Abstract
We calculate the form factors for and decay in dynamical lattice quantum chromodynamics (QCD) using domain-wall light quarks and relativistic -quarks. We use the ()-flavor gauge-field ensembles generated by the RBC and UKQCD collaborations with the domain-wall fermion action and Iwasaki gauge action. For the -quarks we use the anisotropic clover action with a relativistic heavy-quark interpretation. We analyze data at two lattice spacings of , 0.086 fm with unitary pion masses as light as . We simultaneously extrapolate our numerical results to the physical light-quark masses and to the continuum and interpolate in the pion/kaon energy using SU(2) “hard-pion” chiral perturbation theory for heavy-light meson form factors. We provide complete systematic error budgets for the vector and scalar form factors and for both and at three momenta that span the range accessible in our numerical simulations. Next we extrapolate these results to using a model-independent -parametrization based on analyticity and unitarity. We present our final results for and as the coefficients of the series in and the matrix of correlations between them; this provides a parametrization of the form factors valid over the entire allowed kinematic range. Our results agree with other three-flavor lattice-QCD determinations using staggered light quarks, and have comparable precision, thereby providing important independent cross-checks. Both and decays enable determinations of the Cabibbo-Kobayashi-Maskawa matrix element . To illustrate this, we perform a combined -fit of our numerical form-factor data with the experimental measurements of the branching fraction from BABAR and Belle leaving the relative normalization as a free parameter; we obtain , where the error includes statistical and all systematic uncertainties. The same approach can be applied to the decay to provide an alternative determination of once the process has been measured experimentally. Finally, in anticipation of future experimental measurements, we make predictions for and differential branching fractions and forward-backward asymmetries in the Standard Model.
16 More- Received 9 February 2015
DOI:https://doi.org/10.1103/PhysRevD.91.074510
© 2015 American Physical Society