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.

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

References in corpus (19)

• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• High-precision scale setting in lattice QCD
• Angular Distributions of B -> K ll Decays
• Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays
• Scaling studies of QCD with the dynamical HISQ action
• 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
• $B_s\to K\ell \nu$ form factors from lattice QCD
• Measurement of the isospin asymmetry in $B\to K^{(\ast )}{\mu }^{+}{\mu }^{-}$ decays
• Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu }^c$
• Radiative corrections to the lattice gluon action for highly improved staggered quarks (HISQ) and the effect of such corrections on the static potential
• $B_c\to J/\psi$ 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
• $B_c\to B_{s(d)}$ form factors from lattice QCD
• Improved $V_{cs}$ determination using precise lattice QCD form factors for $D\to K\ell \nu$
• 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

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