Continuum limit of hyperon vector coupling $f_1(0)$ from 2+1 flavor domain wall QCD

We determine the hyperon vector couplings $f_1(0)$ for $\Sigma^{-}\rightarrow nl^-\bar{\nu_l}$ and $\Xi^0\rightarrow\Sigma^{+}l^-\bar{\nu_l}$ semileptonic decays in the continuum limit with (2+1)-flavors of dynamical domain-wall fermions, using the Iwasaki gauge action at two different lattice spacings of $a$=0.114(2) and 0.086(2) fm. A theoretical estimation of flavor SU(3)-breaking effect on the vector coupling is required to extract $V_{us}$ from the experimental rate of hyperon beta decays. We obtain the vector couplings $f_1(0)$ for $\Sigma\rightarrow N$ and $\Xi\rightarrow \Sigma$ beta-decays with an accuracy of less than one percent. We then find that lattice results of $f_1(0)$ combined with the best estimate of $|V_{us}|$ with imposing Cabibbo-Kobayashi-Maskawa (CKM) unitarity are slightly deviated from the experimental result of $|V_{us}f_1(0)|$ for the $\Sigma\rightarrow N$ beta-decay. This discrepancy can be attributed to an assumption made in the experimental analysis on $|V_{us}f_1(0)|$, where the induced second-class form factor $g_2$ is set to be zero regardless of broken SU(3) symmetry. We report on this matter and then estimate the possible value of $g_2(0)$, which is evaluated from the experimental decay rate with our lattice result of $f_1(0)$ under the first-row CKM-unitarity condition.