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

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: $f_D=212.5\pm 0.5_{\mathrm{stat}}{}_{-1.5}^{+0.6}{|}_{\mathrm{syst}}$ MeV and $f_{D_s}=248.9\pm 0.2_{\mathrm{stat}}{}_{-1.6}^{+0.5}{|}_{\mathrm{syst}}$ MeV, giving $V_{cd}=0.2184\pm 0.009_{\mathrm{expt}}{}_{-0.0016}^{+0.0008}{|}_{\mathrm{lattice}}$ and $V_{cs}=1.017\pm 0.02_{\mathrm{expt}}{}_{-0.007}^{+0.002}{|}_{\mathrm{lattice}}$. 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.

Comments: To appear in the proceedings of The 6th International Workshop on Charm Physics (CHARM 2013)