Kl3 form factors at the physical point: Toward the continuum limit

We present updated results for the form factors of the kaon semileptonic oKe3 thorn decay process calculated with Nf 1/4 2 thorn 1 nonperturbatively Ooa thorn -improved Wilson quark action and Iwasaki gauge action at the physical point on large volumes of more than o10 fm thorn 4. In addition to our previous calculation at the lattice spacing a 1/4 0.085 fm, we perform a calculation at the second lattice spacing of 0.063 fm. Using the results for the form factors extracted from 3-point functions with the local and also conserved vector currents at the two lattice spacings, continuum extrapolation and interpolation of the momentum transfer are carried out simultaneously to obtain the value of the form factor f thorn o0 thorn at the zero momentum transfer in the continuum limit. After investigation of stability of f thorn o0 thorn against several fit forms and different data, we obtain f thorn o0 thorn 1/4 0.9615o10 thorn o thorn 47 -3 thorn o5 thorn , where the first, second, and third errors are statistical, systematic errors from choice of the fit forms and isospin breaking effect, respectively. Furthermore, we obtain the slope and curvature of the form factors, and the phase space integral from the momentum transfer dependence of the form factors. Combining our value of f thorn o0 thorn and experimental input of the Ke3 decay, one of the Cabibbo-Kobayashi-Maskawa matrix elements jVusj is determined as jVusj 1/4 0.2252o thorn 5-12 thorn , whose error contains the experimental one as well as that in the lattice calculation. This value is reasonably consistent with the ones determined from recent lattice QCD results of f thorn o0 thorn and also the one determined through the kaon leptonic decay process. We observe some tension between our value and jVusj evaluated from the unitarity of the CKM matrix with jVudj, while it depends on the size of the error of jVudj. It is also found that jVusj determined with our phase space integrals through six Ke3 decay processes is consistent with the above one using f thorn o0 thorn .

Automated summary

This paper presents updated results for the form factors of the kaon semileptonic decay process. The calculations were performed using a nonperturbatively Ooa-improved Wilson quark action and Iwasaki gauge action. The values of the form factors were obtained through extrapolation and interpolation at different lattice spacings. By combining the results with experimental data, one of the Cabibbo-Kobayashi-Maskawa matrix elements jVusj was determined. The obtained value is in reasonable agreement with other lattice QCD results and the one obtained from the kaon leptonic decay process.