D→π,lνsemileptonic decays,|Vcd|and second row unitarity from lattice QCD

We present a new calculation of the D→π, lν semileptonic form factor f+D→π(q2) at q2=0 based on “highly improved staggered quark” charm and light valence quarks on MILC Nf=2+1 lattices. Using methods developed recently for HPQCD’s study of D→K, lν decays, we find f+D→π(0)=0.666(29). This signifies a better than factor 2 improvement in errors for this quantity compared to previous calculations. Combining the new result with CLEO-c branching fraction data, we extract the Cabibbo-Kobayashi-Maskawa matrix element |Vcd|=0.225(6)exp(10)lat, where the first error comes from experiment and the second from theory. With a total error of ∼5.3% the accuracy of the direct determination of |Vcd| 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 |Vcd|, HPQCD’s earlier |Vcs|, and |Vcb| from the Fermilab Lattice and MILC collaborations. We find |Vcd|2+|Vcs|2+|Vcb|2=0.976(50), improving on the current PDG2010 value.