Study of Structure of the Mass Gap between Two Spin Multiplets

TL;DR

This paper presents a simple expression for the mass gap between two spin multiplets of heavy-light mesons, validated through a semirelativistic potential model that aligns with recent resonance discoveries.

Contribution

It introduces a straightforward formula for the mass gap between spin multiplets, incorporating heavy quark symmetry and $1/m_Q$ corrections, advancing understanding of meson structure.

Findings

Mass gap approximates to $ ext{Lambda}_{ m Q} - m_q$ in heavy quark limit.

The model successfully predicts and reproduces recent higher resonance data.

Inclusion of $1/m_Q$ corrections refines the mass gap estimate.

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. We also study the case including $1/m_Q$ corrections.