Threshold effects in P-wave bottom-strange mesons

TL;DR

This paper investigates the influence of meson-meson thresholds on the masses of bottom-strange P-wave mesons using a nonrelativistic quark model, extending previous work on charm-strange states to predict properties of unmeasured bottom-strange states.

Contribution

It extends a nonrelativistic quark model to bottom-strange mesons, incorporating meson-meson thresholds and mixing effects, providing predictions where experimental data is lacking.

Findings

Threshold effects significantly lower meson masses.

Coupling with D-wave channels affects state probabilities.

Predictions for bottom-strange meson properties without experimental data.

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