Chiral particle decay of heavy-light mesons in a relativistic potential model

Abstract

Partial decay widths of the heavy-light mesons, $D$, ${D}_{s}$, $B$, and ${B}_{s}$, emitting one chiral particle ($\ensuremath{\pi}$ or $K$) are evaluated in the framework of a relativistic potential model. Decay amplitudes are calculated by keeping the Lorentz invariance as far as possible and use has been made of the Lorentz-boosted relativistic wave functions of the heavy-light mesons. One of predictions of our calculation is very narrow widths of a few keV for yet undiscovered ${B}_{s}({0}^{+},{1}^{+})$ mesons corresponding to $^{2S+1}L_{J}=^{3}P_{0}$ and ``$^{3}P_{1}$'' assuming their masses to be 5617 and 5682 MeV, respectively, as calculated in our former paper. In the course of our calculation, new sum rules are discovered on the decay widths in the limit of ${m}_{Q}\ensuremath{\rightarrow}\ensuremath{\infty}$. Among these rules, $\ensuremath{\Gamma}({D}_{s0}^{*}(2317)\ensuremath{\rightarrow}{D}_{s}+\ensuremath{\pi})=\ensuremath{\Gamma}({D}_{s1}(2460)\ensuremath{\rightarrow}{D}_{s}^{*}+\ensuremath{\pi})$ and $\ensuremath{\Gamma}({B}_{s0}^{*}(5615)\ensuremath{\rightarrow}{B}_{s}+\ensuremath{\pi})=\ensuremath{\Gamma}({B}_{s1}(5679)\ensuremath{\rightarrow}{B}_{s}^{*}+\ensuremath{\pi})$ are predicted to hold with a good accuracy.