Lattice results for $D/D_s$ leptonic and semileptonic decays

TL;DR

This review summarizes recent lattice QCD calculations of $D$ and $D_s$ meson decay constants and form factors, providing precise CKM matrix element extractions and confirming the agreement between lattice results and experimental data.

Contribution

It compiles and compares the latest lattice QCD results for $D$ and $D_s$ meson decays, highlighting improved precision and insights into form factor insensitivity.

Findings

Decay constants $f_D$ and $f_{D_s}$ are precisely determined.

Semileptonic form factors agree well with experimental data.

CKM elements $V_{cd}$ and $V_{cs}$ are extracted with high accuracy.

Abstract

This review article summarizes recent lattice QCD results for $D$ and $D_s$ meson leptonic and semileptonic decays. Knowing the meson decay constants and semileptonic form factors from theory, one can extract CKM elements $V_{cd}$ and $V_{cs}$ from experimental results. At present, the most accurate results for decay constants are from the Fermilab Lattice and MILC Collaborations: $f_D = 212.5 \pm 0.5_{\mathrm{stat}} {}^{+0.6}_{-1.5} |_{\mathrm{syst}}$ MeV and $f_{D_s} = 248.9 \pm 0.2_{\mathrm{stat}} {}^{+0.5}_{-1.6}|_{\mathrm{syst}}$ MeV, giving $V_{cd} = 0.2184 \pm 0.009_{\mathrm{expt}} {}^{+0.0008}_{-0.0016} |_{\mathrm{lattice}}$ and $V_{cs} = 1.017 \pm 0.02_{\mathrm{expt}} {}^{+0.002}_{-0.007} |_{\mathrm{lattice}}$. The shapes of the semileptonic form factors from lattice QCD agree very well with experiment, and the accuracy is currently at the 2-5% level for $D \to \pi\ell\nu$ and 1-2% for $D \to K\ell\nu$. Extracting the CKM elements from the semileptonic decays yields $V_{cd} = 0.225(6)_{\mathrm{expt}}(10)_{\mathrm{lattice}}$ (HPQCD Collaboration) and $V_{cs} = 0.963(5)_{\mathrm{expt}}(14)_{\mathrm{lattice}}$ (HPQCD Collaboration). These lattice calculations also revealed that the semileptonic form factors are insensitive to whether the spectator quark is a light or strange quark.