Structure of Mass Gap between Two Spin Multiplets

TL;DR

This paper derives a simple formula for the mass gap between two spin multiplets of heavy-light mesons, validated by a semirelativistic potential model and numerical results for various mesons.

Contribution

It introduces a universal expression for the mass gap between chiral partner mesons, incorporating heavy quark symmetry and $1/m_Q$ corrections, applicable to multiple meson types.

Findings

Mass gap approximates $ eq ext{Lambda}_Q - m_q$ in heavy quark limit.

The derived formula fits numerical results for $D$, $D_s$, $B$, and $B_s$ mesons.

The model successfully predicts higher resonance masses.

Abstract

Studying our semirelativistic potential model and the numerical results, which succeeds in predicting and reproducing recently discovered higher resonances of $D$, $D_s$, $B$, and $B_s$, we find a simple expression for the mass gap between two spin multiplets of heavy-light mesons, $(0^-,1^-)$ and $(0^+,1^+)$. The mass gap between chiral partners defined by $\Delta M=M(0^+)-M(0^-)$ and/or $M(1^+)-M(1^-)$ is given by $\Delta M=M(0^+)-M(0^-)=M(1^+)-M(1^-)\approx \Lambda_{\rm Q}-m_q$ in the limit of heavy quark symmetry, and including $1/m_Q$ corrections, we have $\Delta M\approx \Lambda_{\rm Q}-m_q+(1.28\times 10^{5}+4.26\times 10^{2}\cdot m_q)/m_Q$ with $\Lambda_{\rm Q}\approx 300$ MeV, a light quark mass $m_q$, and a heavy quark mass $m_Q$. This equation holds both for $D$ and $D_s$ heavy mesons. Our model calculations for the $B$ and $B_s$ also follow this formula.