B -> [pi]lv and Bs -> Klv form factors and Vub from 2+1- avor lattice QCD with domain-wall light quarks and relativistic heavy quarks

Abstract

We calculate the form factors for B → πlν   and B_s → Klν decay in dynamical lattice quantum chromodynamics (QCD) using domain-wall light quarks and relativistic b-quarks. We use the (2+1)-flavor gauge-field ensembles generated by the RBC and UKQCD collaborations with the domain-wall fermion action and Iwasaki gauge action. For the b-quarks we use the anisotropic clover action with a relativistic heavy-quark interpretation. We analyze data at two lattice spacings of a ~ 0.11, 0.086 fm with unitary pion masses as light as Mπ ~ 290 MeV. 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 f+(q2) and f₀(q₂) for both B → πlν and B_s → Klν at three momenta that span the q² range accessible in our numerical simulations. Next we extrapolate these results to q²=0 using a model-independent z-parametrization based on analyticity and unitarity. We present our final results for f+(q²) and f₀(q²) as the coefficients of the series in z 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 B → πlν and B_s → Klν decays enable determinations of the Cabibbo-Kobayashi-Maskawa matrix element |V_ub|. To illustrate this, we perform a combined z-fit of our numerical B →  πlν 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 |V_ub| = 3.61(32) × 10^-3, where the error includes statistical and all systematic uncertainties. The same approach can be applied to the decay B_s → Klν to provide an alternative determination of |V_ub| once the process has been measured experimentally. Finally, in anticipation of future experimental measurements, we make predictions for B → πlν and B_s → Klν differential branching fractions and forward-backward asymmetries in the Standard Model.

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ORCID for J.M. Flynn: orcid.org/0000-0002-6280-1677

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