|V_cd| from D Meson Leptonic Decays

TL;DR

This paper updates the calculation of the D meson decay constant using improved lattice QCD methods, and extracts the CKM matrix element |V_cd| with high precision, confirming consistency with other measurements.

Contribution

The study provides a more precise determination of f_D and |V_cd| using improved lattice techniques and new experimental data, enhancing the accuracy of CKM matrix element extraction.

Findings

f_D = 208.3(3.4) MeV

|V_cd| = 0.223(10)_{exp.}(4)_{lat.}

ratio [f^{D -> \pi}_+(0) / f_D ]_{lat.} = 3.20(15) GeV^{-1}

Abstract

We present an update of the D meson decay constant f_D using the Highly Improved Staggered Quark (HISQ) action for valence charm and light quarks on MILC N_f = 2+1 lattices. The new determination incorporates HPQCD's improved scale r_1^{N_f = 2+1} = 0.3133(23) fm, accurately retuned bare charm quark masses and data from an ensemble that is more chiral than in our previous calculations. We find f_D = 208.3(3.4) MeV. Combining the new f_D with D -> \mu \nu\ branching fraction data from CLEO-c, we extract the CKM matrix element |V_cd| = 0.223(10)_{exp.}(4)_{lat.}. This value is in excellent agreement with |V_cd| from D semileptonic decays and from neutrino scattering experiments and has comparable total errors. We determine the ratio between semileptonic form factor and decay constant and find [f^{D -> \pi}_+(0) / f_D ]_{lat.} = 3.20(15) GeV^{-1} to be compared with the experimental value of [f^{D -> \pi}_+(0) / f_D ]_{exp.} = 3.19(18) GeV^{-1}. Finally, we mention recent preliminary but already more accurate D -> \mu \nu\ branching fraction measurements from BES III and discuss their impact on precision |V_cd| determinations in the future.