CKM matrix elements from K and D decays on the lattice

Abstract

The Standard Model (SM) is the modern theory that best describes the fundamental interactions among particles. So far the SM has allowed physicists to obtain outstanding agreement between experimental data and theoretical predictions. Despite the success in describing fundamental particle physics, we know that the SM is not the final theory of interactions, but just a low-energy approximation of a more general theory. Many of the problems of the Standard Model involve flavor physics, i.e. the branch of physics that studies the transitions between quarks of different flavors. It is thus of crucial importance to determine the fundamental parameters of flavor physics, which in the quark sector are the quark masses and the CKM matrix elements. These quantities, being quarks confined into the hadrons, are non directly measurable in the experiments nor predictable from theory alone. Therefore, a combination of experimental and theoretical inputs is required in order to determine these parameters. The experimental inputs needed to calculate the elements of the CKM matrix are the decay rates of leptonic and semileptonic decays of pseudoscalar mesons. Calculating numerically with lattice QCD (LQCD) the hadronic quantities entering the theoretical expressions for these decay rates and comparing these calculations with the experimental measurements allows us to determine the CKM matrix elements. In this thesis we present an accurate determination of the CKM matrix elements Vus, Vcd and Vcs, through the leptonic and semileptonic decays of K and D mesons. To this purpose we used the gauge configurations produced by the European Twisted Mass (ETM) Collaboration with four flavors of dynamical quarks (Nf = 2 + 1 + 1), which include in the sea, besides the light up and down quarks, assumed to be degenerate, also the strange and the charm quarks with masses close to their physical values. These gauge configurations were generated using the Iwasaki gauge action and the Twisted Mass action at maximal twist. We have extracted the decay constants and the form factors at different values of the quark masses and lattice spacing, allowing us to extrapolate to the physical point through either ChPT or a polynomial expansion. We also studied the 𝑞2 dependence of the form factors, by performing a multi-combined fit of its 𝑎2, 𝑚𝑙 and 𝑞2 dependences. The results for the matrix elements Vus, Vcd and Vcs coming from leptonic and semileptonic decays show a very good agreement, and can be combined with the determinations of Vud and Vcb to perform unitarity tests of the CKM matrix.