$B_s{\pi }^{+}$ scattering and search for X(5568) with lattice QCD

Abstract

We investigate $B_s{\pi }^{+}$ scattering in s-wave using lattice QCD in order to search for an exotic resonance X(5568) with flavor $\bar{b}s\bar{d}u$; such a state was recently reported by D0 but was not seen by LHCb. If X(5568) with $J^P=0^{+}$ exists, it can strongly decay only to $B_s{\pi }^{+}$ and lies significantly below all other thresholds, which makes a lattice search for X(5568) cleaner and simpler than for other exotic candidates. Both an elastic resonance in $B_s{\pi }^{+}$ as well as a deeply bound $B^{+}{\bar{K}}^0$ would lead to distinct signatures in the energies of lattice eigenstates, which are not seen in our simulation. We therefore do not find a candidate for X(5568) with $J^P=0^{+}$ in agreement with the recent LHCb result. The extracted $B_s{\pi }^{+}$ scattering length is compatible with zero within the error.

arXiv comment8 pages, 4 figures, version to appear in Phys. Rev. D, new Section III added which provides details of the calculation, results and conclusions unchanged

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