Near Mass Degeneracy in the Scalar Meson Sector: Implications for $B_{(s)0}^{\ast }$ and $B_{(s)1}^{\mathrm{\prime }}$ Mesons

The empirical observation of near degeneracy of scalar mesons above 1 GeV, namely, the mass of the strange-flavor scalar meson is similar to that of the non-strange one, is at variance with the naive expectation of the quark model. Qualitatively, the approximate mass degeneracy can be understood as a consequence of self-energy effects due to strong coupled channels which will push down the mass of the heavy scalar meson in the strange sector more than that in the non-strange partner. However, it works in the conventional model without heavy quark expansion, but not in the approach of heavy meson chiral perturbation theory as mass degeneracy and the physical masses of $D_{s0}^{\ast }$ and $D_0^{\ast }$ cannot be accounted for simultaneously. In the heavy quark limit, near mass degeneracy observed in the scalar charm sector will imply the same phenomenon in the $B$ system. We have the prediction $M_{B_0^}\approx M_{B_{s0}^}\approx 5715,{\rm MeV}+\delta\Delta_S$ based on heavy quark symmetry and the leading-order QCD correction, where $\delta {\mathrm{\Delta }}_S$ arises from $1\mathrm{/}{m}_Q$ corrections. A crude estimate indicates that $\delta {\mathrm{\Delta }}_S$ is of order $-35$ MeV or less. We stress that the closeness of $B_{s0}^{\ast }$ and $B_0^{\ast }$ masses implied by heavy quark symmetry is not spoiled by $1\mathrm{/}{m}_Q$ or QCD corrections. The mass-shift effect on $K_0^{\ast }(1430)$ is discussed.