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$η_{c}$ leading-twist distribution amplitude and the $B_{c} \to η_{c} ℓ {\bar{ν}}_{ℓ}$ semileptonic decays using QCD sum rules

Long Zeng ^*, Xing-Gang Wu ^†, Dan-Dan Hu^‡, and Yu-Jie Zhang^§

Hai-Bing Fu^∥ and Tao Zhong^¶

Department of Physics, Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, People’s Republic of China

Department of Physics, Guizhou Minzu University, Guiyang 550025, People’s Republic of China and Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

^*Contact author: zlong@cqu.edu.cn
^†Contact author: wuxg@cqu.edu.cn
^‡Contact author: hudd@stu.cqu.edu.cn
^§Contact author: zhangyj@stu.cqu.edu.cn
^∥Contact author: fuhb@gzmu.edu.cn
^¶Contact author: zhongtao1219@sina.com

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Phys. Rev. D 111, 116014 – Published 16 June, 2025

DOI: https://doi.org/10.1103/csrw-9hwp

Abstract

In this paper, we investigate the semileptonic decays $B_{c} \to η_{c} ℓ {\bar{ν}}_{ℓ}$ using the quantum chromodynamics (QCD) sum rules within the framework of Standard Model (SM). We further explore the potential to probe signatures of new physics (NP) beyond the SM through these decays. First, we derive the $ξ$ -moments $⟨ ξ_{2; η_{c}}^{n} ⟩$ of the $η_{c}$ -meson leading-twist distribution amplitude $ϕ_{2; η_{c}}$ using the QCD sum rules within the background field theory. Considering contributions from the vacuum condensates up to dimension-six, the first two nonzero $ξ$ -moments at the scale of 4 GeV are found to be $⟨ ξ_{2; η_{c}}^{2} ⟩ = 0.10 3_{- 0.009}^{+ 0.009}$ and $⟨ ξ_{2; η_{c}}^{4} ⟩ = 0.03 1_{- 0.003}^{+ 0.003}$ . Using these moments, we then fix the Gegenbauer expansion series of $ϕ_{2; η_{c}}$ and apply it to compute the $B_{c} \to η_{c}$ transition form factors (TFFs) using QCD light cone sum rules. Second, we extrapolate those TFFs to physically allowable $q^{2}$ -range via a simplified series expansion, and we obtain $R_{η_{c}} |_{SM} = 0.30 8_{- 0.062}^{+ 0.084}$ . Furthermore, we explore the potential impacts of various NP scenarios on $R_{η_{c}}$ . Specifically, we compute the forward-backward asymmetry $A_{FB} (q^{2})$ , the convexity parameter $C_{F}^{τ} (q^{2})$ , and the longitudinal and transverse polarizations $P_{L} (q^{2})$ and $P_{T} (q^{2})$ for $B_{c} \to η_{c}$ transitions within both the SM and two types of NP scenarios. Our results contribute to a deeper understanding of $B_{c}$ -meson semileptonic decays and provide insights into the search for the NP beyond the SM.

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References (91)

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Phys. Rev. D 111, 116014– Published 16 June, 2025

Vol. 111, Iss. 11 — 1 June 2025

Received 25 March 2025
Accepted 27 May 2025

DOI: https://doi.org/10.1103/csrw-9hwp

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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$η_{c}$ leading-twist distribution amplitude and the $B_{c} \to η_{c} ℓ {\bar{ν}}_{ℓ}$ semileptonic decays using QCD sum rules

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ηc leading-twist distribution amplitude and the Bc→ηcℓν¯ℓ semileptonic decays using QCD sum rules

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Physics Subject Headings (PhySH)

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References (91)

$η_{c}$ leading-twist distribution amplitude and the $B_{c} \to η_{c} ℓ {\bar{ν}}_{ℓ}$ semileptonic decays using QCD sum rules