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$η {- η}^{'}$ mixing and its application in the $B^{+}$ , $D^{+}$ , $D_{s}^{+} \to η^{(')} ℓ^{+} ν_{ℓ}$ decays

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

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

^*Contact author: zhangyj@stu.cqu.edu.cn
^†Contact author: wuxg@cqu.edu.cn
^‡Contact author: hudd@stu.cqu.edu.cn
^§Contact author: zlong@cqu.edu.cn

Phys. Rev. D 112, 076001 – Published 2 October, 2025

DOI: https://doi.org/10.1103/b51l-qdlg

Abstract

In this paper, we take into account the intrinsic charm and gluonic contents into the $η - η^{'}$ mixing scheme and formulate the tetramixing $η - η^{'} - G - η_{c}$ to study the mixing properties of $η^{(')}$ mesons. Using the newly derived mixing parameters, we calculate the transition form factors (TFFs) of $B^{+} / D^{+} / D_{s}^{+} \to η^{(')}$ within the quantum chromodynamics (QCD) light-cone sum rules up to next-to-leading order QCD corrections and twist-4 contributions. Using the extrapolated TFFs, we then calculate the decay widths and branching fractions of the semileptonic decays $B^{+} / D^{+} / D_{s}^{+} \to η^{(')} ℓ^{+} ν_{ℓ}$ . Our results are consistent with the recent Belle and BES-III measurements within reasonable errors.

Physics Subject Headings (PhySH)

Sum rules

Article Text

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Phys. Rev. D 112, 076001– Published 2 October, 2025

Vol. 112, Iss. 7 — 1 October 2025

Received 24 June 2025
Accepted 15 September 2025

DOI: https://doi.org/10.1103/b51l-qdlg

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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$η {- η}^{'}$ mixing and its application in the $B^{+}$ , $D^{+}$ , $D_{s}^{+} \to η^{(')} ℓ^{+} ν_{ℓ}$ decays

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η−η′ mixing and its application in the B+, D+, Ds+→η(′)ℓ+νℓ decays

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$η {- η}^{'}$ mixing and its application in the $B^{+}$ , $D^{+}$ , $D_{s}^{+} \to η^{(')} ℓ^{+} ν_{ℓ}$ decays