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

TL;DR

This paper investigates whether the $X(5568)$ can be described as a $B_s ext{ extpi}$ or $Bar{ extK}$ resonant state using coupled channel analysis, but finds difficulties in interpreting it as a dynamically generated resonance due to regularization issues.

Contribution

The study applies a coupled channel unitarity approach with Heavy Meson Chiral Perturbation Theory to analyze the $X(5568)$ and predicts partner states in other sectors.

Findings

Reproduces the $X(5568)$ spectrum with a pole matching experimental mass and width.

Requires an unphysically large cutoff for regularization, questioning the resonance interpretation.

Predicts partner states in $D$, $D^ extast$, and $B^ extast$ sectors for experimental verification.

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.