Ratio of kaon and pion leptonic decay constants with Nf=2+1+1 Wilson-clover twisted-mass fermions

We present a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (ISOQCD), fK/fπ, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration with Nf=2+1+1 flavors of Wilson-clover twisted-mass quarks, including configurations close to the physical point for all dynamical flavors. The simulations are carried out at three values of the lattice spacing ranging from ∼0.068 to ∼0.092  fm with linear lattice size up to L∼5.5  fm. The scale is set by the particle data group (PDG) value of the pion decay constant, fISOQCDπ=130.4(2)  MeV, at the ISOQCD pion point, MISOQCDπ=135.0(2)  MeV, obtaining for the gradient-flow scales the values w0=0.17383(63)  fm, √t0=0.14436(61)  fm and t0/w0=0.11969(62)  fm. The data are analyzed within the framework of SU(2) chiral perturbation theory without resorting to the use of renormalized quark masses. At the ISOQCD kaon point MISOQCDK=494.2(4)  MeV we get (fK/fπ)ISOQCD=1.1995(44), where the error includes both statistical and systematic uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa matrix element |Vus| and for the first-row Cabibbo-Kobayashi-Maskawa unitarity are discussed.