Relativistic effects in the strong and electromagnetic decays of the $${D^*}$$ D ∗ meson - Man Jia; Wei Li; Su-Yan Pei; Xin-Yao Du; Guo-Zhu Ning; Guo-Li Wang (European Physical Journal C: Particles and Fields)
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 $$Γ (D^{*}(2007)^{0}→ D^{0}π ^{0})=34.6~keV$$ Γ ( D ∗ ( 2007 ) 0 → D 0 π 0 ) = 34.6 keV and $$Γ (D^{*}(2007)^{0}→ D^{0}γ )=19.4~keV$$ Γ ( D ∗ ( 2007 ) 0 → D 0 γ ) = 19.4 keV , and the estimated full width is $$Γ (D^{*}(2007)^{0})=54.0~keV$$ Γ ( D ∗ ( 2007 ) 0 ) = 54.0 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 $${D^{*}→ Dγ }$$ D ∗ → D γ is not a non-relativistic M1 transition, but rather an $$M1+E2+M3+E4$$ M 1 + E 2 + M 3 + E 4 decay. We find that in a strong decay $$D^{*}→ D{π }$$ D ∗ → D π , the non-relativistic contribution is dominant, while in an electromagnetic decay $${D^{*}→ Dγ }$$ D ∗ → D γ , the relativistic correction is dominant.