## Form factors for the processes Bc+ →d0ℓ+νℓ and Bc+ → Ds+ ℓ+ℓ- (ν ν ¯) from lattice QCD FORM FACTORS for the PROCESSES Bc+ →d0ℓ+νℓ ⋯ COOPER, DAVIES, and WINGATE

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##### Publication Date

2022-01-05##### Journal Title

Physical Review D

##### ISSN

2470-0010

##### Publisher

American Physical Society (APS)

##### Volume

105

##### Issue

1

##### Number

ARTN 014503

##### Pages

014503

##### Type

Article

##### This Version

VoR

##### Metadata

Show full item record##### Citation

Cooper, L., Davies, C., & Wingate, M. (2022). Form factors for the processes Bc+ →d0ℓ+νℓ and Bc+ → Ds+ ℓ+ℓ- (ν ν ¯) from lattice QCD FORM FACTORS for the PROCESSES Bc+ →d0ℓ+νℓ ⋯ COOPER, DAVIES, and WINGATE. Physical Review D, 105 (1. ARTN 014503), 014503. https://doi.org/10.1103/PhysRevD.105.014503

##### 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 $\Gamma (B_{c}^{+} \rightarrow D^0 \mu^{+} \nu_{\mu})
/\left|\eta_{\mathrm{EW}} V_{u b}\right|^{2}=4.43(63) \times 10^{12}
\mathrm{~s}^{-1}$. Combining our form factors with those found previously by
HPQCD for $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$, we find
$\left|V_{cb}/V_{ub} \right|^2 \Gamma( B_c^+ \to D^0 \mu^+ \nu_\mu
)/\Gamma(B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}) = 0.257(36)_{B_c \to
D}(18)_{B_c \to J/\psi}$. 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 $B_{c}^{+} \rightarrow J
/ \psi \mu^{+} \nu_{\mu}$ is $5.23{\tiny }(73)_{B_c \to D_s}(54)_{B_c \to
J/\psi} \times 10^{-6}$. 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.

##### Keywords

hep-lat, hep-lat, hep-ph

##### Sponsorship

Science and Technology Facilities Council (ST/P000681/1)

Science and Technology Facilities Council (ST/R002452/1)

Science and Technology Facilities Council (ST/R00689X/1)

##### Identifiers

External DOI: https://doi.org/10.1103/PhysRevD.105.014503

This record's URL: https://www.repository.cam.ac.uk/handle/1810/333414

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