Table 11.

Singlet-octet and quark flavor bases mixing parameter values derived from fits performed within ${\text{EBHLS}}_2$ under the F and $A_{\pm }$ configurations defined in the text. For the configuration F, $\varphi =({\varphi }_q+{\varphi }_s)/2$ whereas $\varphi ={\varphi }_q(={\varphi }_s)$ for the $A_{\pm }$ solutions. Correspondingly, the contributions of the HLS channels for $\sqrt{s}\le 1.05$ GeV to the HVP are also given in each case; they can be compared to Table 7. The main fit properties are noted at the bottom end of the Table

${\text{EBHLS}}_2$ (BS)	Sol. F	Sol. $A_{+}$	Sol. $A_{-}$	Sol. $A_{+}$	Sol. $A_{-}$
	$ϵ={\kappa }_0$     and      ${ϵ}^{\prime }={\kappa }_0^{\prime }$			$ϵand{ϵ}^{\prime }$ free
${\theta }_P$ (deg.)	$-15.89\pm 0.34$	$-16.63\pm 0.30$	$-15.78\pm 0.28$	$-16.63\pm 0.30$	$-15.59\pm 0.28$
${\theta }_0$ (deg.)	$-6.35\pm 0.47$	$-8.04\pm 0.39$	$-8.05\pm 0.33$	$-7.95\pm 0.39$	$-7.71\pm 0.34$
${\theta }_8$ (deg.)	$-24.55\pm 0.30$	$-24.44\pm 0.25$	$-22.83\pm 0.27$	$-24.50\pm 0.25$	$-22.77\pm 0.28$
${\theta }_0-{\theta }_8$ (deg.)	$18.21\pm 0.24$	$16.45\pm 0.23$	$14.85\pm 0.24$	$16.59\pm 0.23$	$15.13\pm 0.24$
$F_0/f_{\pi }$	$1.166\pm 0.006$	$1.190\pm 0.003$	$1.190\pm 0.003$	$1.184\pm 0.003$	$1.187\pm 0.003$
$F_8/f_{\pi }$	$1.293\pm 0.003$	$1.315\pm 0.003$	$1.302\pm 0.003$	$1.309\pm 0.003$	$1.302\pm 0.003$
FKS $\varphi$ (deg.)	$38.85\pm 0.35$	$38.96\pm 0.27$	$38.08\pm 0.29$	$38.09\pm 0.30$	$39.15\pm 0.27$
${\varphi }_q-{\varphi }_s$ (deg.)	$0.39\pm 0.18$	$\equiv 0$	$\equiv 0$	$\equiv 0$	$\equiv 0$
$F_q/f_{\pi }$	$1.008\pm 0.007$	$1.050\pm 0.003$	$1.066\pm 0.004$	$1.044\pm 0.003$	$1.061\pm 0.004$
$F_s/f_{\pi }$	$1.418\pm 0.005$	$1.428\pm 0.004$	$1.405\pm 0.004$	$1.423\pm 0.004$	$1.406\pm 0.004$
$F_s/f_K$	$1.192\pm 0.003$	$1.198\pm 0.003$	$1.181\pm 0.002$	$1.195\pm 0.002$	$1.182\pm 0.002$
$f_K/f_{\pi }$	$1.190\pm 0.002$	$1.193\pm 0.002$	$1.189\pm 0.002$	$1.191\pm 0.002$	$1.190\pm 0.002$
${10}^{10}\times a_{\mu }(HLS)$	$572.52\pm 1.02$	$571.84\pm 0.98$	$572.44\pm 0.98$	$575.00\pm 0.95$	$572.59\pm 0.99$
${\chi }^2/N_{\mathrm{pts}}$	1280/1366	1309/1366	1289/1366	1292/1366	1286/1366
Probability	85.9%	70.6%	82.5%	80.1%	83.5%