Constraints from the 1 / N c Expansion on Properties of Exotic Tetraquark Mesons

Abstract

Scrutinizing the scattering of ordinarymesons in the limiting case of the number of colour degrees of freedomNc of quantumchromodynamics approaching infinity, we formulate Feynman-diagram selection criteria and from these deduce rigorous self-consistency conditions for the manifestation of a tetraquark, a two-quark–two-antiquark bound state, as a pole in the corresponding amplitudes. Our constraints bear rather far-reaching consequences: In particular, all flavour-exotic tetraquarks, composed of four (anti)quarks of disparate flavour, must come in, at least, two variants differing in (and thus readily identifiable by) the large-Nc behaviour of their couplings to two ordinary mesons. Quite generally, irrespective of their flavour composition, all tetraquarks prove to be narrow. Their decay rates behave, for large $N_c$, like $1/N_c^2$ and thus decrease faster than those of ordinary mesons.