Line Shapes of the Z(4430)

TL;DR

This paper analyzes the line shapes of the Z(4430) meson, interpreting it as a charm meson molecule, and predicts its decay widths and line shape features based on its proximity to D_1 D* threshold.

Contribution

It provides a theoretical interpretation of Z(4430) as a D_1 D* molecule and predicts specific line shape features and decay widths consistent with experimental data.

Findings

Predicted full width at half maximum of about 35 MeV.

Line shape for D* D* pi is broader and asymmetric.

Peak in D* D* pi occurs ~6 MeV higher than in psi' pi^+.

Abstract

The Belle Collaboration recently discovered the first manifestly exotic meson: Z^+(4430), which decays into psi' pi^+ and therefore has quark content c c-bar u d-bar. The proximity of its mass to the D_1 D-bar^* threshold has motivated the interpretation of the Z^+ as a charm meson molecule whose constituents are an S-wave superposition of D_1^+ D-bar^{*0}$ and D^{*+} D-bar_1^0$. If this interpretation is correct, the small ratio of the binding energy of the Z^+ to the width Gamma_1 of its constituent D_1 can be exploited to predict properties of its line shapes. Its full width at half maximum in the channel psi' pi^+ should be approximately sqrt{3} Gamma_1 = 35 MeV, which is consistent with the measured width of the Z^+. The Z^+ should also decay into D^* D-bar^* pi through decay of its constituent D_1. The peak in the line shape for D^* D-bar^* pi should be at a higher energy than the peak in the line shape for psi' pi^+ by about Gamma_1/sqrt{12} = 6 MeV. The line shape in D^* D-bar^* pi should also be broader and asymmetric, with a shoulder on the high energy side that can be attributed to a threshold enhancement in the production of D_1 D-bar^*.