Threshold effects in P-wave bottom-strange mesons

Abstract

Using a nonrelativistic constituent quark model in which the degrees of freedom are quark-antiquark and meson-meson components, we have recently shown that the $D^{(\ast )}K$ thresholds play an important role in lowering the mass of the physical $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ states. This observation is also supported by other theoretical approaches such as lattice-regularised QCD or chiral unitary theory in coupled channels. Herein, we extend our computation to the lowest $P$-wave $B_s$ mesons, taking into account the corresponding $J^P=0^{+}$, $1^{+}$ and $2^{+}$ bottom-strange states predicted by the naive quark model and the $BK$ and $B^{\ast }K$ thresholds. We assume that mixing with $B_s^{(\ast )}\eta$ and isospin-violating decays to $B_s^{(\ast )}\pi$ are negligible. This computation is important because there is no experimental data in the $b\bar{s}$ sector for the equivalent $j_q^P=1/2^{+}$ ($D_{s0}^{\ast }(2317)$, $D_{s1}(2460)$) heavy-quark multiplet and, as it has been seen in the $c\bar{s}$ sector, the naive theoretical result can be wrong by more than $100\mathrm{MeV}$. Our calculation allows to introduce the coupling with the $D$-wave $B^{\ast }K$ channel and to compute the probabilities associated with the different Fock components of the physical state.

Comments: 7 pages and 5 figures. arXiv admin note: substantial text overlap with arXiv:1603.07000