Triangle Singularities and XYZ Quarkonium Peaks

TL;DR

This paper analyzes how anomalous branch points from crossed-channel exchanges can enhance threshold cusps, potentially explaining XYZ quarkonium peaks like Zc(3900) and Zb(10610).

Contribution

It reveals that specific anomalous singularities near thresholds can significantly enhance observed peaks, providing a novel explanation for XYZ states.

Findings

Anomalous branch points can enhance threshold cusps near resonance masses.

The effect occurs only within a narrow mass range of crossed-channel resonances.

Estimated size of threshold enhancements matches observed XYZ peaks.

Abstract

We discuss analytical properties of partial waves derived from projection of a 4-legged amplitude with crossed-channel exchanges in the kinematic region of the direct channel that corresponds to the XYZ peaks in charmonium and bottomonium. We show that in general partial waves can develop anomalous branch points in the vicinity of the direct channel physical region. In a specific case, when these branch points lie on the opposite side of the unitary cut they pinch the integration contour in a dispersion relation and if the pinch happens close to threshold, the normal threshold cusp is enhanced. We show that this effect only occurs if masses of resonances in the crossed channel are in a specific, narrow range. We estimate the size of threshold enhancements originating from these anomalous singularities in reactions where the Zc(3900) and the Zb(10610) peaks have been observed.