Study of Kaon semileptonic decays on the lattice using twisted-mass fermions and stochastic techiniques for the light-meson propagators

Abstract

The first chapter will start introducing some basic notions about flavour physics. We will recall the basis of the Standard Model paying a particular attention to the CKM flavour mixing matrix. We will illustrate some of its related theoretical features and the (phenomenological) determination of its matrix elements. We will then move to leptonic and semileptonic kaon decays, introducing the semileptonic form factors, which are the subject of the present work, ending the chapter introducing weak and strong CP violation, with the latter which is responsible of the neutron electric dipole dipole moment generation. The second chapter will be dedicated to the introduction of the calculation technique employed in this work: lattice QCD. After a general introduction we will present the Twisted Mass action used by the ETMC and we will also discuss a particular choice for the boundary conditions used in our lattice simulations, the so–called twisted boundary condition. Chapter three will explain in details the methods which we will employ in our anal- ysis of the form factors as well as the stochastic techniques which are good candidates to be used in a future calculation of the neutron EDM. In chapter four we will present the results of this work. We will start introduc- ing some basic information about the ETMC simulation which we have analyzed and then we will discuss statistical and systematic error analysis, present our form factor’s analysis strategy and give our final physical results followed by a final discussion of the present status of our stochastic techniques.