Chiral Particle Decay of Heavy-Light Mesons in a Relativistic Potential Model

TL;DR

This paper calculates decay widths of heavy-light mesons emitting chiral particles using a relativistic potential model, predicts very narrow widths for certain B_s mesons, and discovers new sum rules relating decay widths in the heavy quark limit.

Contribution

It introduces a relativistic framework for decay width calculations of heavy-light mesons and predicts narrow widths and new decay sum rules in the heavy quark limit.

Findings

Predicted narrow widths of a few keV for certain B_s mesons.

Discovered new sum rules for decay widths in the heavy quark limit.

Predicted equal decay widths for specific D_s and B_s meson transitions.

Abstract

Partial decay widths of the heavy-light mesons, $D, D_s, B,$ and $B_s$, emitting one chiral particle ($\pi$ 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 undsicovered $B_s(0^+, 1^+)$ mesons corresponding to ${^{2S+1}L_J}={^3P_0}$ and $"{^3P_1}"$ 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 $m_Q\to \infty$. Among these rules, $ \Gamma(D_{s0}^*(2317)\to D_s+\pi)=\Gamma (D_{s1}(2460)\to D_s^*+\pi) $ and $ \Gamma(B_{s0}^*(5615)\to B_s+\pi)=\Gamma (B_{s1}(5679)\to B_s^*+\pi) $ are predicted to hold with a good accuracy.