How can $X^{\pm}(5568)$ escape detection?

Abstract

Multi-quark states were predicted by Gell-Mann when the quark model was first formulated. Recently, numerous exotic states that are considered to be multi-quark states have been experimentally confirmed (four-quark mesons and five-quark baryons). Theoretical research indicates that the four-quark state might comprise molecular and/or tetraquark structures. We consider that the meson containing four different flavors $su\bar b\bar d$ should exist and decay via the $X(5568)\to B_sπ$ channel. However, except for the D0 collaboration, all other experimental collaborations have reported negative observations for $X(5568)$ in this golden portal. This contradiction has stimulated the interest of both theorists and experimentalists. To address this discrepancy, we propose that the assumed $X(5568)$ is a mixture of a molecular state and tetraquark, which contributes destructively to $X(5568)\to B_sπ$. The cancellation may be accidental and it should be incomplete. In this scenario, there should be two physical states with the same flavor ingredients, with spectra of $5344\pm307$ and $6318\pm315$. $X(5568)$ lies in the error range of the first state. We predict the width of the second state (designated as $S_2$) as $Γ(X_{S_2}\to B_sπ)=224\pm97$ MeV. We strongly suggest searching for it in future experiments.