Relativistic effects in the strong and electromagnetic decays of the meson

Man Jia; Wei Li; Su-Yan Pei; Xin-Yao Du; Guo-Zhu Ning; Guo-Li Wang

doi:10.1140/epjc/s10052-025-13974-9

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 282
https://doi.org/10.1140/epjc/s10052-025-13974-9

Regular Article - Theoretical Physics

Relativistic effects in the strong and electromagnetic decays of the $D^{}$ ${D^}$ meson

Man Jia¹^,2^,3, Wei Li⁴, Su-Yan Pei¹^,2^,3, Xin-Yao Du¹^,2^,3, Guo-Zhu Ning¹^,2^,3 and Guo-Li Wang¹^,2^,3^a

¹ Department of Physics, Hebei University, 071002, Baoding, China
² Hebei Key Laboratory of High-precision Computation and Application of Quantum Field Theory, Hebei University, 071002, Baoding, China
³ Hebei Research Center of the Basic Discipline for Computational Physics, Hebei University, 071002, Baoding, China
⁴ College of Science, Hebei Agriculture University, 071001, Baoding, China

^a wgl@hbu.edu.cn

Received: 17 December 2024
Accepted: 19 February 2025
Published online: 12 March 2025

Abstract

In this paper, we solve the complete Salpeter equation and use the obtained relativistic wave function to calculate the strong and radiative electromagnetic decays of the $D^{*}$ ${D^*}$ meson. We obtain the results $Γ (D^{*} {(2007)}^{0} \to D^{0} π^{0}) = 34.6 keV$ $\Gamma (D^{*}(2007)^{0}\rightarrow D^{0}\pi ^{0})=34.6~\textrm{keV}$ and $Γ (D^{*} {(2007)}^{0} \to D^{0} γ) = 19.4 keV$ $\Gamma (D^{*}(2007)^{0}\rightarrow D^{0}\gamma )=19.4~\textrm{keV}$ , and the estimated full width is $Γ (D^{*} {(2007)}^{0}) = 54.0 keV$ $\Gamma (D^{*}(2007)^{0})=54.0~\textrm{keV}$ . The focus of this study is on the relativistic corrections. In our method, the wave function of the D meson is not a pure S-wave, but includes both a non-relativistic S-wave and a relativistic P-wave, while the wave function of the $D^{*}$ $$D^*$$ meson includes a non-relativistic S-wave as well as both relativistic P-wave and D-wave. Therefore, in this case, the decay $D^{*} \to D γ$ ${D^{*}\rightarrow {D}\gamma }$ is not a non-relativistic M1 transition, but rather an $M 1 + E 2 + M 3 + E 4$ $$M1+E2+M3+E4$$ decay. We find that in a strong decay $D^{*} \to D π$ $D^{*}\rightarrow {D}{\pi }$ , the non-relativistic contribution is dominant, while in an electromagnetic decay $D^{*} \to D γ$ ${D^{*}\rightarrow {D}\gamma }$ , the relativistic correction is dominant.

© The Author(s) 2025

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