Tensor form factor for the D → π(K) transitions with Twisted Mass fermions.

Vittorio Lubicz,Silvano Simula,Giorgio Salerno,Cecilia Tarantino,Lorenzo Riggio

doi:10.1051/epjconf/201817513022

Abstract

We present a preliminary lattice calculation of the D → π and D → K tensor form factors fT (q2) as a function of the squared 4-momentum transfer q2. ETMC recently computed the vector and scalar form factors f+(q2) and f0(q2) describing D → π(K)lv semileptonic decays analyzing the vector current and the scalar density. The study of the weak tensor current, which is directly related to the tensor form factor, completes the set of hadronic matrix element regulating the transition between these two pseudoscalar mesons within and beyond the Standard Model where a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV and with the valence heavy quark in the mass range from ≃ 0.7 mc to ≃ 1.2mc. The matrix element of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As for the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data. We will present preliminary results on the removal of such hypercubic lattice effects.

Highlights

Introduction and simulation detailsPrecise measurements of hadron weak decays can constrain the Standard Model (SM) and place bounds on New Physics (NP) models
In Ref. [1], we presented the first N f = 2 + 1 + 1 lattice QCD (LQCD) calculation of the vector and scalar form factors f+D→π(K)(q2) and f0D→π(K)(q2) governing the semileptonic D → π(K) ν decays, using the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with N f = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light massdegenerate quarks, the strange and charm quarks with masses close to their physical values [2, 3]
In our calculations quark momenta are injected on the lattice using non-periodic boundary conditions [4, 5] and the matrix elements of the tensor current are determined for many kinematical conditions, in which parent and child mesons are either moving or at rest

Summary

Introduction and simulation details

Precise measurements of hadron weak decays can constrain the Standard Model (SM) and place bounds on New Physics (NP) models. The data exhibit a remarkable breaking of Lorentz symmetry due to hypercubic effects for both D → π and D → K form factors The presence of these effects has already been observed in Ref. Previous lattice calculations used only a limited number of kinematical conditions (typically the D-meson at rest) We argue that this may obscure the presence of hypercubic effects in the lattice data. In [1] the subtraction of the observed hypercubic effects was achieved by considering a more general decomposition of the matrix element, which contains, beside the usual Lorentz-covariant part, additional hypercubic form factors proportional to a2. To further validate the method, to apply it in the case of the tensor current In this contribution we present the subtraction of hypercubic artefacts and the determination of the tensor D → π(K) form factors.

Lattice calculation of the tensor matrix elements and hypercubic effects

Global fit