Open Access

Revisiting $B_{c}^{-} \to J / ψ (η_{c}) L^{-}$ decays within the SM and beyond in QCD factorization

Wei-Jun Deng ^1,4, Fang-Min Cai ², Xin-Qiang Li ^3,5,*, Yan Shi³, and Ya-Dong Yang^2,3

¹School of Computational Science and Electronics, Hunan Institute of Engineering, Xiangtan 411104, China
²Institute of Particle and Nuclear Physics, Henan Normal University, Xinxiang 453007, China
³Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University, Wuhan, Hubei 430079, China
⁴School of Physics and Electronics, Hunan University, Changsha 410082, China
⁵Center for High Energy Physics, Peking University, Beijing 100871, China

^*Contact author: xqli@mail.ccnu.edu.cn

Phys. Rev. D 112, 035013 – Published 11 August, 2025

DOI: https://doi.org/10.1103/31cd-lgtk

Abstract

Motivated by the deviations observed between the experimental measurements and the Standard Model (SM) predictions of the branching ratios of ${\bar{B}}_{s}^{0} \to D_{s}^{+} π^{-}$ and ${\bar{B}}_{d}^{0} \to D^{+} K^{-}$ decays, we revisit the two-body hadronic $B_{c}^{-} \to J / ψ (η_{c}) L^{-}$ decays, with $L = π, K^{(*)}, ρ$ , both within the SM and beyond. Since these processes are also mediated by the quark-level $b \to c \bar{u} d (s)$ transitions and hence dominated by the color-allowed tree topology, the QCD factorization is generally expected to hold in the heavy-quark limit. First, we update the SM predictions of the observables of these decays by including the nonfactorizable vertex corrections to the hadronic matrix elements of the SM four-quark operators up to the next-to-next-to-leading order (NNLO) in $α_{s}$ . It is found that, relative to the leading-order results, the branching ratios of these decays up to the next-to-leading-order (NLO) and NNLO corrections are always enhanced, with a relative amount given by $δ_{NLO} = (B^{NLO} - B^{LO}) / B^{LO} \approx + 6 %$ and $δ_{NNLO} = (B^{NNLO} - B^{LO}) / B^{LO} \approx + 9 %$ , respectively. To minimize the uncertainties brought by the Cabibbo-Kobayashi-Maskawa matrix element $V_{c b}$ as well as the $B_{c} \to J / ψ (η_{c})$ and $B_{(s)} \to D_{(s)}^{(*)}$ transition form factors, we construct ratios of the nonleptonic decay rates with respect to the corresponding differential semileptonic decay rates evaluated at $q^{2} = m_{L}^{2}$ (for $R_{J / ψ (η_{c}) L}$ and $R_{(s) L}^{(*)}$ ) or integrated over the whole $q^{2}$ range (for $R_{π / μ ν_{μ}}$ ), which are then used to constrain the model-independent new physics (NP) Wilson coefficients. After considering the latest Belle data on ${\bar{B}}^{0} \to D^{(*) +} π (K)^{-}$ decays and the updated fitting results of the $B_{(s)} \to D_{(s)}^{(*)}$ transition form factors, we find that the deviations can still be explained by the NP four-quark operators with $(1 + γ_{5}) \otimes (1 - γ_{5})$ and $(1 + γ_{5}) \otimes (1 + γ_{5})$ structures, while the solution with $γ^{μ} (1 + γ_{5}) \otimes γ_{μ} (1 - γ_{5})$ structure does not work anymore, under the combined constraints from the ratios $R_{(s) L}^{(*)}$ at the $2 σ$ level. Furthermore, the ratio $R_{π / μ ν_{μ}}$ , once measured precisely, could provide complementary constraint on these NP Wilson coefficients allowed by $R_{(s) L}^{(*)}$ . With the large $B_{c}$ events expected at the Large Hadron Collider, we hope to obtain more precise measurements of these observables, which can be exploited to discriminate the different NP scenarios responsible for the deviations observed in the two-body nonleptonic $B$ -meson decays.

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Phys. Rev. D 112, 035013– Published 11 August, 2025

Vol. 112, Iss. 3 — 1 August 2025

Received 30 May 2025
Accepted 16 July 2025

DOI: https://doi.org/10.1103/31cd-lgtk

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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Revisiting $B_{c}^{-} \to J / ψ (η_{c}) L^{-}$ decays within the SM and beyond in QCD factorization

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Revisiting Bc−→J/ψ(ηc)L− decays within the SM and beyond in QCD factorization

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Revisiting $B_{c}^{-} \to J / ψ (η_{c}) L^{-}$ decays within the SM and beyond in QCD factorization