Improved <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math> determination using precise lattice QCD form factors for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>K</mml:mi><mml:mo>ℓ</mml:mo><mml:mi>ν</mml:mi></mml:math>
Bipasha Chakraborty, W. G. Parrott, Chris Bouchard, C. T. H. Davies, J. Koponen, G. Peter Lepage
Abstract
We provide a 0.8%-accurate determination of V cs from combining experimental results for the differential rate of D K semileptonic decays with precise form factors that we determine from lattice QCD. This is the first time that V cs has been determined with an accuracy that allows its difference from 1 to be seen. Our lattice QCD calculation uses the highly improved staggered quark (HISQ) action for all valence quarks on gluon field configurations generated by the MILC Collaboration that include the effect of u, d, s, and c HISQ quarks in the sea. We use eight gluon field ensembles with five values of the lattice spacing ranging from 0.15 fm to 0.045 fm and include results with physical u=d quarks for the first time. Our calculated form factors cover the full q 2 range of the physical decay process and enable a Standard Model test of the shape of the differential decay rate as well as the determination of V cs from a correlated weighted average over q 2 bins. We obtain jV cs j 0.966353 latt 39 exp 19 EW 40 EM , where the uncertainties come from lattice QCD, experiment, short-distance electroweak, and electromagnetic corrections, respectively. This last uncertainty, neglected for D Kl hitherto, now needs attention if the uncertainty on V cs is to be reduced further. We also determine V cs values in good agreement using the measured total branching fraction and the rates extrapolated to q 2 0. Our form factors enable tests of lepton flavor universality violation. We find the ratio of branching fractions for D 0 K -with and e in the final state to be R =e 0.97792 latt 50 EM in the Standard Model, with the uncertainty dominated by that from electromagnetic corrections.