Structure of mass gap between two spin multiplets

Studying our semirelativistic potential model and the numerical results, which succeeds in predicting and reproducing recently discovered higher resonances of D, Ds, B, and Bs, 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−)≈ΛQ−mq in the limit of heavy quark symmetry, and including 1/mQ corrections, we have ΔM≈ΛQ−mq+(1.28×105+4.26×102⋅mq)/mQ with ΛQ≈300MeV, a light quark mass mq, and a heavy quark mass mQ. This equation holds both for D and Ds heavy mesons. Our model calculations for the B and Bs also follow this formula.