Structure of Mass Gap between Two Spin Multiplets

Matsuki, Takayuki; Morii, Toshiyuki; Sudoh, Kazutaka

Structure of Mass Gap between Two Spin Multiplets

Authors

Matsuki, Takayuki

Morii, Toshiyuki

Sudoh, Kazutaka

Description

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 $ΔM=M(0^+)-M(0^-)$ and/or $M(1^+)-M(1^-)$ is given by $ΔM=M(0^+)-M(0^-)=M(1^+)-M(1^-)\approx Λ_{\rm Q}-m_q$ in the limit of heavy quark symmetry, and including $1/m_Q$ corrections, we have $ΔM\approx Λ_{\rm Q}-m_q+(1.28\times 10^{5}+4.26\times 10^{2}\cdot m_q)/m_Q$ with $Λ_{\rm Q}\approx 300$ 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.
6 pages, 2 figures