Improved analysis of the scalar and vector form factors of kaon semileptonic decays with N_f = 2 twisted-mass fermions

TL;DR

This study uses lattice QCD simulations with twisted-mass fermions to precisely analyze the scalar and vector form factors of kaon semileptonic decays, providing results consistent with experimental data and refining the determination of the Cabibbo angle.

Contribution

First direct continuum limit calculation of the vector form factor at zero momentum transfer using N_f=2 twisted-mass fermions.

Findings

Computed f_+(0) = 0.9544(68), statistical error only.

Determined the ratio f_K / f_π = 1.190(8) at the physical point.

Estimated |V_{us}| from K_{l3} and K_{l2} decays as 0.2266(17) and 0.2258(16).

Abstract

We investigate the vector and scalar form factors relevant for K_{\ell 3} semileptonic decays using maximally twisted-mass fermions with two flavors of dynamical quarks (N_f = 2). The simulations cover pion masses as light as 260 MeV and four values of the lattice spacing, ranging from ~0.05 up to ~0.1 fm, which allow to compute directly, for the first time, the continuum limit for the vector form factor at zero-momentum transfer, f_+(0). The preliminary result is f_+(0) = 0.9544(68), where the error is statistical only. We also extrapolate both form factors to the physical point and study their momentum dependence. Our results are in good agreement with those obtained from a dispersion analyses of the experimental data. Together with the form factors, we analyze the ratio of the leptonic decay constants f_K / f_\pi, by imposing the constraint coming from the Callan-Treiman theorem, obtaining at the physical point f_K / f_\pi = 1.190(8). Combining our results for f_+(0) and f_K / f_\pi with the experimental measurements of the leptonic and semilpetonic decay rates, and using the determination of |V_{ud}| from nuclear beta decays, we determine the values of the Cabibbo angle |V_{us}| from both K_{\ell 3} and K_{\ell 2} decays, obtaining |V_{us}|^{K_{\ell 3}} = 0.2266(17) and $|V_{us}|^{K_{\ell 2}} = 0.2258(16).