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arXiv · 1711.03925

Constraints from the $1/N_{\rm c}$ Expansion on Properties of Exotic Tetraquark Mesons

Wolfgang Lucha·Dmitri Melikhov·Hagop Sazdjian
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Abstract

Scrutinizing the scattering of ordinary mesons in the limiting case of the number of colour degrees of freedom $N_{\rm c}$ of quantum chromodynamics 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-$N_{\rm c}$ 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 $N_{\rm c},$ like $1/N_{\rm c}^2$ and thus decrease faster than those of ordinary mesons.

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Wolfgang Lucha, Dmitri Melikhov, Hagop Sazdjian. 2017-11-10. Constraints from the $1/N_{\rm c}$ Expansion on Properties of Exotic Tetraquark Mesons. https://arxiv.org/abs/1711.03925

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