$D\to\pi$ and $D\to K$ semileptonic form factors with $N_f=2+1+1$ twisted mass fermions

TL;DR

This paper presents a lattice QCD calculation of $D o\pi$ and $D o K$ semileptonic form factors using $N_f=2+1+1$ twisted mass fermions, providing results that agree well with experimental data across most of the kinematic range.

Contribution

It provides the first comprehensive lattice determination of these form factors with $N_f=2+1+1$ dynamical quarks, including hypercubic effects and multiple lattice spacings.

Findings

Form factors determined across the full kinematic range from $q^2=0$ to $q^2_{max}$.

Good agreement with experimental data except at high $q^2$ values.

Hypercuic effects are significant and included in the analysis.

Abstract

We present a lattice determination of the vector and scalar form factors of the $D\to\pi(K)\ell\nu$ semileptonic decays, which are relevant for the extraction of the CKM matrix elements $|V_{cd}|$ and $|V_{cs}|$ from experimental data. 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. The matrix elements of both vector and scalar currents are determined for a plenty of kinematical conditions in which parent and child mesons are either moving or at rest. Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum limit the vector and scalar form factors are determined in the whole kinematical region from $q^2 = 0$ up to $q^2_{\rm max} = (M_D - M_{\pi(K)})^2$ accessible in the experiments, obtaining a good overall agreement with experiments, except in the region at high values of $q^2$ where some deviations are visible.