Form factors for the processes $B_c^{+}\to D^0{\ell }^{+}{\nu }_{\ell }$ and $B_c^{+}\to D_s^{+}{\ell }^{+}{\ell }^{-}(\nu \overline{\nu })$ from lattice QCD

Abstract

We present results of the first lattice QCD calculations of the weak matrix elements for the decays $B_c^{+}\to D^0{\ell }^{+}{\nu }_{\ell }$, $B_c^{+}\to D_s^{+}{\ell }^{+}{\ell }^{-}$ and $B_c^{+}\to D_s^{+}\nu \overline{\nu }$. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the continuum limit with physical quark masses. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with three different lattice spacings and including 2+1+1 flavours of sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for all of the valence quarks. The uncertainty on the decay widths from our form factors is similar in size to that from the present value for $V_{ub}$. We obtain the ratio $\Gamma (B_c^{+}\to D^0{\mu }^{+}{\nu }_{\mu })/{\left|{\eta }_{\mathrm{EW}}{V}_{ub}\right|}^2=4.43(63)\times 10^{12}{\mathrm{s}}^{-1}$. Combining our form factors with those found previously by HPQCD for $B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu }$, we find ${\left|V_{cb}/V_{ub}\right|}^2\Gamma (B_c^{+}\to D^0{\mu }^{+}{\nu }_{\mu })/\Gamma (B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu })=0.257(36{)}_{B_c\to D}(18{)}_{B_c\to J/\psi }$. We calculate the differential decay widths of $B_c^{+}\to D_s^{+}{\ell }^{+}{\ell }^{-}$ across the full $q^2$ range, and give integrated results in $q^2$ bins that avoid possible effects from charmonium and $u\overline{u}$ resonances. For example, we find that the ratio of differential branching fractions integrated over the range $q^2=1{\mathrm{GeV}}^2-6{\mathrm{GeV}}^2$ for $B_c^{+}\to D_s^{+}{\mu }^{+}{\mu }^{-}$ and $B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu }$ is $5.23(73{)}_{B_c\to D_s}(54{)}_{B_c\to J/\psi }\times 10^{-6}$. We also give results for the branching fraction of $B_c^{+}\to D_s^{+}\nu \overline{\nu }$. Prospects for reducing our errors in the future are discussed.

arXiv comment28 pages, 29 figures. Version as published in Physical Review D

References in corpus (52)

• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• The three loop relation between the \bar {MS} and the pole quark masses
• Chiral Multiplets of Heavy-Light Mesons
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2018
• High-precision scale setting in lattice QCD
• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• Angular Distributions of B -> K ll Decays
• Model-independent description of $B\to \pi l\nu$ decays and a determination of $|V_{ub}|$
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD
• Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays
• Heavy-to-Light Form Factors in the Final Hadron Large Energy Limit of QCD
• Constrained Curve Fitting
• Twisted Boundary Conditions in Lattice Simulations
• 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
• $B\to K{\ell }^{+}{\ell }^{-}$ decay at large hadronic recoil
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• New strategies for New Physics search in B -> K* nu anti-nu, B -> K nu anti-nu and B -> X(s) nu anti-nu decays
• Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks
• Neutral B-meson mixing from full lattice QCD at the physical point
• Rare decay B -> K ll form factors from lattice QCD
• Predicting positive parity $B_s$ mesons from lattice QCD
• Semileptonic $B_c$ Decay and Heavy Quark Spin Symmetry
• Second Order Power Corrections in the Heavy Quark Effective Theory II. Baryon Form Factors
• $B_s\to K\ell \nu$ form factors from lattice QCD
• Phenomenology of semileptonic B-meson decays with form factors from lattice QCD
• Analyticity, Shapes of Semileptonic Form Factors, and B to pi l nu
• 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
• Measurement of the isospin asymmetry in $B\to K^{(\ast )}{\mu }^{+}{\mu }^{-}$ decays
• Fitting Correlated Data
• Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu }^c$
• Gradient flow and scale setting on MILC HISQ ensembles
• Lattice study of semileptonic form factors with twisted boundary conditions
• Radiative corrections to the lattice gluon action for highly improved staggered quarks (HISQ) and the effect of such corrections on the static potential
• 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
• Measurement of the lifetime of the $B_c^{+}$ meson using the $B_c^{+}\to J/\psi {\pi }^{+}$ decay mode
• Hadronic effects and observables in $B\to \pi {\ell }^{+}{\ell }^{-}$ decay at large recoil
• Determination of quark masses from ${\mathbf{n}}_{\mathbf{f}}=4$ lattice QCD and the RI-SMOM intermediate scheme
• The pseudoscalar meson electromagnetic form factor at high $Q^2$ from full lattice QCD
• $B_c\to B_{s(d)}$ form factors from lattice QCD
• Improved $V_{cs}$ determination using precise lattice QCD form factors for $D\to K\ell \nu$
• Renormalising vector currents in lattice QCD using momentum-subtraction schemes
• Effects of non-equilibrated topological charge distributions on pseudoscalar meson masses and decay constants
• Fast Fits for Lattice QCD Correlators
• Renormalisation of the tensor current in lattice QCD and the $J/\psi$ tensor decay constant
• Determination of ${\overline{m}}_b/{\overline{m}}_c$ and ${\overline{m}}_b$ from $n_f=4$ lattice QCD$+$QED
• Toward accurate form factors for $B$-to-light meson decay from lattice QCD
• $|V_{ub}|$ determination and testing of lepton flavour universality in semileptonic $B_c\to D^{(\ast )}$ decays

Cited by in corpus (6)

• $B\to K$ and $D\to K$ form factors from fully relativistic lattice QCD
• Relativistic description of the semileptonic decays of bottom mesons
• Right-handed interactions in puzzling $B$-decays
• Assessing Lepton Flavor Universality Violations in Semileptonic Decays
• Study of angular observables in exclusive semileptonic $B_c$ decays
• Self-consistent optimization of the $z$-Expansion for $B$ meson decays