Threshold effects in P-wave bottom-strange mesons

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 $100\,{\rm MeV}$. 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.