Structure of 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 $\Delta M=M(0^{+})-M(0^{-})=M(1^{+})-M(1^{-})\approx {\Lambda }_{\mathrm{Q}}-m_q$ in the limit of heavy quark symmetry, and including $1/m_Q$ corrections, we have $\Delta M\approx {\Lambda }_{\mathrm{Q}}-m_q+(1.28\times 10^5+4.26\times 10^2\cdot m_q)/m_Q$ with ${\Lambda }_{\mathrm{Q}}\approx 300$ 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.

Comments: 6 pages, 2 figures