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

TLDR: In this article, the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (ISOQCD) was determined by using the gauge ensembles produced by the Extended Twisted Mass Collaboration with the Wilson-clover twisted-mass quarks.

Abstract: We present a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (ISOQCD), ${f}_{K}/{f}_{\ensuremath{\pi}}$, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration with ${N}_{f}=2+1+1$ 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 $\ensuremath{\sim}0.068$ to $\ensuremath{\sim}0.092\text{ }\text{ }\mathrm{fm}$ with linear lattice size up to $L\ensuremath{\sim}5.5\text{ }\text{ }\mathrm{fm}$. The scale is set by the particle data group (PDG) value of the pion decay constant, ${f}_{\ensuremath{\pi}}^{\text{ISO}\mathrm{QCD}}=130.4(2)\text{ }\text{ }\mathrm{MeV}$, at the ISOQCD pion point, ${M}_{\ensuremath{\pi}}^{\text{ISO}\mathrm{QCD}}=135.0(2)\text{ }\text{ }\mathrm{MeV}$, obtaining for the gradient-flow scales the values ${w}_{0}=0.17383(63)\text{ }\text{ }\mathrm{fm}$, $\sqrt{{t}_{0}}=0.14436(61)\text{ }\text{ }\mathrm{fm}$ and ${t}_{0}/{w}_{0}=\phantom{\rule{0ex}{0ex}}0.11969(62)\text{ }\text{ }\mathrm{fm}$. 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 ${M}_{K}^{\text{ISO}\mathrm{QCD}}=494.2(4)\text{ }\text{ }\mathrm{MeV}$ we get $({f}_{K}/{f}_{\ensuremath{\pi}}{)}^{\text{ISO}\mathrm{QCD}}=1.1995(44)$, where the error includes both statistical and systematic uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{us}|$ and for the first-row Cabibbo-Kobayashi-Maskawa unitarity are discussed.