Line Shapes of the X(3872)

TL;DR

This paper models the line shapes of the X(3872) resonance considering its possible molecular or virtual state nature, accounting for the D^{*0} width and inelastic channels, and fits experimental data to determine its bound or virtual state status.

Contribution

It introduces a simple approximation for the line shapes of X(3872) that includes the D^{*0} width and inelastic effects, and applies it to experimental data analysis.

Findings

X(3872) is likely a bound state just below the D^{*0} Dbar^0 threshold.

A virtual state just above the threshold cannot be ruled out.

The model successfully fits the experimental line shapes from Belle data.

Abstract

If the quantum numbers of the X(3872) are J^{PC}=1^{++}, the measurement of its mass implies that it is either a loosely-bound hadronic molecule whose constituents are a superposition of the charm mesons pairs D^{*0} Dbar^0 and D^0 Dbar^{*0} or else it is a virtual state of these charm mesons. Its binding energy is small enough that the decay width of a constituent D^{*0} or Dbar^{*0} has a significant effect on the line shapes of the X resonance. We develop a simple approximation to the line shapes that takes into account the effect of the D^{*0} width as well as inelastic scattering channels of the charm mesons. We carry out a simultaneous fit to the line shapes in the J/psi pi^+ pi^- and D^0 Dbar^0 pi^0 channels measured in the decays B^+ to K^+ + X by the Belle Collaboration. The best fit corresponds to the X(3872) being a bound state just below the D^{*0} Dbar^0 threshold, but a virtual state just above the D^{*0} D-ar^0 threshold is not excluded.