$B\to \pi \ell \nu$ at zero recoil from lattice QCD with physical $u/d$ quarks

Abstract

The exclusive semileptonic decay $B\to \pi \ell \nu$ is a key process for the determination of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$ from the comparison of experimental rates as a function of $q^2$ with theoretically determined form factors. The sensitivity of the form factors to the $u/d$ quark mass has meant significant systematic uncertainties in lattice QCD calculations at unphysically heavy pion masses. Here we give the first lattice QCD calculations of this process for u/d quark masses going down to their physical values, calculating the $f_0$ form factor at zero recoil to 3\%. We are able to resolve a long-standing controversy by showing that the soft-pion theorem result $f_0(q_{max}^2)=f_B/f_{\pi }$ does hold as $m_{\pi }\to 0$. We use the Highly Improved Staggered Quark formalism for the light quarks and show that staggered chiral perturbation theory for the $m_{\pi }$ dependence is almost identical to continuum chiral perturbation theory for $f_0$, $f_B$ and $f_{\pi }$. We also give results for other processes such as $B_s\to K\ell \nu$.

arXiv comment16 pages, 6 figures

References in corpus (38)

• Improved Nonrelativistic QCD for Heavy Quark Physics
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• Massive Fermions in Lattice Gauge Theory
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Constrained Curve Fitting
• Flavor-Symmetry Restoration and Symanzik Improvement for Staggered Quarks
• Pion and Kaon masses in Staggered Chiral Perturbation Theory
• The Upsilon spectrum and m_b from full lattice QCD
• Partial Flavor Symmetry Restoration for Chiral Staggered Fermions
• Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks
• $|V_{ub}|$ from $B\to \pi \ell \nu$ decays and (2+1)-flavor lattice QCD
• B-meson decay constants from improved lattice NRQCD and physical u, d, s and c sea quarks
• Precise heavy-light meson masses and hyperfine splittings from lattice QCD including charm quarks in the sea
• The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea
• $B\to \pi \ell \nu$ 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
• B-meson decay constants: a more complete picture from full lattice QCD
• Pseudoscalar Decay Constants in Staggered Chiral Perturbation Theory
• Precise determination of the lattice spacing in full lattice QCD
• $B_s\to K\ell \nu$ form factors from lattice QCD
• The ${\rm Y}$ and ${{\rm Y}}^{\prime }$ Leptonic Widths, $a_{\mu }^b$ and $m_b$ from full lattice QCD
• Relativistic Heavy Quark Effective Action
• Improved B -> pi l nu_l form factors from the lattice
• The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks
• Precise B, B_s and B_c meson spectroscopy from full lattice QCD
• The Decay $B\to \pi \ell \nu$ in Heavy Quark Effective Theory
• Heavy-light mesons with staggered light quarks
• Staggered Chiral Perturbation Theory for Heavy-Light Mesons
• Radiative corrections to the lattice gluon action for highly improved staggered quarks (HISQ) and the effect of such corrections on the static potential
• Prediction of the bottomonium D-wave spectrum from full lattice QCD
• The Low-Lying Dirac Spectrum of Staggered Quarks
• Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory
• Matching lattice and continuum axial-vector and vector currents with NRQCD and HISQ quarks
• Bottomonium hyperfine splittings from lattice NRQCD including radiative and relativistic corrections
• Radiative improvement of the lattice NRQCD action using the background field method with applications to quarkonium spectroscopy
• B --> pi and B --> K transitions in partially quenched chiral perturbation theory
• B decays on the lattice
• Semileptonic Form Factors

Cited by in corpus (21)

• FLAG Review 2019
• FLAG Review 2021
• Scalar contributions to $b\to c(u)\tau \nu$ transitions
• Neutral B-meson mixing from full lattice QCD at the physical point
• $B\to K$ and $D\to K$ form factors from fully relativistic lattice QCD
• FLAG Review 2024
• Challenges in Semileptonic B Decays
• New methods for B meson decay constants and form factors from lattice NRQCD
• Flavor Anomalies in Heavy Quark Decays
• The $\bar{B}\to \pi$ form factors from QCD and their impact on $|V_{ub}|$
• Precision calculations of $B_{d,s}\to \pi ,K$ decay form factors in soft-collinear effective theory
• Form factors of $B\to \pi \ell \nu$ and a determination of $|V_{ub}|$ with Möbius domain-wall-fermions
• The size of the pion from full lattice QCD with physical $u$, $d$, $s$ and $c$ quarks
• Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$
• Nonperturbative comparison of clover and HISQ quarks in lattice QCD and the properties of the phi meson
• Continuum limit of the leading order HQET form factor in $B_s\to K\ell \nu$ decays
• Form factor ratios for $B_s\to K\ell \nu$ and $B_s\to D_s\ell \nu$ semileptonic decays and $|V_{ub}/V_{cb}|$
• Toward accurate form factors for $B$-to-light meson decay from lattice QCD
• Extraction of bare Form Factors for ${\mathrm{B}}_{\mathrm{s}}\to \mathrm{K}\ell \nu$ Decays in non-perturbative HQET
• Quark flavor physics and lattice QCD
• Semileptonic $B$ decays and $|V_{xb}|$ update