$B_s\to D_s^{\ast }$ Form Factors for the full $q^2$ range from Lattice QCD

Abstract

We compute the Standard Model semileptonic vector and axial-vector form factors for $B_s\to D_s^{\ast }$ decay across the full $q^2$ range using lattice QCD. We use the Highly Improved Staggered Quark (HISQ) action for all valence quarks, enabling us to normalise weak currents nonperturbatively. We use gluon field configurations including $u$, $d$, $s$ and $c$ HISQ sea quarks and multiple HISQ heavy quarks with masses from the $c$ mass up to that of the $b$ on our finest lattices. We determine the physical form factors, with which we construct the differential and total rates for $\Gamma (B_s^0\to D_s^{\ast -}{\ell }^{+}{\nu }_{\ell })$. We find ${\Gamma }_{\ell =e}/|{\eta }_{\mathrm{EW}}{V}_{cb}{|}^2=2.07(17{)}_{\mathrm{latt}}(2{)}_{\mathrm{EM}}\times 10^{13}{\mathrm{s}}^{-1}$, ${\Gamma }_{\ell =\mu }/|{\eta }_{\mathrm{EW}}{V}_{cb}{|}^2=2.06(16{)}_{\mathrm{latt}}(2{)}_{\mathrm{EM}}\times 10^{13}{\mathrm{s}}^{-1}$ and ${\Gamma }_{\ell =\tau }/|{\eta }_{\mathrm{EW}}{V}_{cb}{|}^2=5.14(37{)}_{\mathrm{latt}}(5{)}_{\mathrm{EM}}\times 10^{12}{\mathrm{s}}^{-1}$, where ${\eta }_{\mathrm{EW}}$ contains the electroweak correction to $G_F$, the first uncertainty is from our lattice calculation, and the second allows for long-distance QED effects. We compute the ratio $R(D_s^{\ast -})\equiv {\Gamma }_{\ell =\tau }/{\Gamma }_{\ell =\mu }=0.2490(60{)}_{\mathrm{latt}}(35{)}_{\mathrm{EM}}$ and obtain a value for the ratio of decay rates ${\Gamma }_{\ell =\mu }(B_s\to D_s)/{\Gamma }_{\ell =\mu }(B_s\to D_s^{\ast })=0.443(40{)}_{\mathrm{latt}}(4{)}_{\mathrm{EM}}$, which agrees well with recent LHCb results. We determine $|V_{cb}|=42.2(1.5{)}_{\mathrm{latt}}(1.7{)}_{\exp }(0.4{)}_{\mathrm{EM}}\times 10^{-3}$ by combining our lattice results across the full q^2 range with experimental results from LHCb. A comparison of our results to the normalised differential decay rate from LHCb shows good agreement. We also test the impact of new physics couplings on observables sensitive to lepton flavor universality violation.

arXiv comment32 pages, 23 figures. arXiv admin note: text overlap with arXiv:2007.06957

References in corpus (53)

• The NumPy array: a structure for efficient numerical computation
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• Mesons with Beauty and Charm: Spectroscopy
• On the B to D* tau nu Sensitivity to New Physics
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2018
• High-precision scale setting in lattice QCD
• Dispersive Bounds on the Shape of B -> D^(*) l nu Form Factors
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD
• Measurement of the ratio of branching fractions $\mathcal{B}(B_c^{+}\to J/\psi {\tau }^{+}{\nu }_{\tau })$/$\mathcal{B}(B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu })$
• Combined analysis of semileptonic $B$ decays to $D$ and $D^{\ast }$: $R(D^{(\ast )})$, $|V_{cb}|$, and new physics
• The $B\to D\ell \nu$ form factors at nonzero recoil and $|V_{cb}|$ from $2+1$-flavor lattice QCD
• Precision Corrections to Dispersive Bounds on Form Factors
• $B\to Dl\nu$ Form Factors at Non-Zero Recoil and Extraction of $|V_{cb}|$
• Twisted Boundary Conditions in Lattice Simulations
• Measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$ with a semileptonic tagging method
• $R(D^{\ast })$, $|V_{cb}|$, and the Heavy Quark Symmetry relations between form factors
• Spectroscopy of B_c Mesons in the Relativized Quark Model
• Scaling studies of QCD with the dynamical HISQ action
• Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks
• Leptonic and Semileptonic Decays of Charm and Bottom Hadrons
• A fresh look at the determination of |V_cb| from B-> D^* l nu
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• Precise heavy-light meson masses and hyperfine splittings from lattice QCD including charm quarks in the sea
• The $V_{cb}$ puzzle: an update
• Update of $|V_{cb}|$ from the $\bar{B}\to D^{\ast }\ell \bar{\nu }$ form factor at zero recoil with three-flavor lattice QCD
• Theory determination of $\bar{B}\to D^{(\ast )}{\ell }^{-}\bar{\nu }$ form factors at $\mathcal{O}(1/m_c^2)$
• Observation of two excited B${}_{\mathrm{c}}^{+}$ states and measurement of the B${}_{\mathrm{c}}^{+}$(2S) mass in pp collisions at $\sqrt{s}=$ 13 TeV
• $B_s\to K\ell \nu$ form factors from lattice QCD
• High-Precision $f_{B_s}$ and HQET from Relativistic Lattice QCD
• The hadronic vacuum polarization contribution to $a_{\mu }$ from full lattice QCD
• $B_s\to D_s\ell \nu$ Form Factors for the full $q^2$ range from Lattice QCD with non-perturbatively normalized currents
• Heavy-Quark Expansion for ${\bar{B}}_s\to D_s^{(\ast )}$ Form Factors and Unitarity Bounds beyond the $SU(3{)}_F$ Limit
• Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu }^c$
• Lattice QCD calculation of the $B_{(s)}\to D_{(s)}^{\ast }\ell \nu$ form factors at zero recoil and implications for $|V_{cb}|$
• $R(J/\psi )$ and $B_c^{-}\to J/\psi {\ell }^{-}{\bar{\nu }}_{\ell }$ Lepton Flavor Universality Violating Observables from Lattice QCD
• Observation of an excited $B_c^{+}$ state
• Lattice study of semileptonic form factors with twisted boundary conditions
• Prediction of the $D_s^{\ast }$ width from a calculation of its radiative decay in full lattice QCD
• $B_c\to J/\psi$ Form Factors for the full $q^2$ range from Lattice QCD
• Lattice QCD form factor for $B_s\to D_s^{\ast }l\nu$ at zero recoil with non-perturbative current renormalisation
• V_cs from D_s to ϕlν semileptonic decay and full lattice QCD
• Matching lattice and continuum axial-vector and vector currents with NRQCD and HISQ quarks
• Model-Independent Bounds on $R(J/\psi )$
• $B_c\to B_{s(d)}$ form factors from lattice QCD
• Improved $V_{cs}$ determination using precise lattice QCD form factors for $D\to K\ell \nu$
• Observation of $B_c^{+}\to J/\psi D^{(\ast )}{K}^{(\ast )}$ decays
• Lepton Flavor Universality tests through angular observables of $\overline{B}\to D^{(\ast )}\ell \overline{\nu }$ decay modes
• Bottomonium precision tests from full lattice QCD: hyperfine splitting, ${\rm Y}$ leptonic width and $b$ quark contribution to $e^{+}{e}^{-}\to$ hadrons
• Remarks on the Standard Model predictions for $R(D)$ and $R(D^{\ast })$
• Measurement of the shape of the $B_s^0\to D_s^{\ast -}{\mu }^{+}{\nu }_{\mu }$ differential decay rate
• Optimized Lepton Universality Tests in $B\to V\ell \bar{\nu }$ decays
• Semi-inclusive studies of semileptonic $B_s$ decays at Belle

Cited by in corpus (8)

• 50 Years of Quantum Chromodynamics
• FLAG Review 2024
• Relativistic description of the semileptonic decays of bottom mesons
• $|V_{cb}|$, Lepton Flavour Universality and $SU(3{)}_F$ symmetry breaking in $B_s\to D_s^{(\ast )}\ell {\nu }_{\ell }$ decays through unitarity and lattice QCD
• Form factors and branching fraction calculations for $B_s\to D_s^{(\ast )}{\ell }^{+}{\nu }_{\ell }$ in view of LHCb observation
• Prediction of various observables for $B_s^0\to D_s^{(\ast )-}{\ell }^{+}{\nu }_{\ell }$ within covariant confined quark model
• The nonfactorizable QED correction to the ${\overline{B}}_s$ $\to$ $D_s^{(\ast )}\ell {\bar{\nu }}_{\ell }$ decays
• Probing $D_s^{\ast }$-meson longitudinal twist-2 LCDA