Kaon semileptonic vector form factor with $N_f=2+1+1$ Twisted Mass fermions

TL;DR

This study calculates the kaon semileptonic vector form factor using advanced lattice QCD simulations with 4 dynamical flavors, providing a precise value that supports Standard Model unitarity.

Contribution

First lattice QCD determination of the $K_{l3}$ vector form factor with $N_f=2+1+1$ twisted-mass fermions at multiple pion masses and fine lattice spacings.

Findings

Obtained $f_+(0)=0.9683(65)$ with combined statistical and systematic errors.

Derived $|V_{us}|=0.2234(16)$ consistent with Standard Model unitarity.

Validated the effectiveness of twisted-mass fermions in precise form factor calculations.

Abstract

We investigate the vector form factor relevant for the $K_{\ell 3}$ semileptonic decay using maximally twisted-mass fermions with 4 dynamical flavours ($N_f=2+1+1$). Our simulations feature pion masses ranging from $210$ MeV to approximately $450$ MeV and lattice spacing values as small as $0.06$fm. Our main result for the vector form factor at zero 4-momentum transfer is $f_+(0)=0.9683(65)$ where the uncertainty is both statistical and systematic. By combining our result with the experimental value of $f_+(0)|V_{us}|$ we obtain $|V_{us}|=0.2234(16)$, which satisfies the unitarity constraint of the Standard Model at the permille level.