the Z+X background to the estimation from data

The reconstructed four-lepton invariant mass distribution is shown in Fig. 5 for the three 4 final states and is compared with the expectations from signal and background processes.

Fig. 5.

Fig. 5

Four-lepton mass distribution in three final states: 4e upper), 4μ (center), and 2e2μ (lower). Points with error bars represent the data and stacked histograms represent the expected distributions for the signal and background processes. The SM Higgs boson signal with mH=125GeV, denoted as H(125), the ZZ and rare electroweak backgrounds are normalized to the SM expectation, the Z+X background to the estimation from data

The number of candidates observed in the data and the expected yields for 137fb-1, for the backgrounds and H boson signal after the full event selection, are given in Table 3 for each of the 22 reconstructed event categories (described in Sect. 6.2) for the 105<m4<140GeV mass window around the Higgs boson peak. Fig. 6 shows the number of expected and observed events for each of the categories.

Table 3.

Number of expected background and signal events and number of observed candidates after full analysis selection, for each event category, in the mass range 105<m4<140GeV and for an integrated luminosity of 137fb-1. The yields are given for the different production modes. The uncertainties listed are statistical only. Signal is estimated from MC simulation at mH=125GeV, ZZ and rare electroweak backgrounds are also estimated from MC simulation, and Z+X is estimated from data

Reconstructed event category Signal Background Expected Observed
ggH VBF WH ZH tt¯H bb¯H tH qq¯ZZ ggZZ EW Z+X Signal Total
Untagged-0j-pT4[0,10] 27.7 0.09 0.03 0.03 0.00 0.15 0.00 71.5 3.06 0.01 3.21 27.9 ± 0.1 106 ± 0 114
Untagged-0j-pT4[10,200] 96.2 1.69 0.60 0.77 0.01 1.01 0.00 98.1 11.6 0.35 37.8 100 ± 0 248 ± 1 278
Untagged-1j-pT4[0,60] 26.8 1.51 0.56 0.48 0.01 0.45 0.01 25.3 3.02 0.64 14.2 29.8 ± 0.1 72.9 ± 0.4 74
Untagged-1j-pT4[60,120] 13.5 1.31 0.51 0.41 0.02 0.11 0.01 7.81 0.82 0.62 7.95 15.9 ± 0.1 33.1 ± 0.3 20
Untagged-1j-pT4[120,200] 3.51 0.60 0.17 0.17 0.01 0.02 0.00 1.15 0.19 0.25 1.63 4.48 ± 0.05 7.69 ± 0.16 11
Untagged-2j-pT4[0,60] 3.45 0.29 0.15 0.14 0.08 0.09 0.02 2.14 0.32 0.63 4.75 4.20 ± 0.06 12.1 ± 0.2 14
Untagged-2j-pT4[60,120] 5.26 0.56 0.24 0.19 0.12 0.04 0.03 2.19 0.30 0.72 4.14 6.43 ± 0.06 13.8 ± 0.2 15
Untagged-2j-pT4[120,200] 3.07 0.40 0.16 0.13 0.07 0.01 0.02 0.75 0.14 0.34 1.19 3.86 ± 0.05 6.28 ± 0.14 7
Untagged-pT4>200 2.79 0.62 0.21 0.17 0.07 0.01 0.02 0.43 0.21 0.21 0.73 3.89 ± 0.04 5.47 ± 0.11 3
Untagged-2j-mjj>350 0.77 0.16 0.06 0.04 0.05 0.01 0.01 0.34 0.06 0.31 1.71 1.12 ± 0.02 3.54 ± 0.14 3
VBF-1jet-tagged 15.5 3.29 0.22 0.16 0.00 0.13 0.01 6.85 1.53 0.20 2.44 19.3 ± 0.1 30.3 ± 0.2 27
VBF-2jet-tagged-mjj[350,700] 0.83 1.19 0.01 0.01 0.00 0.01 0.00 0.19 0.07 0.11 0.14 2.05 ± 0.03 2.55 ± 0.05 2
VBF-2jet-tagged-mjj>700 0.43 1.96 0.00 0.00 0.00 0.00 0.00 0.07 0.05 0.12 0.03 2.40 ± 0.02 2.67 ± 0.03 1
VBF-3jet-tagged-mjj>350 2.52 2.35 0.06 0.06 0.03 0.03 0.05 0.62 0.21 0.64 2.43 5.11 ± 0.05 9.01 ± 0.17 12
VBF-2jet-tagged-pT4>200 0.44 0.79 0.01 0.01 0.01 0.00 0.01 0.03 0.03 0.04 0.06 1.26 ± 0.02 1.42 ± 0.03 0
VBF-rest 2.48 0.94 0.13 0.09 0.04 0.04 0.01 0.98 0.20 0.39 2.18 3.74 ± 0.05 7.49 ± 0.17 5
VH-hadronic-tagged-mjj[60,120] 4.11 0.25 1.09 0.96 0.13 0.06 0.02 1.69 0.22 0.52 2.93 6.62 ± 0.06 12.0 ± 0.2 12
VH-rest 0.57 0.03 0.09 0.06 0.03 0.01 0.00 0.16 0.02 0.06 0.33 0.79 ± 0.02 1.36 ± 0.06 0
VH-leptonic-tagged-pT4[0,150] 0.33 0.04 0.85 0.26 0.10 0.03 0.03 2.16 0.36 0.19 1.11 1.64 ± 0.02 5.47 ± 0.13 10
VH-leptonic-tagged-pT4>150 0.02 0.01 0.21 0.06 0.04 0.00 0.01 0.05 0.01 0.03 0.08 0.35 ± 0.01 0.52 ± 0.03 0
tt¯H-leptonic-tagged 0.02 0.01 0.02 0.02 0.68 0.00 0.03 0.08 0.01 0.23 0.21 0.79 ± 0.01 1.32 ± 0.07 0
tt¯H-hadronic-tagged 0.18 0.05 0.03 0.05 0.86 0.01 0.03 0.03 0.01 0.82 1.06 1.22 ± 0.01 3.15 ± 0.14 2

Fig. 6.

Fig. 6

Distributions of the expected and observed number of events for the reconstructed event categories in the mass region 105<m4<140GeV. Points with error bars represent the data and stacked histograms represent the expected numbers of the signal and background events. The yields of the different H boson production mechanisms with mH=125GeV, denoted as H(125), and those of the ZZ and rare electroweak backgrounds are normalized to the SM expectations, while the Z+X background yield is normalized to the estimate from the data

The reconstructed invariant masses of the Z1 and Z2 dilepton systems are shown in Fig. 7 for 118<m4<130GeV, together with their 2D distribution in the 105<m4<140GeV mass region. The distribution of the discriminants used for event categorization along with the corresponding working point values are shown in Fig. 8.

Fig. 7.

Fig. 7

Distribution of the Z1 (upper left) and Z2 (upper right) reconstructed masses in the 118<m4<130GeV mass region and their 2D distribution (lower) in the 105<m4<140GeV mass region. The stacked histograms and the red and blue scales represent expected distributions of the signal and background processes and the points represent the data. The yields of the different H boson production mechanisms with mH=125GeV, denoted as H(125), and those of the ZZ and rare electroweak backgrounds are normalized to the SM expectations, while the Z+X background yield is normalized to the estimate from the data

Fig. 8.

Fig. 8

Distribution of categorization discriminants in the mass region 118<m4<130GeV: D2jetVBF (upper), D1jetVBF (center), D2jetVH (lower) = max(D2jetWH,D2jetZH). Points with error bars represent the data and stacked histograms represent expected distributions of the signal and background processes. The SM Higgs boson signal with mH=125GeV, denoted as H(125), and the ZZ backgrounds and rare electroweak backgrounds are normalized to the SM expectation, the Z+X background to the estimation from data. The vertical dashed lines denote the working points used in the event categorization. The SM H boson signal is separated into two components: the production mode which is targeted by the specific discriminant, and other production modes, where the gluon fusion process dominates.

The results presented in Sects. 10.1 and 10.2 are extracted with a two-dimensional likelihood fit that relies on two variables, the four-lepton invariant mass m4 and the matrix element kinematic discriminant D. The fiducial cross section measurements are extracted with a one-dimensional likelihood fit that relies only on the four-lepton invariant mass. The fit procedure and results are presented in Sect. 10.3. The fit is performed in the 105<m4<140GeV mass region. The parameters of interest (POIs) are estimated with their corresponding confidence intervals using a profile likelihood ratio test statistic [117, 118], in which the experimental and theoretical uncertainties are incorporated via NPs. The choice of the POIs depends on the specific measurement under consideration, while the remaining parameters are treated as NPs. All the POIs considered in the analysis are forced to be greater than or equal to zero; this reflects the fact that the signal yield is substantially larger than the background yield in the mass range studied. Negative POIs would imply negative signal strength modifiers and a negative probability density function (pdf). We define a two-dimensional pdf as the product of two one-dimensional pdfs:

f(m4,D)=P(m4)P(D|m4). 6

The first term, P(m4), is the unbinned analytical shape described in Sect. 8 for signals and Sect. 7 for backgrounds. The second term, P(D|m4), is a binned template of D that is conditional to m4. This is achieved by creating a two-dimensional template of m4 vs. D and normalizing it to 1 for each bin of m4.

In almost all sub-categories we use a decay-only kinematic discriminant (D=Dbkgkin) to separate the H boson signal from the background as defined in Eq. (3). Conversely, in the sub-categories of the VBF-2jet-tagged, the D=DbkgVBF+dec discriminant (defined in Eq. (4)) is used, which is sensitive to the VBF production mechanism. Similarly, in two sub-categories of the VH-hadronic-tagged category, the D=DbkgVH+dec discriminant (defined in Eq. (5)) is used.

The ggH, VBF, WH, ZH and tt¯H samples are used to build different signal templates for each of the nineteen STXS production bins described in Sect. 6.1. Irreducible background templates are built starting from qq¯ZZ and ggZZ samples. Finally, reducible background templates are built using data driven methods described in Sect. 7.2. Following the described procedure, P(D|m4) templates are obtained for the twenty-two event categories and the three final states (4μ, 4e, 2e2μ).

The unbinned likelihood function, L(μ), is defined as the product over N observed events:

L(μ)=1Nevents(i=119μiSijkfSijk(m4,D)+BjkfBjk(m4,D))e-iμiSijk+Bjk, 7

where μi is the signal strength modifier for the production bin i, Sijk are the predicted SM rates of events in the production bin i that are observed in the reconstructed event category j and final state k, Bjk are the predicted background rates in the reconstructed event category j and final state k, fSijk(m4,D) are the pdfs for the signal, and fBjk(m4,D) the pdfs for the background.

The correlation of the kinematic discriminants Dbkgkin, DbkgVBF+dec, and DbkgVH+dec with the four-lepton invariant mass is shown in Fig. 9 for the mass interval 105<m4<140GeV. Their distributions for the mass interval 118<m4<130GeV are shown in Fig. 10.

Fig. 9.

Fig. 9

Distribution of three different kinematic discriminants versus m4: Dbkgkin (upper), DbkgVBF+dec (middle) and DbkgVH+dec (lower) shown in the mass region 105<m4<140GeV. The blue scale represents the expected total number of ZZ, rare electroweak, and Z+X background events. The red scale represents the number of expected SM H boson signal events for mH=125GeV. The points show the data from the categories listed in the legend

Fig. 10.

Fig. 10

Distribution of kinematic discriminants in the mass region 118<m4<130GeV: (uppper) Dbkgkin , (center) DbkgVBF+dec, (lower) DbkgVH+dec. Points with error bars represent the data and stacked histograms represent expected distributions of the signal and background processes. The yields of the different H boson production mechanisms with mH=125GeV, denoted as H(125), and those of the ZZ and rare electroweak backgrounds are normalized to the SM expectations, while the Z+X background yield is normalized to the estimate from the data. In the center and lower figures the SM H boson signal is separated into two components: the production mode which is targeted by the specific discriminant, and other production modes, where the gluon fusion process dominates

Signal strength modifier

A simultaneous fit to all categories is performed to extract the signal strength modifier, defined as the ratio of the observed H boson yield in the H4 decay channel to the standard model expectation.

The combined measurement of the inclusive signal strength modifier is measured to be μ=0.94-0.11+0.12 or μ=0.94±0.07(stat)-0.06+0.07(theo)-0.05+0.06(exp) at a fixed mass value mH=125.38GeV, which is the current most precise measurement of the H boson mass published by the CMS Collaboration [119]. In all subsequent fits, mH is fixed to this value. The dominant experimental sources of systematic uncertainty are the uncertainties in the lepton identification efficiencies and luminosity measurement, while the dominant theoretical source is the uncertainty in the total gluon fusion cross section. The contributions to the total uncertainty from experimental and theoretical sources are found to be similar in magnitude. The signal strength modifiers are further studied in terms of the five main SM Higgs boson production mechanisms, namely ggH, VBF, ZH, WH, and tt¯H. The contributions of the bb¯H and tH production modes are also taken into account. The relative normalizations of the bb¯H and the gluon fusion contributions are kept fixed in the fit, and so are the tH and tt¯H ones. The results are shown in Fig. 11 for the observed and expected profile likelihood scans of the inclusive signal strength modifier and those for the signal strength modifiers of the five main SM Higgs boson production mechanisms. The corresponding numerical values, including the decomposition of the uncertainties into statistical and systematic components, as well as the expected uncertainties, are given in Table 4.

Fig. 11.

Fig. 11

(Upper) The observed and expected profile likelihood scans of the inclusive signal strength modifier. The scans are shown both with (solid line) and without (dashed line) systematic uncertainties. (Lower) Results of likelihood scans for the signal strength modifiers corresponding to the five main SM H boson production mechanisms, compared to the SM prediction shown as a vertical dashed line. The thick black lines indicate the one standard deviation confidence intervals including both statistical and systematic sources. The thick red lines indicate the statistical uncertainties corresponding to the one standard deviation confidence intervals

Table 4.

Best fit values and ±1 standard deviation uncertainties for the expected and observed signal strength modifiers at mH=125.38GeV. The statistical and systematic uncertainties are given separately

Expected Observed
μtt¯H,tH 1.00-0.77+1.23(stat)-0.06+0.51(syst) 0.17-0.17+0.88(stat)-0.00+0.42(syst)
μWH 1.00-1.00+1.83(stat)-0.00+0.75(syst) 1.66-1.66+1.52(stat)-0.00+0.85(syst)
μZH 1.00-1.00+4.79(stat)-0.00+6.76(syst) 0.00-0.00+4.38(stat)-0.00+3.24(syst)
μVBF 1.00-0.44+0.53(stat)-0.12+0.18(syst) 0.48-0.37+0.46(stat)-0.10+0.14(syst)
μggH,bb¯H 1.00±0.10(stat)-0.10+0.12(syst) 0.99±0.09(stat)-0.09+0.11(syst)
μ 1.00-0.07+0.08(stat)-0.08+0.10(syst) 0.94±0.07(stat)-0.08+0.09(syst)

The dependence of the measured signal strengths on the profiling of mH is checked and found to have a small impact both on the inclusive results and those in terms of the five main H boson production mechanisms, well within the measurement uncertainties. The best fit signal value changes at most by 4% and the profiled value of the mass is found to be mH=125.09-0.14+0.15(stat)GeV. It is important to note here that the precise determination of mH and the systematic uncertainties that enter its measurement are beyond the scope of this analysis.

Two signal strength modifiers, μfμggH,tt¯H,bb¯H,tH and μVμVBF,VH, are introduced for the fermion and vector-boson induced contributions to the expected SM cross section. A two-parameter fit is performed simultaneously to the events reconstructed in all categories, leading to μf=0.96-0.12+0.14 and μV=0.82-0.31+0.36. The expected values for mH=125.38GeV are μf=1.00-0.13+0.15 and μV=1.00-0.33+0.39. The 68 and 95% CL contours in the (μf,μV) plane are shown in Fig. 12 and the SM predictions lie within the 68% CL regions of this measurement.

Fig. 12.

Fig. 12

Result of the 2D likelihood scan for the μfμggH,tt¯H,bb¯H,tH and μVμVBF,VH signal strength modifiers. The solid and dashed contours show the 68 and 95% CL regions, respectively. The cross indicates the best fit value, and the diamond represents the expected value for the SM Higgs boson

Simplified template cross section

The results for the H boson product of cross section times branching fraction for HZZ decay, (σB)obs, and comparisons with the SM expectation, (σB)SM, for the stages of production bins defined in Sect. 6.1, are shown in Fig. 13 for the stage 0 and in Fig. 14 for the merged stage 1.2. The corresponding numerical values are given in Tables 5 and 6 .

Fig. 13.

Fig. 13

The measured product of cross section times branching fraction for HZZ decay (σB)obs and the SM predictions (σB)SM for the stage 0 STXS production bins and the inclusive measurement at mH=125.38GeV. Points with error bars represent measured values and black dashed lines with gray uncertainty bands represent the SM predictions. In the bottom panel ratios of the measured cross sections and the SM predictions are shown along with the uncertainties for each of the bins and the inclusive measurement

Fig. 14.

Fig. 14

The measured cross sections (σB)obs and the SM predictions (σB)SM for HZZ decay and the merged stage 1.2 STXS production bins at mH=125.38GeV. Points with error bars represent measured values and black dashed lines with gray uncertainty bands represent the SM predictions. In the bottom panel ratios of the measured cross sections and the SM predictions are shown with corresponding uncertainties for each of the bins

Table 5.

Best fit values and ±1 standard deviation uncertainties for the measured cross sections (σB)obs, the SM predictions (σB)SM, and their ratio for the stage 0 STXS production bins at mH=125.38GeV for HZZ decay

(σB)obs (fb) (σB)SM (fb) (σB)obs/(σB)SM
ttH 3-3+16 15.9±1.4 0.16-0.16+0.98
VH-lep 41-35+52 25.9±0.8 1.56-1.34+1.99
qqH 61-44+53 122±6 0.50-0.36+0.44
ggH 1214-125+135 1192±95 1.02-0.10+0.11
Inclusive 1318-122+130 1369±164 0.96-0.09+0.10

Table 6.

Best fit values and ±1 standard deviation uncertainties for the measured cross sections (σB)obs, the SM predictions (σB)SM, and their ratio for the merged stage 1.2 STXS production bins at mH=125.38GeV for HZZ decay

(σB)obs (fb) (σB)SM (fb) (σB)obs/(σB)SM
ggH-0j/pT[0,10] 145-40+45 164±11 0.89-0.24+0.28
ggH-0j/pT[10,200] 611-90+98 561±87 1.09-0.16+0.17
ggH-1j/pT[0,60] 214-87+78 177±18 1.21-0.49+0.44
ggH-1j/pT[60,120] 59-53+44 121±14 0.48-0.44+0.37
ggH-1j/pT[120,200] 53-22+25 20±4 2.62-1.08+1.24
ggH-2j/pT[0,60] 0-0+27 35±6 0.00-0.00+0.76
ggH-2j/pT[60,120] 78-37+41 51±9 1.53-0.73+0.81
ggH-2j/pT[120,200] 27-19+22 26±6 1.06-0.72+0.87
ggH-2j/mjj>350 4-4+72 23±3 0.17-0.17+3.2
ggH/pT>200 7-7+8 15±6 0.47-0.47+0.56
qqH-rest 11-11+161 71±5 0.15-0.15+2.27
qqH-2j/mjj[60,120] 12-12+30 12.1±1.2 1.01-1.01+2.45
qqH-2j/mjj[350,700] 15-15+23 10.5±0.7 1.41-1.41+2.21
qqH-2j/mjj>700 0-0+12 15±1 0.00-0.00+0.77
qqH-3j/mjj>350 43-43+30 8.9±0.5 4.84-4.84+3.38
qqH-2j/pT>200 0-0+3 4.2±0.2 0.00-0.00+0.72
VH-lep/pTH[0,150] 56-40+58 22.3±1.1 2.49-1.79+2.60
VH-lep/pTH>150 0-0+10 3.6±0.1 0.00-0.00+2.79
ttH 0-0+15 15.9±1.4 0.00-0.00+0.91

As discussed, the set of THU uncertainties described in Sect. 9.2 is not considered for the STXS measurements: THU uncertainties are model dependent and should be only considered in the interpretation of the results. Therefore, the THU uncertainties are included in the SM predictions of the cross section. The correlation matrices are shown in Fig. 15. The dominant experimental sources of systematic uncertainty are the same as for the signal strength modifiers measurement, while the dominant theoretical source is the uncertainty in the category migration for the ggH process.

Fig. 15.

Fig. 15

Correlation matrices between the measured cross sections for the stage 0 (upper) and the merged stage 1.2 (lower) for HZZ decay

Fiducial cross section

In this section the cross section measurement for the process ppH4 within a fiducial volume that closely matches the reconstruction level selection is presented. In particular, the integrated fiducial cross section is measured as well as differential cross sections as a function of the transverse momentum of the H boson (pTH), its rapidity (|yH|), the number of associated jets (Nj), and the transverse momentum of the leading jet (pTj). These measurements are largely independent of the assumptions on the relative fractions and kinematic distributions of the individual production modes. The definition of the fiducial volume is based on generator-level quantities and is identical to that in Ref. [18]. In order to reduce the experimental uncertainties, only jets with pTj>30GeV and |ηj|<2.5 are considered for the differential cross sections as a function of jet observables. An increase in model dependence compared to Ref. [25] is observed when using the ZZ candidate selection at reconstruction level where the candidate with the best Dbkgkin discriminant value is chosen. Therefore, the fiducial cross section measurement is performed using the event selection algorithm in Ref. [25]. Specifically, the Z1 candidate is chosen to be the one with m(Z1) closest to the nominal Z boson mass, and in cases where multiple Z2 candidates satisfy all criteria, the pair of leptons with the largest sum of the transverse momenta magnitudes is chosen. The full fiducial volume definition is detailed in Table 7 and the acceptance for various SM production modes is given in Table 8.

Table 7.

Summary of requirements used in the definition of the fiducial phase space for the H4 cross section measurements

Requirements for the H4 fiducial phase space
Lepton kinematics and isolation
Leading lepton pT pT>20GeV
Next-to-leading lepton pT pT>10GeV
Additional electrons (muons) pT pT>7(5)GeV
Pseudorapidity of electrons (muons) |η|< 2.5 (2.4)
Sum of scalar pT of all stable particles within ΔR<0.3 from lepton <0.35pT
Event topology
Existence of at least two same-flavor OS lepton pairs, where leptons satisfy criteria above
Inv. mass of the Z1 candidate 40<mZ1<120GeV
Inv. mass of the Z2 candidate 12<mZ2<120GeV
Distance between selected four leptons ΔR(i,j)>0.02 for any ij
Inv. mass of any opposite sign lepton pair m+->4GeV
Inv. mass of the selected four leptons 105<m4<140GeV

Table 8.

Summary of the fraction of signal events for different SM signal production modes within the fiducial phase space (acceptance Afid), reconstruction efficiency (ϵ) for signal events in the fiducial phase space, and ratio of the number of reconstructed events outside the fiducial phase space to that of the reconstructed events in the fiducial phase space (fnonfid). For all production modes the values given are for mH=125GeV. Also shown in the last column is the factor (1+fnonfid)ϵ which regulates the signal yield for a given fiducial cross section, as shown in Eq. (8). The uncertainties listed are statistical only. The theoretical uncertainty in Afid for the SM is less than 1%

Signal process Afid ϵ fnonfid (1+fnonfid)ϵ
ggH (powheg) 0.402 ± 0.001 0.598 ± 0.002 0.054 ± 0.001 0.631 ± 0.002
VBF 0.445 ± 0.002 0.615 ± 0.002 0.043 ± 0.001 0.641 ± 0.003
WH 0.329 ± 0.002 0.604 ± 0.003 0.078 ± 0.002 0.651 ± 0.004
ZH 0.340 ± 0.003 0.613 ± 0.005 0.082 ± 0.004 0.663 ± 0.006
tt¯H 0.315 ± 0.004 0.588 ± 0.007 0.181 ± 0.009 0.694 ± 0.010

A maximum likelihood fit of the signal and background parameterizations to the observed 4 mass distribution, Nobs(m4), is performed to extract the integrated fiducial cross section for the process ppH4 (σfid). The fit is carried out inclusively (i.e., without any event categorization) and does not use the Dbkgkin observable in order to minimize the model dependence. The fit is performed simultaneously in all final states and assumes a H boson mass mH=125.38GeV, while the branching fractions of the H boson to different final states (4e,4μ,2e2μ) are free parameters in the fit. The systematic uncertainties described in Sect. 9 are included in the form of NPs and the results are obtained using an asymptotic approach [118] with a test statistic based on the profile likelihood ratio [117]. This procedure accounts for the unfolding of detector effects from the observed distributions and is the same as in Refs. [25, 120].

The number of expected events in each final state f and in each bin i of a given observable is expressed as a function of m4 as:

Nexpf,i(m4)=Nfidf,i(m4)+Nnonfidf,i(m4)+Nnonresf,i(m4)+Nbkgf,i(m4)=jϵi,jf1+fnonfidf,iσfidf,jLPres(m4)+Nnonresf,iPnonres(m4)+Nbkgf,iPbkg(m4). 8

The shape of the resonant signal contribution, Pres(m4), is described by a double-sided Crystal Ball function as discussed in Sect. 8, and the normalization is used to extract the fiducial cross section. The non-resonant signal function, Pnonres(m4), is determined by the WH, ZH, and tt¯H contributions where one of the leptons from the H boson decay is lost or not selected. It is modeled by a Landau distribution with shape parameters constrained in the fit to be within a range determined from simulation. This contribution is referred to as the “combinatorial signal” and is treated as a background in this measurement.

The quantity ϵi,jf represents the detector response matrix that maps the number of expected events in bin j of a given observable at the fiducial level to the number of expected events in bin i at the reconstruction level. This response matrix is determined using simulated signal samples and includes corrections for residual differences between data and simulation. In the case of the integrated fiducial cross section measurement, the response matrices become single numbers, which are listed in Table 8 for different SM production mechanism.

An additional resonant contribution arises from events which are accepted but do not originate from the fiducial phase space. These events are due to detector effects that cause differences between the quantities used for the fiducial phase space definition and the corresponding quantities at the reconstruction level. This contribution is treated as background and is referred to as the “non-fiducial signal” contribution. A simulated sample is used to verify that the shape of the distribution for these events is identical to that of the fiducial signal, and its normalization is fixed to the corresponding fraction of the fiducial signal. The value of this fraction, which we denote as fnonfid, is determined from simulation for each of the signal models studied. The value of fnonfid for different signal models is shown in Table 8.

The integrated fiducial cross section is measured to be

σfid=2.84-0.31+0.34=2.84-0.22+0.23(stat)-0.21+0.26(syst)fb

at mH=125.38GeV. This can be compared to the SM expectation σfidSM=2.84±0.15fb. The measured inclusive fiducial cross sections in different final states and integrated as a function of center-of-mass energy are shown in Fig. 16. The corresponding numerical values, including the decomposition of the uncertainties into statistical and systematic components, and the corresponding expected uncertainties, are given in Table 9.

Fig. 16.

Fig. 16

The measured inclusive fiducial cross section in different final states (upper) and integrated as a function of s (lower). The acceptance is calculated using powheg at s=13TeV and HRes [107, 109] at s= 7 and 8TeV, and the total gluon fusion cross section and uncertainty are taken from Ref. [58]. The fiducial volume for s=69TeV uses the lepton isolation definition from Ref. [25] and the SM predictions and measurements are calculated at mH=125.0GeV, while for s=1214TeV the definition described in the text is used and SM predictions and measurements are calculated at mH=125.38GeV

Table 9.

The measured inclusive fiducial cross section and ±1 standard deviation uncertainties for different final states and data-taking periods at mH=125.38GeV. The statistical and systematic uncertainties are given separately for the inclusive measurements

2e2μ (fb) 4μ (fb) 4e (fb) Inclusive (fb)
2016 1.22-0.30+0.38 0.89-0.19+0.22 1.07-0.33+0.44 3.19-0.56+0.68=3.19-0.45+0.48(stat)-0.33+0.48(syst)
2017 1.64-0.35+0.41 0.82-0.18+0.21 0.56-0.22+0.29 3.01-0.50+0.60=3.01-0.41+0.44(stat)-0.27+0.41(syst)
2018 1.17-0.24+0.27 0.66-0.13+0.15 0.73-0.20+0.24 2.57-0.38+0.42=2.57-0.31+0.33(stat)-0.23+0.27(syst)
2016–2018 1.31-0.19+0.20 0.78-0.10+0.10 0.76-0.16+0.18 2.84-0.31+0.34=2.84-0.22+0.23(stat)-0.21+0.26(syst)

The measured differential cross sections as a function of the H boson transverse momentum and rapidity are shown in Fig. 17. The corresponding numerical values are given in Tables 10 and 11 . Finally, the measured differential cross sections as a function of the number of associated jets and the transverse momentum of the leading jet are shown in Fig. 18. The corresponding numerical values are given in Tables 12 and 13.

Fig. 17.

Fig. 17

Differential cross sections as a function of pTH (upper) and |yH| (lower). The acceptance and theoretical uncertainties in the differential bins are calculated using powheg. The sub-dominant component of the signal (VBF+VH+tt¯H) is denoted as XH

Table 10.

The measured differential fiducial cross section and ±1 standard deviation uncertainties for the pTH observable at mH=125.38GeV. The breakdown of the total uncertainty (unc.) into statistical and systematic components is given

Bin range (GeV) dσfid (fb) unc. (stat) (syst)
0–10 0.32 -0.10+0.11 -0.09+0.10 -0.03+0.04
10–20 0.67 -0.13+0.14 -0.12+0.13 -0.05+0.06
20–30 0.41 -0.10+0.12 -0.10+0.11 -0.04+0.04
30–45 0.51 -0.10+0.12 -0.10+0.11 -0.04+0.04
45–80 0.45 -0.09+0.10 -0.09+0.10 -0.03+0.04
80–120 0.30 -0.07+0.08 -0.07+0.07 -0.02+0.02
120–200 0.19 -0.05+0.06 -0.05+0.06 -0.01+0.01
200–13000 0.03 -0.02+0.02 -0.01+0.02 -0.00+0.00

Table 11.

The measured differential fiducial cross section and ±1 standard deviation uncertainties for the |yH| observable at mH=125.38GeV. The breakdown of the total uncertainty (unc.) into statistical and systematic components is given

Bin range dσfid (fb) unc. (stat) (syst)
0.0–0.15 0.41 -0.08+0.10 -0.08+0.09 -0.03+0.05
0.15–0.3 0.36 -0.07+0.08 -0.07+0.07 -0.02+0.03
0.3–0.6 0.62 -0.11+0.13 -0.10+0.11 -0.05+0.07
0.6–0.9 0.57 -0.10+0.12 -0.10+0.10 -0.04+0.06
0.9–1.2 0.36 -0.09+0.10 -0.08+0.09 -0.03+0.05
1.2–2.5 0.64 -0.13+0.15 -0.12+0.13 -0.05+0.08

Fig. 18.

Fig. 18

Differential cross sections as a function of the number of associated jets (upper), and pT of the leading jet (lower). The acceptance and theoretical uncertainties in the differential bins are calculated using powheg. The sub-dominant component of the signal (VBF+VH+tt¯H) is denoted as XH

Table 12.

The measured differential fiducial cross section and ±1 standard deviation uncertainties for the Nj observable at mH=125.38GeV. The breakdown of the total uncertainty (unc.) into statistical and systematic components is given

Bin range dσfid (fb) unc. (stat) (syst)
0 2.00 -0.26+0.29 -0.20+0.21 -0.17+0.20
1 0.64 -0.14+0.15 -0.13+0.14 -0.04+0.06
2 0.23 -0.08+0.09 -0.08+0.09 -0.01+0.02
3 0.03 -0.03+0.05 -0.03+0.05 -0.00+0.01
4 0.00 -0.00+0.03 -0.00+0.03 -0.00+0.01

Table 13.

The measured differential fiducial cross section and ±1 standard deviation uncertainties for the pTj observable at mH=125.38GeV. The breakdown of the total uncertainty (unc.) into statistical and systematic components is given

Bin range (GeV) dσfid (fb) unc. (stat) (syst)
30–55 0.52 -0.14+0.16 -0.13+0.15 -0.04+0.05
55–95 0.21 -0.09+0.10 -0.09+0.10 -0.02+0.03
95–200 0.16 -0.06+0.07 -0.05+0.06 -0.01+0.02
200–13000 0.04 -0.02+0.03 -0.02+0.03 -0.01+0.01

For all the fiducial measurements the dominant systematic uncertainties are those on the lepton identification efficiencies and luminosity measurement, while the theoretical uncertainties are smaller. In order to assess the model dependence of the measurement, the unfolding procedure is repeated using different response matrices created by varying the relative fraction of each SM production mode within its experimental constraints. The uncertainty is negligible with respect to the experimental systematic uncertainties.

Summary

Several measurements of the Higgs boson production in the four-lepton final state at s=13TeV have been presented, using data samples corresponding to an integrated luminosity of 137fb-1. Thanks to a large signal-to-background ratio and the complete reconstruction of the final state decay products, this channel enables a detailed study of the Higgs boson production properties. The measured signal strength modifier is μ=0.94±0.07(stat)-0.06+0.07(theo)-0.05+0.06(exp) and the integrated fiducial cross section is measured to be σfid=2.84-0.22+0.23(stat)-0.21+0.26(syst)fb with a standard model prediction of 2.84±0.15fb for the same fiducial region.. The signal strength modifiers for the main Higgs boson production modes are also reported. A new set of measurements, designed to quantify the different Higgs boson production processes in specific kinematical regions of phase space, have also been presented. The differential cross sections as a function of the transverse momentum and rapidity of the Higgs boson, the number of associated jets, and the transverse momentum of the leading associated jet are determined. All results are consistent, within their uncertainties, with the expectations for the standard model Higgs boson.

Acknowledgements

We gratefully acknowledge the LHC Higgs Working Group for its role in developing stage 1.2 of the simplified template cross section framework.

We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid and other centers for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC, the CMS detector, and the supporting computing infrastructure provided by the following funding agencies: BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RIF (Cyprus); SENESCYT (Ecuador); MoER, ERC PUT and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); NKFIA (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); MES (Latvia); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom, RAS, RFBR, and NRC KI (Russia); MESTD (Serbia); SEIDI, CPAN, PCTI, and FEDER (Spain); MOSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA).

Individuals have received support from the Marie-Curie program and the European Research Council and Horizon 2020 Grant, contract Nos. 675440, 724704, 752730, and 765710 (European Union); the Leventis Foundation; the Alfred P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium) under the “Excellence of Science – EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z191100007219010; the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Deutsche Forschungsgemeinschaft (DFG), under Germany’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306, and under project number 400140256 - GRK2497; the Lendület (“Momentum”) Program and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, the New National Excellence Program ÚNKP, the NKFIA research grants 123842, 123959, 124845, 124850, 125105, 128713, 128786, and 129058 (Hungary); the Council of Science and Industrial Research, India; the Ministry of Science and Higher Education and the National Science Center, contracts Opus 2014/15/B/ST2/03998 and 2015/19/B/ST2/02861 (Poland); the National Priorities Research Program by Qatar National Research Fund; the Ministry of Science and Higher Education, project no. 0723-2020-0041 (Russia); the Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa del Principado de Asturias; the Thalis and Aristeia programs cofinanced by EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand); the Kavli Foundation; the Nvidia Corporation; the SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA).

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is our standard statement: Release and preservation of data used by the CMS Collaboration as the basis for publications is guided by the CMS policy as written in its document “CMS data preservation, re-use and open access policy” (https://cmsdocdb.cern.ch/cgi-bin/PublicDocDB/RetrieveFile?docid=6032&filename=CMSDataPolicyV1.2.pdf&version=2)].

Declaration

Conflict of interest

The authors declare that they have no conflict of interest.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is our standard statement: Release and preservation of data used by the CMS Collaboration as the basis for publications is guided by the CMS policy as written in its document “CMS data preservation, re-use and open access policy” (https://cmsdocdb.cern.ch/cgi-bin/PublicDocDB/RetrieveFile?docid=6032&filename=CMSDataPolicyV1.2.pdf&version=2)].


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