D-meson semileptonic decays to pseudoscalars from four-flavor lattice QCD

We present lattice-QCD calculations of the hadronic form factors for the semileptonic decays D → π`ν, D → K`ν, and Ds → K`ν. Our calculation uses the highly improved staggered quark (HISQ) action for all valence and sea quarks and includesNf = 2+1+1 MILC ensembles with lattice spacings ranging from a ≈ 0.12 fm down to 0.042 fm. At most lattice spacings, an ensemble with physical-mass light quarks is included. The HISQ action allows all the quarks to be treated with the same relativistic light-quark action, allowing for nonperturbative renormalization using partial conservation of the vector current. We combine our results with experimental measurements of the differential decay rates to determine |Vcd| = 0.2238(11)Expt(15)QCD(04)EW(02)SIB[22]QED and |Vcs| = 0.9589(23)Expt(40)QCD(15)EW(05)SIB[95]QED. This result for |Vcd| is the most precise to date, with a lattice-QCD error that is, for the first time for the semileptonic extraction, at the same level as the experimental error. Using recent measurements from BES III, we also give the first-ever determination of |Vcd|s = 0.258(15)Expt(01)QCD[03]QED from Ds → Klν. Our results also furnish new Standard Model calculations of the lepton flavor universality ratios RD→π μ/e = 0.98671(17) QCD[500]QED, RD→K μ/e = 0.97606(16) QCD[500]QED, and RDs→K μ/e = 0.98099(10) QCD[500]QED, which are consistent within 2σ with experimental measurements. Our extractions of |Vcd| and |Vcs|, when combined with a value for |Vcb|, provide the most precise test of second-row CKM unitarity, finding agreement with unitarity at the level of one standard deviation.