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 f 0 (980), X (3872) and Z (4430) are studied in detail. The f 0 (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.
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D.V. Bugg (2008) studied this question.
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