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

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