$B \to \pi \ell \nu$ 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

Flynn, J. M.; Izubuchi, T.; Kawanai, T.; Lehner, C.; Soni, A.; Van de Water, R. S.; Witzel, O.

doi:10.1103/PhysRevD.91.074510

Title: $$B \to \pi \ell \nu$$ 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

Journal Article · Tue Apr 14 00:00:00 EDT 2015 · Physical Review. D, Particles, Fields, Gravitation and Cosmology

DOI:https://doi.org/10.1103/PhysRevD.91.074510· OSTI ID:1221234

Flynn, J. M. ^[1]; Izubuchi, T. ^[2]; Kawanai, T. ^[2]; Lehner, C. ^[2]; Soni, A. ^[2]; Van de Water, R. S. ^[3]; Witzel, O. ^[4]

Univ. of Southampton, Southampton (United Kingdom)
Brookhaven National Lab. (BNL), Upton, NY (United States)
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Boston Univ., Boston, MA (United States)

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 M_π ≈ 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|. Furthermore, 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. 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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Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Contributing Organization:: RBC Collaboration; UKQCD Collaboration

Grant/Contract Number:: AC02-07CH11359

OSTI ID:: 1221234

Alternate ID(s):: OSTI ID: 1180799

Report Number(s):: FERMILAB-PUB-15-019-T; arXiv eprint number arXiv:1501.05373; TRN: US1600873

Journal Information:: Physical Review. D, Particles, Fields, Gravitation and Cosmology, Vol. 91, Issue 7; ISSN 1550-7998

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 100 works

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Title: $$B \to \pi \ell \nu$$ 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

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