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

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

Comments: 15 pages, 2 figures, revised version published in EPJC