Relativistic effects in the strong and electromagnetic decays of ${D^*}$ 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 $\Gamma(D^{*}(2007)^{0}\to D^{0}\pi^{0})=34.6~\rm{keV}$ and $\Gamma(D^{*}(2007)^{0}\rightarrow D^{0}\gamma)=19.4~\rm{keV}$, and the estimated full width is $\Gamma(D^{*}(2007)^{0})=54.0~\rm{keV}$.} 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.