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

Abstract

We present a new calculation of the $D \rightarrow \pi, l \nu$ semileptonic form factor $f^{D \rightarrow \pi}_+(q^2)$ 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 $D \rightarrow K, l \nu$ decays, we find $f^{D \rightarrow \pi}_+(0) = 0.666(29)$. 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 $\sim5.3$\% 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.