How Resonances can synchronise with Thresholds

TL;DR

This paper investigates how resonances can synchronize with thresholds through a cusp mechanism, analyzing specific mesons to understand the interplay between resonances and threshold effects in particle physics.

Contribution

It introduces a detailed analysis of threshold cusps and their role in resonance formation, applying the concept to mesons like fo(980), X(3872), and Z(4430).

Findings

fo(980) exemplifies the locking mechanism.

X(3872) cannot be explained by a cusp alone.

Z(4430) can be modeled as a resonance or a cusp.

Abstract

The mechanism by which a threshold may capture a resonance is examined. It involves a threshold cusp interfering constructively with either or both (i) a resonance produced via confinement, (ii) attractive t- and u-channel exchanges. The fo(980), X(3872) and Z(4430) are studied in detail. The fo(980) provides a valuable model of the locking mechanism. The X(3872) is too narrow to be fitted by a cusp, and requires either a resonance or virtual state. The Z(4430) can be fitted as a resonance but also can be fitted successfully by a cusp with no nearby resonant pole.