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Relativistic effects in M1 radiative decays of heavy-light mesons

Budker Institute of Nuclear Physics of SB RAS, 630090 Novosibirsk, Russia and Novosibirsk State University, 630090 Novosibirsk, Russia

^*Contact author: A.E.Bondar@inp.nsk.su
^†Contact author: A.I.Milstein@inp.nsk.su

Phys. Rev. D 112, 054037 – Published 22 September, 2025

DOI: https://doi.org/10.1103/gnyk-r31j

Abstract

We discuss the M1 radiative transitions $D^{*} \to D γ$ , $D_{s}^{*} \to D_{s} γ$ , $B^{*} \to B γ$ , and $B_{s}^{*} \to B_{s} γ$ . A relativistic potential model is proposed. The corresponding Hamiltonian, when expanded to terms of the order of $v^{2} / c^{2}$ , where $v$ are the quark velocities, coincides with the Breit Hamiltonian. This model allows making predictions for the widths of radiative transitions of mesons with one light quark. Taking into account relativistic effects is especially important for the transitions $D_{s}^{* +} \to D_{s}^{+} γ$ and $D^{* +} \to D^{+} γ$ , where there is a large compensation in the magnitude of the magnetic moment of these mesons. Our results are consistent with known experimental data.

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References (45)

J. P. Lees et al., Measurement of the $D^{*} (2010)^{+}$ meson width and the $D^{*} (2010)^{+} - D^{0}$ mass difference, Phys. Rev. Lett. 111, 111801 (2013).
R. L. Workman, V. D. Burkert, V. Crede et al., Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
V. L. Eletsky and Y. I. Kogan, Calculation of $D^{*} \to D γ$ and $D^{*} \to D π$ decay widths from QCD sum rules, Z. Phys. C 28, 155 (1985).
E. Iltan, T. M. Aliev, and N. K. Pak, Radiative $D^{*}$ meson decays in QCD sum rules, Phys. Lett. B 334, 169 (1994).
H. G. Dosch and S. Narison, $B^{*} B π (γ)$ couplings and $D^{*} \to D π (γ)$ decays within a $1 / M$ -expansion in full QCD, Phys. Lett. B 368, 163 (1996).
W. Y. P. Hwang, S. L. Zhu, and Z. S. Yang, $D^{*} \to D γ$ and $B^{*} \to B γ$ as derived from QCD sum rules, Mod. Phys. Lett. A 12, 3027 (1997).
E. Iltan, T. M. Aliev, D. A. Demir, and N. K. Pak, Radiative $B^{*} \to B γ$ and $D^{*} \to D γ$ decays in light cone QCD sum rules, Phys. Rev. D 54, 857 (1996).
H. D. Li, C. D. Lü, C. Wang, Y. M. Wang, and Y. B. Wei, QCD calculations of radiative heavy meson decays with subleading power corrections, J. High Energy Phys. 04 (2020) 023.
P. J. O’Donnell and Q. P. Xu, Strong and radiative $D^{*}$ decays, Phys. Lett. B 336, 113 (1994).
M. A. Ivanov and Y. M. Valit, Radiative and hadronic decays of heavy vector mesons, Z. Phys. C 67, 633 (1995).
A. Deandrea, N. Di Bartolomeo, R. Gatto, G. Nardulli, and A. D. Polosa, A Constituent quark meson model for heavy meson processes, Phys. Rev. D 58, 034004 (1998).
P. Colangelo, F. De Fazio, and G. Nardulli, $D^{*}$ radiative decays and strong coupling of heavy mesons with soft pions in a QCD relativistic potential model, Phys. Lett. B 334, 175 (1994).
H. B. Deng, X. L. Chen, and W. Z. Deng, Meson decays in an extended Nambu–Jona-Lasinio model with heavy quark flavors, Chin. Phys. C 38, 013103 (2014).
A. H. Orsland and H. Hogaasen, Strong and electromagnetic decays for excited heavy mesons, Eur. Phys. J. C 9, 503 (1999).
W. Jaus, Semileptonic, radiative, and pionic decays of $B$ , $B^{*}$ and $D$ , $D^{*}$ mesons, Phys. Rev. D 53, 1349 (1996).
J. L. Goity and W. Roberts, Radiative transitions in heavy mesons in a relativistic quark model, Phys. Rev. D 64, 094007 (2001).
D. Ebert, R. N. Faustov, and V. O. Galkin, Radiative M1 decays of heavy light mesons in the relativistic quark model, Phys. Lett. B 537, 241 (2002).
H. M. Choi, Decay constants and radiative decays of heavy mesons in light-front quark model, Phys. Rev. D 75, 073016 (2007).
C. Y. Cheung and C. W. Hwang, Strong and radiative decays of heavy mesons in a covariant model, J. High Energy Phys. 04 (2014) 177.
D. Becirevic and B. Haas, $D^{*} \to D π$ and $D^{*} \to D γ$ decays: Axial coupling and magnetic moment of $D^{*}$ meson, Eur. Phys. J. C 71, 1734 (2011).
G. C. Donald, C. T. H. Davies, J. Koponen, and G. P. Lepage, Prediction of the $D_{s}^{*}$ width from a calculation of its radiative decay in full lattice QCD, Phys. Rev. Lett. 112, 212002 (2014).
M. Ablikim et al., First experimental study of the purely leptonic decay $D_{s}^{* +} \to e^{+} ν_{e}$ , Phys. Rev. Lett. 131, 141802 (2023).
C. T. Tran, M. A. Ivanov, P. Santorelli, and Q. C. Vo, Radiative decays $D_{(s)}^{*} \to D_{(s)} γ$ in covariant confined quark model, Chin. Phys. C 48, 023103 (2024).
B. Pullin and R. Zwicky, Radiative decays of heavy-light mesons and the $f_{H, H^{*}, H_{1}}^{(T)}$ decay constants, J. High Energy Phys. 09 (2021) 023.
P. Colangelo, F. De Fazio, and G. Nardulli, Radiative heavy meson transitions, Phys. Lett. B 316, 555 (1993).
F. E. Close and E. S. Swanson, Dynamics and decay of heavy-light hadrons, Phys. Rev. D 72, 094004 (2005).
M. Jia, W. Li, S. Y. Pei, X. Y. Du, G. Z. Ning, and G. L. Wang, Relativistic effects in the strong and electromagnetic decays of the $D^{*}$ meson, Eur. Phys. J. C 85, 282 (2025).
B. Mohan, C. M. A., and R. Dhir, Systematic study of charm meson M1 radiative transitions, arXiv:2506.10560.
Karliner and J. L. Rosner, Single-photon decays in systems with at least one heavy quark, arXiv:2305.00354.
H. M. Pilkuhn, Relativistic Particle Physics (Springer-Verlag, New York, 1979).
R. N. Lee, A. I. Milstein, and M. Schumacher, Relativistic corrections to the electromagnetic polarizabilities of compound systems, Phys. Rev. A 64, 032507 (2001).
https://inspirehep.net/literature?sort=mostrecent&size=25&page=1&q=CMS-PAS-BPH-24-011. First fully exclusive reconstruction of radiative decays of the $B^{* +}$ , $B^{* 0}$ , and $B_{s}^{* 0}$ mesons and measurement of their masses in proton-proton collisions at $\sqrt{s} = 13 TeV$ .
A. Hayrapetyan et al. (CMS Collaboration), First exclusive reconstruction of the $B^{* +}$ , $B^{* 0}$ , and $B_{s}^{* 0}$ mesons and precise measurement of their masses, arXiv:2508.05820.
A. E. Bondar and A. I. Milstein, Phenomenology of Ds1 mesons radiative transitions, Phys. Rev. D 111, 114019 (2025).
S. Godfrey and N. Isgur, Mesons in a relativized quark model with chromodynamics, Phys. Rev. D 32, 189 (1985).
J. E. Bartelt et al., Observation of the radiative decay $D^{* +} \to D^{+} γ$ , Phys. Rev. Lett. 80, 3919 (1998).
J. L. Rosner and M. B. Wise, Meson masses from SU(3) and heavy quark symmetry, Phys. Rev. D 47, 343 (1993).
J. L. Goity and C. P. Jayalath, Strong and electromagnetic mass splittings in heavy mesons, Phys. Lett. B 650, 22 (2007).
M. Karliner and J. L. Rosner, Status of isospin splittings in mesons and baryons, Phys. Rev. D 100, 073006 (2019).
R. J. Dowdall, C. T. H. Davies, T. C. Hammant, and R. R. Horgan, Precise heavy-light meson masses and hyperfine splittings from lattice QCD including charm quarks in the sea, Phys. Rev. D 86, 094510 (2012).
S. Bhatnagar and E. Gebrehana, Radiative decays of heavy-light quarkonia through $M 1$ and $E 1$ transitions in the framework of the Bethe-Salpeter equation, Phys. Rev. D 102, 094024 (2011).
S. Godfrey, K. Moats, and E. S. Swanson, $B$ and $B_{s}$ meson spectroscopy, Phys. Rev. D 94, 054025 (2016).
Q. F. Lü, T. T. Pan, Y. Y. Wang, E. Wang, and D. M. Li, Excited bottom and bottom-strange mesons in the quark model, Phys. Rev. D 94, 074012 (2016).
V. Kher, N. Devlani, and A. K. Rai, Spectroscopy, decay properties and Regge trajectories of the $B$ and $B_{s}$ mesons, Chin. Phys. C 41, 093101 (2017).
V. Patel, R. Chaturvedi, and A. K. Rai, Spectroscopic properties of $B$ and $B_{s}$ meson using screened potential, arXiv:2201.01120.

Phys. Rev. D 112, 054037– Published 22 September, 2025

Vol. 112, Iss. 5 — 1 September 2025

Received 30 July 2025
Accepted 2 September 2025

DOI: https://doi.org/10.1103/gnyk-r31j

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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Relativistic effects in M1 radiative decays of heavy-light mesons

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