Study of Structure of the Mass Gap between Two Spin Multiplets

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.