Three-body $D\bar{D}\pi$ dynamics for the X(3872)

TL;DR

This study examines how dynamical pions influence the properties of the X(3872) resonance, revealing that pion dynamics significantly reduce the resonance width and affect line shapes, with minimal impact on the pole residue.

Contribution

It provides a detailed analysis of the impact of dynamical pions on the X(3872), highlighting the reduction in width and the weak sensitivity of the pole residue to pion effects.

Findings

Dynamical pions reduce the width of X(3872) by about a factor of 2 near threshold.

The pole residue of X(3872) is weakly affected by pion dynamics.

Coupled-channel effects have a moderate impact on the results.

Abstract

We investigate the role played by the three-body $D\bar{D}\pi$ dynamics on the near-threshold resonance X(3872) charmonium state, which is assumed to be formed by nonperturbative $D\bar D^*$ dynamics. It is demonstrated that, as compared to the naive static-pions approximation, the imaginary parts that originate from the inclusion of dynamical pions reduce substantially the width from the $D\bar{D}\pi$ intermediate state. In particular, for a resonance peaked at 0.5 MeV below the $D^0\bar D^{*0}$ threshold, this contribution to the width is reduced by about a factor of 2, and the effect of the pion dynamics on the width grows as long as the resonance is shifted towards the $D^0\bar{D^0}\pi^0$ threshold. Although the physical width of the $X$ is dominated by inelastic channels, our finding should still be of importance for the $X$ line shapes in the $D\bar{D}\pi$ channel below $D{\bar D}^*$ threshold. For example, in the scattering length approximation, the imaginary part of the scattering length includes effects of all the pion dynamics and does not only stem from the $D^*$ width. Meanwhile, we find that another important quantity for the $X$ phenomenology, the residue at the $X$ pole, is weakly sensitive to dynamical pions. In particular, we find that the binding energy dependence of this quantity from the full calculation is close to that found from a model with pointlike $D\bar D^*$ interactions only, consistent with earlier claims. Coupled-channel effects (inclusion of the charged $D\bar{D}^*$ channel) turn out to have a moderate impact on the results.