Can $X(5568)$ be described as a $B_s\pi$, $B\bar{K}$ resonant state?

Abstract

The D0 Collaboration has recently seen a resonant-like peak in the $B_s\pi$ invariant mass spectrum, claimed to be a new state called $X(5568)$. Using a $B_s\pi$--$B\bar{K}$ coupled channel analysis, implementing unitarity, and with the interaction derived from Heavy Meson Chiral Perturbation Theory, we are able to reproduce the reported spectrum, with a pole that can be associated to the claimed $X(5568)$ state, and with mass and width in agreement with the ones reported in the experimental analysis. However, if the $T$-matrix regularization is performed by means of a momentum cutoff, the value for the latter needed to reproduce the spectrum is $\Lambda =2.80\pm 0.04\text{GeV}$, much larger than a "natural" value $\Lambda \simeq 1\text{GeV}$. In view of this, it is difficult to interpret the nature of this new state. This state would not qualify as a resonance dynamically generated by the unitarity loops. Assuming the observed peak to correspond to a physical state, we make predictions for partners in the $D$, $D^{\ast }$, and $B^{\ast }$ sectors. Their observation (or lack thereof) would shed light into this issue.