Form factors of the D to pik ell nu semileptonic decays and determination of the CKM matrix elements |Vcd| and |Vcs| with Nf=2+1+1 twisted mass Lattice QCD

Abstract

In this thesis we present the first Nf = 2+1+1 LQCD calculation of the vector and scalar form factors f Dπ(K) + (q 2 ) and f Dπ(K) 0 (q 2 ) governing the semileptonic D → π(K)`ν decays, using the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with Nf = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass-degenerate quarks, also the strange and the charm quarks with masses close to their physical values. At variance with most of the existing LQCD calculations, which provide only the value of the vector form factor at zero 4-momentum transfer, we have evaluated both the vector and scalar form factors in the whole experimentally accessible range in q 2 , i.e. from q 2 = 0 up to q 2 max = (MD − Mπ(K)) 2 . An overall agreement with the momentum dependence of the experimental data from BELLE, BABAR, CLEO and BESIII has been found, although some deviations have been observed at high values of q 2 . The knowledge of the form factors in the full kinematical range allowed us to perform the first determination of the CKM matrix elements |Vcd| and |Vcs| in a truly consistent way within the SM. We show that a more precise and consistent determination of |Vcd| and |Vcs|, compared to those based only on the vector form factor at q 2 = 0, can be obtained.