Update of kaon semileptonic form factor using $N_f=2+1$ PACS10 configurations

TL;DR

This paper updates the calculation of kaon semileptonic form factors using large-volume lattice QCD configurations close to physical quark masses, improving precision in determining the CKM matrix element |V_{us}|.

Contribution

It provides new lattice QCD results for kaon semileptonic form factors with reduced systematic errors, utilizing extensive configurations near the physical point.

Findings

Form factors are computed with controlled continuum extrapolation.

The value of |V_{us}| is extracted and compared with previous results.

Systematic errors at zero momentum transfer are estimated.

Abstract

We calculate the form factors for the kaon semileptonic decay process using the PACS10 configurations, whose physical volume is more than (10 fm)$^4$ very close to the physical point. The configurations were generated with the Iwasaki gauge action and $N_f=2+1$ stout-smeared nonperturbatively $O(a)$-improved Wilson quark action at the three lattice spacings, 0.085, 0.063, and 0.041 fm. We present updated results for the form factors, and discuss their continuum extrapolations, momentum transfer interpolation, and short chiral extrapolation to tune the simulated pion and kaon masses to the physical ones. From the results with various analyses, the systematic error of the form factor at the zero momentum transfer is estimated. The value of $|V_{us}|$ is determined using our result, and is compared with those using the previous calculations and also those determined through the kaon leptonic decay process.