Prediction of positive parity $B_s$ mesons and search for the $X(5568)$

Abstract

We use a combination of quark-antiquark and $B^{(\ast )}K$ interpolating fields to predict the mass of two QCD bound states below the $B^{\ast }K$ threshold in the quantum channels $J^P=0^{+}$ and $1^{+}$. The mesons correspond to the b-quark cousins of the $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ and have not yet been observed in experiment, even though they are expected to be found by LHCb. In addition to these predictions, we obtain excellent agreement of the remaining p-wave energy levels with the known $B_{s1}(5830)$ and $B_{s2}^{\ast }(5840)$ mesons. The results from our first principles calculation are compared to previous model-based estimates. More recently the D0 collaboration claimed the existence of an exotic resonance $X(5568)$ with exotic flavor content $\bar{b}s\bar{d}u$. If such a state with $J^P=0^{+}$ exists, only the decay into $B_s\pi$ is open which makes a lattice search for this state much cleaner and simpler than for other exotic candidates involving heavy quarks. We conclude, however, that we do not find such a candidate in agreement with a recent LHCb result.

Comments: 7 pages; Proceedings for the 34th International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK