$B\to \pi \ell \nu$ and $B_s\to K\ell \nu$ form factors and $|V_{ub}|$ from 2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks

Abstract

We calculate the $B\to \pi \ell \nu$ and $B_s\to K\ell \nu$ form factors in dynamical lattice QCD. We use the (2+1)-flavor RBC-UKQCD gauge-field ensembles generated with the domain-wall fermion and Iwasaki gauge actions. For the $b$ quarks we use the anisotropic clover action with a relativistic heavy-quark interpretation. We analyze two lattice spacings $a\approx 0.11,0.086$ fm and unitary pion masses as light as $M_{\pi }\approx 290$ 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. We provide complete error budgets for the form factors $f_{+}(q^2)$ and $f_0(q^2)$ at three momenta that span the $q^2$ range accessible in our numerical simulations. We extrapolate these results to $q^2=0$ using a model-independent $z$-parametrization and present our final form factors as the $z$-coefficients and the matrix of correlations between them. Our results agree with other lattice determinations using staggered light quarks and provide important independent cross-checks. Both $B\to \pi \ell \nu$ and $B_s\to K\ell \nu$ decays enable a determination of the CKM matrix element $|V_{ub}|$. To illustrate this, we perform a combined $z$-fit of our numerical $B\to \pi \ell \nu$ form-factor data with the experimental branching-fraction measurements leaving the relative normalization as a free parameter; we obtain $|V_{ub}|=3.61(32)\times 10^{-3}$, where the error includes statistical and systematic uncertainties. This approach can be applied to $B_s\to K\ell \nu$ decay to determine $|V_{ub}|$ once the process has been measured experimentally. Finally, in anticipation of future measurements, we make predictions for $B\to \pi \ell \nu$ and $B_s\to K\ell \nu$ Standard-Model differential branching fractions and forward-backward asymmetries.

arXiv commentV3: References and discussions added. Large tables move to appendix. 39 pages, 22 tables, 23 figures. Version published in Physical Review D

References in corpus (59)

• On the Viability of Lattice Perturbation Theory
• Evidence for an excess of B -> D(*) Tau Nu decays
• The Chroma Software System for Lattice QCD
• Chiral Fermions from Lattice Boundaries
• New Results on B->pi, K, eta Decay Formfactors from Light-Cone Sum Rules
• Axial symmetries in lattice QCD with Kaplan fermions
• Improved Nonrelativistic QCD for Heavy Quark Physics
• Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil
• Chiral Multiplets of Heavy-Light Mesons
• Massive Fermions in Lattice Gauge Theory
• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• The QCD spectrum with three quark flavors
• Model-independent description of $B\to \pi l\nu$ decays and a determination of $|V_{ub}|$
• Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory
• High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Constraints on Form Factors For Exclusive Semileptonic Heavy to Light Meson Decays
• Constrained Curve Fitting
• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• Flavor Physics in the Quark Sector
• Comment on the heavy-->light form factors
• A new class of variance reduction techniques using lattice symmetries
• Lattice QCD inputs to the CKM unitarity triangle analysis
• B Meson Semileptonic Form Factors from Unquenched Lattice QCD
• Comment on form factor shape and extraction of |V_ub| from B --> pi l nu
• Study of B --> pi l nu and B --> rho l nu Decays and Determination of |V_ub|
• Study of Exclusive B->X_u l nu Decays and Extraction of |V_{ub}| using Full Reconstruction Tagging at the Belle Experiment
• The B -> pi l nu semileptonic form factor from three-flavor lattice QCD: A model-independent determination of |V(ub)|
• A Precision Model Independent Determination of |Vub| from B -> pi e nu
• Measurement of the decay $B^0\to {\pi }^{-}{\ell }^{+}\nu$ and determination of $|V_{ub}|$
• Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays
• Next-to-leading-order corrections to $B\to \pi$ form factors in $k_T$ factorization
• Branching fraction and form-factor shape measurements of exclusive charmless semileptonic B decays, and determination of |V_{ub}|
• Lattice-Constrained Unitarity Bounds for ${\bar{B}}^0\to {\pi }^{+}{l}^{-}{\bar{\nu }}_l$ Decays
• The semileptonic decays $B/B_s\to (\pi ,K)(l^{+}{l}^{-},l\nu ,\nu \bar{\nu })$ in the perturbative QCD approach beyond the leading-order
• The Semileptonic Decays $B\to \pi l\nu$ and $D\to \pi l\nu$ from Lattice QCD
• Determination of alpha_s from the QCD static energy
• $B_s\to K\ell \nu$ form factors from lattice QCD
• Relativistic Heavy Quark Effective Action
• Analyticity, Shapes of Semileptonic Form Factors, and B to pi l nu
• Precise B, B_s and B_c meson spectroscopy from full lattice QCD
• Mobius Fermions: Improved Domain Wall Chiral Fermions
• Heavy meson chiral perturbation theory in finite volume
• Precise determination of the strong coupling constant in Nf=2+1 lattice QCD with the Schrödinger functional scheme
• B, Bs -> K form factors: an update of light-cone sum rule results
• Two-loop Corrections to the B to pi Form Factor from QCD Sum Rules on the Light-Cone and |V(ub)|
• The Realistic Lattice Determination of alpha_s(M_Z) Revisited
• Application of heavy-quark effective theory to lattice QCD: II. Radiative corrections to heavy-light currents
• Extrapolation and unitarity bounds for the $B\to \pi$ form factor
• Nonperturbative tuning of an improved relativistic heavy-quark action with application to bottom spectroscopy
• B-meson decay constants from 2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks
• Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory
• High statistics determination of the strong coupling constant in Taylor scheme and its OPE Wilson coefficient from lattice QCD with a dynamical charm
• ${\mathbf{B}}_{\mathbf{s}}\to {\mathbf{K}}^{(\ast )}\mathbf{\ell }\bar{\nu }$, Angular Analysis, S-wave Contributions and $|{\mathbf{V}}_{\mathbf{ub}}|$
• Perturbative renormalization factors in domain-wall QCD with improved gauge actions
• Hard Pion Chiral Perturbation Theory for $B\to \pi$ and $D\to \pi$ Formfactors
• Charmless weak $B_s$ decays in the relativistic quark model
• SU(2) chiral perturbation theory for Kl3 decay amplitudes
• B-->pi and B-->K transitions in standard and quenched chiral perturbation theory
• The D234 action for light quarks

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