Abstract
The properties of possibly existing tetraquarks are studied in the large-Nc limit of QCD by means of four-point correlation functions of meson currents. The necessity of a detailed analysis of the singularities of Feynman diagrams, by means of the Landau equations, to recognize those diagrams that might contribute to the formation of tetraquark states, is emphasized. It is found, in general, that tetraquarks, if they exist, should have narrow widths of the order of N-2c.
Highlights
In the limit of large numbers of colour, Nc, with a simultaneous decrease of the coupling constant g as Nc−1/2, QCD simplifies and provides many qualitative predictions for hadron physics [1, 2]
That if tetraquarks exist as bound states in the large-Nc limit with finite masses, the crucial point is, even if they contribute to subleading diagrams, the qualitative property of their decay widths: are they broad or narrow? In the latter case, they might be observable
The analysis of the s-channel singularities of Feynman diagrams is crucial for the detection of the possible presence of tetraquark intermediate states in correlation functions of meson currents
Summary
In the limit of large numbers of colour, Nc, with a simultaneous decrease of the coupling constant g as Nc−1/2, QCD simplifies and provides many qualitative predictions for hadron physics [1, 2]. At leading order of Nc, QCD correlation functions of quark colour-neutral bilinear operators have only non-interacting ordinary mesons as intermediate states, made essentially of a pair of quark and antiquark fields, together with gluon fields [2] This result, together with the fact that quark quadrilinear colour-neutral operators can always be decomposed, by means of Fierz transformations, into combinations involving colour-neutral quark bilinears, has been considered as a sign of the nonexistence of stable exotic mesons, like tetraquarks, made of two quark and two antiquark fields, together with gluons, surviving the above limit [3]. He has shown that, generally, they should be narrow, with decay widths of the order of Nc−1 [4]. The possibility of smaller decay widths has been reported in [7]
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