# $D$ meson Semileptonic Decay Form Factors at $q^2 = 0$

## TL;DR

This paper presents preliminary lattice QCD calculations of $D$ meson semileptonic decay form factors at zero momentum transfer, improving precision and analyzing implications for CKM matrix unitarity.

## Contribution

It provides the first high-precision lattice QCD determination of $f_+^{\pi,K}(0)$ at multiple lattice spacings and quark masses, using advanced chiral perturbation theory and effective theory extrapolations.

## Key findings

- Improved precision in $f_+^{\pi,K}(0)$ form factors.
- Determined CKM matrix elements $|V_{cs}|$ and $|V_{cd}|$.
- Discussed implications for CKM unitarity.

## Abstract

We discuss preliminary results for the vector form factors $f_+^{\{\pi,K\}}$ at zero-momentum transfer for the decays $D\to\pi\ell\nu$ and $D\to K \ell\nu$ using MILC's $N_f = 2+1+1$ HISQ ensembles at four lattice spacings, $a \approx 0.042, 0.06, 0.09$, and 0.12 fm, and various HISQ quark masses down to the (degenerate) physical light quark mass. We use the kinematic constraint $f_+(q^2)= f_0(q^2)$ at $q^2 = 0$ to determine the vector form factor from our study of the scalar current, which yields $f_0(0)$. Results are extrapolated to the continuum physical point in the framework of hard pion/kaon SU(3) heavy-meson-staggered $\chi$PT and Symanzik effective theory. Our calculation improves upon the precision achieved in existing lattice-QCD calculations of the vector form factors at $q^2=0$. We show the values of the CKM matrix elements $|V_{cs}|$ and $|V_{cd}|$ that we would obtain using our preliminary results for the form factors together with recent experimental results, and discuss the implications of these values for the second row CKM unitarity.