$D\to \pi ,l\nu$ Semileptonic Decays, $|V_{cd}|$ and 2${}^{nd}$ Row Unitarity from Lattice QCD

Abstract

We present a new calculation of the $D\to \pi ,l\nu$ semileptonic form factor $f_{+}^{D\to \pi }(q^2)$ at $q^2=0$ based on HISQ charm and light valence quarks on MILC $N_f=2+1$ lattices. Using methods developed recently for HPQCD's study of $D\to K,l\nu$ decays, we find $f_{+}^{D\to \pi }(0)=0.666(29)$. This signifies a better than factor of two improvement in errors for this quantity compared to previous calculations. Combining the new result with CLEO-c branching fraction data, we extract the CKM matrix element $|V_{cd}|=0.225(6{)}_{exp.}(10{)}_{lat.}$, where the first error comes from experiment and the second from theory. With a total error of $\sim 5.3$\% the accuracy of direct determination of $|V_{cd}|$ from $D$ semileptonic decays has become comparable to (and in good agreement with) that from neutrino scattering. We also check for second row unitarity using this new $|V_{cd}|$, HPQCD's earlier $|V_{cs}|$ and $|V_{cb}|$ from the Fermilab Lattice \& MILC collaborations. We find $|V_{cd}{|}^2+|V_{cs}{|}^2+|V_{cb}{|}^2=0.976(50)$, improving on the current PDG2010 value.

Comments: 7 pages, 7 figures, and 4 tables