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$B_sπ^+$ scattering and search for X(5568) with lattice QCD

We investigate $B_sπ^+$ 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 $B_sπ^+$ 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 $B_sπ^+$ 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 $B_sπ^+$ scattering length is compatible with zero within the error.