Tensor form factor for the $D \to \pi(K)$ transitions with Twisted Mass fermions

TL;DR

This paper reports a preliminary lattice QCD calculation of the tensor form factors for $D o \pi$ and $D o K$ transitions, expanding the understanding of these processes beyond the Standard Model.

Contribution

It provides the first lattice computation of the $D o \pi(K)$ tensor form factors using twisted mass fermions, including analysis of hypercubic effects and multiple kinematic conditions.

Findings

Tensor form factors computed for various $q^2$ values.

Observation of Lorentz symmetry breaking due to hypercubic effects.

Preliminary results on hypercubic effect removal.

Abstract

We present a preliminary lattice calculation of the $D \to \pi$ and $D \to K$ tensor form factors $f_T(q^2)$ as a function of the squared 4-momentum transfer $q^2$. ETMC recently computed the vector and scalar form factors $f_+(q^2)$ and $f_0(q^2)$ describing $D \to \pi(K) \ell \nu$ 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 $N_f = 2 + 1 + 1$ 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 $\simeq 0.7\, m_c$ to $\simeq 1.2\, m_c$. 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.