$P$-wave coupled-channel scattering of $B_s\pi,\,B_s^*\pi,\,B\overline K,\,B^{*}\overline K$ and the puzzling $X(5568)$

TL;DR

This paper investigates the nature of the $X(5568)$ resonance using coupled-channel scattering theory and finds no evidence of it being a dynamically generated molecular state, challenging previous interpretations.

Contribution

The study applies unitarized Heavy Meson Chiral Perturbation Theory to analyze the $P$-wave coupled-channel scattering and demonstrates the non-existence of a $X(5568)$ pole as a molecular state.

Findings

No $X(5568)$ pole is found in the $T$-matrix.

The results disfavor the molecular interpretation of $X(5568)$.

The model's parameters are tightly constrained by symmetry and naturalness.

Abstract

The D0 Collaboration has recently reported a narrow peak structure in the $B_s^0\pi^\pm$ invariant-mass spectrum, that is called $X(5568)$. Its proposed quantum numbers $J^P=0^+/1^+$ are not determined unambiguously, and we show that one can fit the data assuming $J^P=1^-$ with the same mass and width for the resonance signal. The corresponding isovector $P$-wave coupled-channel scattering involving the states $B_s\pi$, $B_s^*\pi$, $B \overline{K}$ and $B^*\overline K$ is studied employing leading-order Heavy Meson Chiral Perturbation Theory, which is then unitarized making use of standard techniques from Unitary Chiral Perturbation Theory. The subtraction constants that appear in the unitarization process are determined by a $u$-channel crossing symmetry constraint or by naturalness arguments, being the numerical values obtained in both cases quite closed, and no further freedom is left in the model. A crucial point is that if the $X(5568)$ is $1^-$ and decaying into $B_s^0\pi^\pm$ then it should appear as a pole in the $T$-matrix elements. It finally turns out that no $X(5568)$ pole is found that can be qualified as dynamically generated from the isovector $P$-wave coupled-channel dynamics. This result disfavors the interpretation of the $X(5568)$ within a "molecular" picture.