Tetraquark Cusp Effects from Diquark Pair Production

Abstract

We present the first study of the cusp effect (the movement of resonant poles due to the proximity of multiparticle thresholds) caused by the creation of diquark-antidiquark pairs. The cusp profile for such states is obtained from constituent counting rules. We compare the effectiveness of diquark cusps in moving resonant poles with that from a phenomenological form commonly used for meson-pair creation, and find that mesons tend to be more effective at lower energies $(e.g.$, the $K\overline{K}$ threshold), while diquarks tend to be more effective at the charm [$X(3872)$] scales and above.

Comments: 11 pages, 6 figures, pdflatex. New section added to discuss physical meaning of diquark thresholds; calculations unchanged. Version accepted by Phys. Rev. D