K → π 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 semileptonic K -> pi l upsilon decay which are relevant for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element vertical bar V-us vertical bar from experimental data. Our results are based on the gauge configurations produced by the European Twisted Mass Collaboration with N-f = 2 + 1 + 1 dynamical fermions, which include in the sea, besides two light mass degenerate quarks, also the strange and the charm quarks. We use data simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV. Our final result for the vector form factor at zero momentum transfer is f(+)(0) = 0.9709(46), where the uncertainty is both statistical and systematic combined in quadrature. Using the latest experimental value of f+(0)vertical bar V-us vertical bar from K-l3 decays, we obtain vertical bar V-us vertical bar = 0.2230(11), which allows us to test the unitarity constraint of the Standard Model below the permille level once the determination of vertical bar V-ud vertical bar from super allowed nuclear beta decays is adopted. A slight tension with unitarity at the level of similar to 2 standard deviations is observed. Moreover, we present our results for the semileptonic scalar f(0)(q(2)) and vector f(+)(q(2)) form factors in the whole range of values of the squared four-momentum transfer q(2) measured in K-l3 decays, obtaining a very good agreement with the momentum dependence of the experimental data. We provide a set of synthetic data points representing our results for the vector and scalar form factors at the physical point for several selected values of q(2).