Relativistic effects in the strong and electromagnetic decays of the \({D^*}\) meson

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 \({D^*}\) meson. We obtain the results \(\Gamma (D^{*}(2007)^{0}\rightarrow D^{0}\pi ^{0})=34.6~\textrm{keV}\) and \(\Gamma (D^{*}(2007)^{0}\rightarrow D^{0}\gamma )=19.4~\textrm{keV}\), and the estimated full width is \(\Gamma (D^{*}(2007)^{0})=54.0~\textrm{keV}\). 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 \(D^*\) meson includes a non-relativistic S-wave as well as both relativistic P-wave and D-wave. Therefore, in this case, the decay \({D^{*}\rightarrow {D}\gamma }\) is not a non-relativistic M1 transition, but rather an \(M1+E2+M3+E4\) decay. We find that in a strong decay \(D^{*}\rightarrow {D}{\pi }\), the non-relativistic contribution is dominant, while in an electromagnetic decay \({D^{*}\rightarrow {D}\gamma }\), the relativistic correction is dominant.