# Charm hadrons and lattice QCD

## TL;DR

This paper reviews lattice QCD calculations of charm hadron properties, including semileptonic decay form factors and neutral D mixing matrix elements, using configurations with 2+1+1 flavors and multiple lattice spacings.

## Contribution

It presents new lattice QCD results for charm hadron form factors and mixing matrix elements, improving precision with simulations at various lattice spacings and light pion masses.

## Key findings

- Determined form factors for D→πℓν decays relevant for CKM matrix extraction.
- Calculated matrix elements for D meson mixing within the Standard Model.
- Used gauge configurations with 2+1+1 flavors at multiple lattice spacings.

## Abstract

We review two lattice calculations involving charm hadrons: a determination of the vector and scalar form factors of the semileptonic $D \to \pi \ell \nu$ decays, which are relevant for the extraction of the CKM matrix element $\lvert V_{cd} \rvert$ from experimental data, and a calculation of the matrix elements of four-fermion operators relevant to the description of the neutral D mixing in the Standard Model and its extensions. Both analyses are 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.