Vector form factor in K_l3 semileptonic decay with two flavors of dynamical domain-wall quarks

We calculate the vector form factor in K \to \pi l \nu semileptonic decays at zero momentum transfer f_+(0) from numerical simulations of two-flavor QCD on the lattice. Our simulations are carried out on 16^3 \times 32 at a lattice spacing of a \simeq 0.12 fm using a combination of the DBW2 gauge and the domain-wall quark actions, which possesses excellent chiral symmetry even at finite lattice spacings. The size of fifth dimension is set to L_s=12, which leads to a residual quark mass of a few MeV. Through a set of double ratios of correlation functions, the form factor calculated on the lattice is accurately interpolated to zero momentum transfer, and then is extrapolated to the physical quark mass. We obtain f_+(0)=0.968(9)(6), where the first error is statistical and the second is the systematic error due to the chiral extrapolation. Previous estimates based on a phenomenological model and chiral perturbation theory are consistent with our result. Combining with an average of the decay rate from recent experiments, our estimate of f_+(0) leads to the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |V_{us}|=0.2245(27), which is consistent with CKM unitarity. These estimates of f_+(0) and |V_{us}| are subject to systematic uncertainties due to the finite lattice spacing and quenching of strange quarks, though nice consistency in f_+(0) with previous lattice calculations suggests that these errors are not large.