Where does the X(5568) structure come from?

Abstract

We study the semi-exclusive production of $\pi^\pm B_s^0$ pairs in hadron colliders which is associated with the $X(5568)$ structure observed by the D0 Collaboration in 2016, but that was not confirmed by LHCb and CMS later. The reason of its appearance in the D0 and absence in LHCb and CMS is discussed in this letter. In a semi-exclusive process, one might miss the third particle which is produced together with the $\pi^\pm B_s^0$ simultaneously. In the three-body Dalitz plot, once the remaining region is narrow enough after the kinematic cuts, its reflection to another invariant mass distribution will accumulate a large number of events within a specific energy region. If there is an enhancement in the remaining region, it will make the reflection structure more pronounced. The precise line shape of the reflection will depend on the specific interaction form. A combined study of different cone cuts and the low-energy dynamics, e.g. the Landau singularity, demonstrates that the $X(5568)$ structure could come from this kinematic reflection. This conclusion can be checked by both searching for the enhancement in another invariant mass distribution, such as $B_s^0\bar{B}^0$, and the cone cut dependence of the $X(5568)$ mass. Such a combined study can be used to distinguish the effects of the triangle singularity from a genuine state. We also propose how to avoid this kinematic reflection in future experimental analysis.