Momentum dependence of kaon semileptonic form factors with Nf=2+1+1 Twisted Mass fermions

We present a lattice QCD determination of the vector and scalar form factors of the kaon semileptonic decay $K \to \pi \ell \nu$, which is relevant for the determination of the CKM matrix element $|V_{us}|$ from experimental data. Our results are based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2+1+1 dynamical fermions. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV. Our estimate for the vector form factor at zero 4-momentum transfer is $f_+(0) = 0.9709 (46)$, where the uncertainty is both statistical and systematic. By combining our result with the latest experimental value of $f_+(0)|V_{us}|$ we obtain $|V_{us}| = 0.2230 (11)$, which satisfies the unitarity constraint of the Standard Model at the permille level using the updated determination of $|V_{ud}|$ coming from superallowed nuclear $\beta$ decays. We present also the momentum dependence of the vector and scalar form factors in the whole range of values of the squared 4-momentum transfer measured in $K_{\ell 3}$ decays, obtaining a good agreement with the experimental data.