# $$B \to \pi \ell \nu$$ 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 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 + (q ^{2}) and f _{0}(q ^{2}) for both B → πℓν and B _{s} → Kℓν at three momenta that span the q ^{2} range accessible in our numerical simulations. Next we extrapolate these results to q ^{2} = 0 using a model-independent z-parametrization based on analyticity and unitarity. We present our final results for f _{+}(q ^{2}) and f _{0}(q ^{2})as the coefficientsmore »

- Authors:

- 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)

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- Contributing Org.:
- RBC Collaboration; UKQCD Collaboration

- OSTI Identifier:
- 1221234

- Alternate Identifier(s):
- OSTI ID: 1180799

- Report Number(s):
- FERMILAB-PUB-15-019-T

Journal ID: ISSN 1550-7998; arXiv eprint number arXiv:1501.05373; TRN: US1600873

- Grant/Contract Number:
- AC02-07CH11359

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review. D, Particles, Fields, Gravitation and Cosmology

- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 7; Journal ID: ISSN 1550-7998

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Flynn, J. M., Izubuchi, T., Kawanai, T., Lehner, C., Soni, A., Van de Water, R. S., and Witzel, O.
```*$B \to \pi \ell \nu$ 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*. United States: N. p., 2015.
Web. doi:10.1103/PhysRevD.91.074510.

```
Flynn, J. M., Izubuchi, T., Kawanai, T., Lehner, C., Soni, A., Van de Water, R. S., & Witzel, O.
```*$B \to \pi \ell \nu$ 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*. United States. doi:10.1103/PhysRevD.91.074510.

```
Flynn, J. M., Izubuchi, T., Kawanai, T., Lehner, C., Soni, A., Van de Water, R. S., and Witzel, O. Tue .
"$B \to \pi \ell \nu$ 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". United States. doi:10.1103/PhysRevD.91.074510. https://www.osti.gov/servlets/purl/1221234.
```

```
@article{osti_1221234,
```

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},

author = {Flynn, J. M. and Izubuchi, T. and Kawanai, T. and Lehner, C. and Soni, A. and Van de Water, R. S. and Witzel, O.},

abstractNote = {We calculate the form factors for B → πℓν and Bs → 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 Bs → 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 Bs → Kℓν decays enable determinations of the Cabibbo-Kobayashi-Maskawa matrix element |Vub|. 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 |Vub| = 3.61(32)×10-3, where the error includes statistical and all systematic uncertainties. The same approach can be applied to the decay Bs → Kℓν to provide an alternative determination of |Vub| once the process has been measured experimentally. In anticipation of future experimental measurements, we make predictions for B → πℓν and Bs → Kℓν differential branching fractions and forward-backward asymmetries in the Standard Model.},

doi = {10.1103/PhysRevD.91.074510},

journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},

issn = {1550-7998},

number = 7,

volume = 91,

place = {United States},

year = {2015},

month = {4}

}

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