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Model-independent determination of $B_{c}^{+} \to η_{c} ℓ^{+} ν$ form factors

Christopher W. Murphy^* and Amarjit Soni^†

Department of Physics, Brookhaven National Laboratory, Upton, New York 11973, USA

^*chrismurphybnl@gmail.com
^†adlersoni@gmail.com

Phys. Rev. D 98, 094026 – Published 27 November, 2018

DOI: https://doi.org/10.1103/PhysRevD.98.094026

Abstract

We derive model-independent bounds on the form factors for the decay $B_{c}^{+} \to η_{c} ℓ^{+} ν$ including full mass effects, i.e., $ℓ = e, μ$ , and $τ$ . The bounds are obtained by using the Boyd-Grinstein-Lebed parametrization for the form factors, and fitting to the preliminary lattice data of the HPQCD Collaboration. Our main result after bounding the form factors is the Standard Model prediction for the ratio of branching fractions $R (η_{c}) = B (B_{c}^{+} \to η_{c} τ^{+} ν_{τ}) / B (B_{c}^{+} \to η_{c} μ^{+} ν_{μ})$ . We find $R (η_{c}) |_{SM} = 0.3 1_{- 0.02}^{+ 0.04}$ , and argue that a measurement of $R (η_{c})$ is within the reach of LHCb during the high-luminosity run of the LHC. In addition, using the heavy-quark spin symmetry of the $B_{c}$ meson we relate our results for $B_{c}^{+} \to η_{c} ℓ^{+} ν$ to those for $B_{c}^{+} \to J / ψ ℓ^{+} ν$ yielding the estimate $R (J / ψ) |_{SM} = 0.26 \pm 0.02$ in good agreement with other determinations.

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Phys. Rev. D 98, 094026– Published 27 November, 2018

Vol. 98, Iss. 9 — 1 November 2018

Received 31 August 2018

DOI: https://doi.org/10.1103/PhysRevD.98.094026

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Model-independent determination of $B_{c}^{+} \to η_{c} ℓ^{+} ν$ form factors

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Model-independent determination of Bc+→ηcℓ+ν form factors

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Model-independent determination of $B_{c}^{+} \to η_{c} ℓ^{+} ν$ form factors