Lattice QCD calculation of the $B_{(s)}\to D_{(s)}^{\ast }\ell \nu$ form factors at zero recoil and implications for $|V_{cb}|$

Abstract

We present results of a lattice QCD calculation of $B\to D^{\ast }$ and $B_s\to D_s^{\ast }$ axial vector matrix elements with both states at rest. These zero recoil matrix elements provide the normalization necessary to infer a value for the CKM matrix element $|V_{cb}|$ from experimental measurements of ${\bar{B}}^0\to D^{\ast +}{\ell }^{-}\bar{\nu }$ and ${\bar{B}}_s^0\to D_s^{\ast +}{\ell }^{-}\bar{\nu }$ decay. Results are derived from correlation functions computed with highly improved staggered quarks (HISQ) for light, strange, and charm quark propagators, and nonrelativistic QCD for the bottom quark propagator. The calculation of correlation functions employs MILC Collaboration ensembles over a range of three lattice spacings. These gauge field configurations include sea quark effects of charm, strange, and equal-mass up and down quarks. We use ensembles with physically light up and down quarks, as well as heavier values. Our main results are ${\mathcal{F}}^{B\to D^{\ast }}(1)=0.895\pm 0.010_{\mathrm{stat}}\pm {0.024}_{\mathrm{sys}}$ and ${\mathcal{F}}^{B_s\to D_s^{\ast }}(1)=0.883\pm 0.010_{\mathrm{stat}}\pm 0.028_{\mathrm{sys}}$. We discuss the consequences for $|V_{cb}|$ in light of recent investigations into the extrapolation of experimental data to zero recoil.

23 pages. v3: Typos corrected. v2: Improved treatment of finite volume effects. Small change to some results (but smaller than the quoted uncertainties). Version accepted for publication in Phys. Rev. D

References in corpus (19)

• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• High Precision determination of the pi, K, D and D_s decay constants from lattice QCD
• $R(D^{\ast })$, $|V_{cb}|$, and the Heavy Quark Symmetry relations between form factors
• Correlations among new CP violating effects in Delta F = 2 observables
• Update: Precision D_s decay constant from full lattice QCD using very fine lattices
• Scaling studies of QCD with the dynamical HISQ action
• Extraction of $|V_{cb}|$ from $B\to D^{(\ast )}\ell {\nu }_{\ell }$ and the Standard Model predictions of $R(D^{(\ast )})$
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• Precision determination of the CKM element Vcb
• Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks
• B-meson decay constants: a more complete picture from full lattice QCD
• $B\to D^{(\ast )}$ Form Factors from QCD Light-Cone Sum Rules
• Measurement of the form factors of the decay B0 -> D*- ell+ nu and determination of the CKM matrix element |Vcb|
• Radiative corrections to the lattice gluon action for highly improved staggered quarks (HISQ) and the effect of such corrections on the static potential
• Tensions and correlations in $|V_{cb}|$ determinations
• Matching lattice and continuum axial-vector and vector currents with NRQCD and HISQ quarks
• Precise determination of the CKM matrix element $\left|V_{cb}\right|$ with ${\bar{B}}^0\to D^{\ast +}{\ell }^{-}{\bar{\nu }}_{\ell }$ decays with hadronic tagging at Belle
• $|V_{cb}|$ from the ${\bar{B}}^0\to D^{\ast +}{\ell }^{-}\bar{\nu }$ zero-recoil form factor using $2+1+1$ flavour HISQ and NRQCD
• $\overline{B}\to D^{\ast }\ell \overline{\nu }$ at non-zero recoil

Cited by in corpus (46)

• FLAG Review 2019
• FLAG Review 2021
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2018
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2021
• 50 Years of Quantum Chromodynamics
• $B\to P$ and $B\to V$ Form Factors from $B$-Meson Light-Cone Sum Rules beyond Leading Twist
• The $V_{cb}$ puzzle: an update
• Footprints of New Physics in $b\to c\tau \nu$ Transitions
• Theory determination of $\bar{B}\to D^{(\ast )}{\ell }^{-}\bar{\nu }$ form factors at $\mathcal{O}(1/m_c^2)$
• Heavy-Quark Expansion for ${\bar{B}}_s\to D_s^{(\ast )}$ Form Factors and Unitarity Bounds beyond the $SU(3{)}_F$ Limit
• Semileptonic form factors for $B\to D^{\ast }\ell \nu$ at nonzero recoil from 2 + 1-flavor lattice QCD
• Addressing $R_{D^{(\ast )}}$, $R_{K^{(\ast )}}$, muon $g-2$ and ANITA anomalies in a minimal $R$-parity violating supersymmetric framework
• FLAG Review 2024
• $R(J/\psi )$ and $B_c^{-}\to J/\psi {\ell }^{-}{\bar{\nu }}_{\ell }$ Lepton Flavor Universality Violating Observables from Lattice QCD
• Challenges in Semileptonic B Decays
• Lepton-flavour non-universality of $\bar{B}\to D^{\ast }\ell \bar{\nu }$ angular distributions in and beyond the Standard Model
• The role of right-handed neutrinos in $b\to c\tau \bar{\nu }$ anomalies
• Lattice QCD form factor for $B_s\to D_s^{\ast }l\nu$ at zero recoil with non-perturbative current renormalisation
• $B_c\to J/\psi$ Form Factors for the full $q^2$ range from Lattice QCD
• Flavor Anomalies in Heavy Quark Decays
• Unitarity Bounds for Semileptonic Decays in Lattice QCD
• Revisit to the $b\to c\tau \nu$ transition: in and beyond the SM
• Investigation of Effects of New Physics in ${\Lambda }_b\to {\Lambda }_c\tau {\bar{\nu }}_{\tau }$ Decay
• Model-Independent Bounds on $R(J/\psi )$
• $B\to D^{\ast }\ell {\nu }_{\ell }$ semileptonic form factors from lattice QCD with Möbius domain-wall quarks
• $B_s\to D_s^{\ast }$ Form Factors for the full $q^2$ range from Lattice QCD
• Precision Model-Independent Bounds from Global Analysis of $b\to c\ell \nu$ Form Factors
• Semileptonic decays $B/B_s\to (D^{(\ast )},D_s^{(\ast )})l{\nu }_l$ in the PQCD approach with the lattice QCD input
• The $D_s$-meson leading-twist distribution amplitude within the QCD sum rules and its application to the $B_s\to D_s$ transition form factor
• Lepton Flavor Universality tests through angular observables of $\overline{B}\to D^{(\ast )}\ell \overline{\nu }$ decay modes
• Tests of the Standard Model in $B\to D\ell {\nu }_{\ell }$, $B\to D^{\ast }\ell {\nu }_{\ell }$ and $B_c\to J/\psi \ell {\nu }_{\ell }$
• Model-Independent Prediction of $R({\eta }_c)$
• Form factor ratios for $B_s\to K\ell \nu$ and $B_s\to D_s\ell \nu$ semileptonic decays and $|V_{ub}/V_{cb}|$
• Measurement of the shape of the $B_s^0\to D_s^{\ast -}{\mu }^{+}{\nu }_{\mu }$ differential decay rate
• Static Energy in ($2+1+1$)-Flavor Lattice QCD: Scale Setting and Charm Effects
• Implication of $b\to c\tau \nu$ flavor anomalies on $B_s\to D_s^{\ast }\tau \nu$ decay observables
• New physics footprints in the angular distribution of $B_s\to D_s^{\ast }(\to D_s\gamma ,D_s\pi )\tau \nu$ decays
• ${\bar{B}}_c\to {\eta }_c$, ${\bar{B}}_c\to J/\psi$ and $\bar{B}\to D^{(\ast )}$ semileptonic decays including new physics
• First lattice QCD calculation of $J/\psi$ semileptonic decay containing $D$ and $D_s$ particles
• Hints and challenges in heavy flavor physics
• Continuity and Semileptonic $B_{(s)}\to D_{(s)}$ Form Factors
• Quark flavor physics and lattice QCD
• Probing $D_s^{\ast }$-meson longitudinal twist-2 LCDA
• Closing the Gap on $R_{D^{\ast }}$ by including longitudinal effects
• Semileptonic $B\to D^{(\ast )}\ell \nu$ Decay Form Factors using the Oktay-Kronfeld Action
• Extraction of $B_s\to D_s^{(\ast )}$ form factors from $N_f=2$ lattice QCD