Using Line Shapes to Discriminate between Binding Mechanisms for the X(3872)

Understand

We construct line shapes for the X(3872) that generalize the Flatte and zero-range line shapes that have been considered previously.

• These line shapes are associated with scattering amplitudes that are exactly unitary for real values of the interaction parameters and can be derived from a renormalizable quantum field theory.
• The new line shapes can be used to discriminate between the alternative binding mechanisms in which the X(3872) is generated either dynamically by charm meson interactions or by a resonance near the D^{*0} Dbar^0 threshold.
• If the resonance is identified with the P-wave charmonium state chi'_{c1}, the interaction parameters can be constrained by using charmonium phenomenology.