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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 proposedquantum numbers $J^P=0^+/1^+$ are not determined unambiguously, and we showthat one can fit the data assuming $J^P=1^-$ with the same mass and width forthe resonance signal. The corresponding isovector $P$-wave coupled-channelscattering involving the states $B_s\pi$, $B_s^*\pi$, $B \overline{K}$ and$B^*\overline K$ is studied employing leading-order Heavy Meson ChiralPerturbation Theory, which is then unitarized making use of standard techniquesfrom Unitary Chiral Perturbation Theory. The subtraction constants that appearin the unitarization process are determined by a $u$-channel crossing symmetryconstraint or by naturalness arguments, being the numerical values obtained inboth cases quite closed, and no further freedom is left in the model. A crucialpoint is that if the $X(5568)$ is $1^-$ and decaying into $B_s^0\pi^\pm$ thenit should appear as a pole in the $T$-matrix elements. It finally turns outthat no $X(5568)$ pole is found that can be qualified as dynamically generatedfrom the isovector $P$-wave coupled-channel dynamics. This result disfavors theinterpretation of the $X(5568)$ within a "molecular" picture.

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

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