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Abstract
Considering four-point correlation functions of color-singlet quark bilinears, we investigate, in the large-N_{mathrm {c}} limit of QCD, the subleading diagrams that involve, in the s-channel of meson–meson scattering amplitudes, two-quark–two-antiquark intermediate states. The latter contribute, together with gluon exchanges, to the formation, at the hadronic level, of two-meson and tetraquark intermediate states. It is shown that the two-meson contributions, which are predictable, in general, from leading-order N_{mathrm {c}}-behaviors, consistently satisfy the constraints resulting from the 1/N_{mathrm {c}} expansion procedure and thus provide a firm basis for the extraction of tetraquark properties from N_{mathrm {c}}-subleading diagrams. We find that, in general, tetraquarks, if they exist in compact form, should have narrow decay widths, of the order of N_{mathrm {c}}^{-2}. For the particular case of exotic tetraquarks, involving four different quark flavors, two different types of tetraquark are needed, each having a preferred decay channel, to satisfy the consistency constraints.
Highlights
On the other hand, it is generally admitted that in ’t Hooft’s large-Nc limit of QCD [14], with the coupling constant g scaling as Nc−1/2 and with the quark fields belonging to the fundamental representation of the color gauge group SU(Nc), the theory catches the main properties of confinement, while being liberated from secondary screening phenomena, such as quark pair creation or inelasticity effects
Considering four-point correlation functions of color-singlet quark bilinears, we investigate, in the largeNc limit of QCD, the subleading diagrams that involve, in the s-channel of meson–meson scattering amplitudes, two-quark–two-antiquark intermediate states
It is generally admitted that in ’t Hooft’s large-Nc limit of QCD [14], with the coupling constant g scaling as Nc−1/2 and with the quark fields belonging to the fundamental representation of the color gauge group SU(Nc), the theory catches the main properties of confinement, while being liberated from secondary screening phenomena, such as quark pair creation or inelasticity effects. Applying this approach to color-neutral quark bilinear operators, Witten has shown that in this limit the related QCD correlation functions are saturated by noninteracting meson states [15]
Summary
It is generally admitted that in ’t Hooft’s large-Nc limit of QCD [14], with the coupling constant g scaling as Nc−1/2 and with the quark fields belonging to the fundamental representation of the color gauge group SU(Nc), the theory catches the main properties of confinement, while being liberated from secondary screening phenomena, such as quark pair creation or inelasticity effects. Considering a class of candidate operators, he showed that if tetraquarks exist in the large-Nc limit as bound states with finite masses, they should have narrow widths, of the order of Nc−1, like those of the ordinary mesons, and would be observable [17] In complement to the latter result, Knecht and Peris have stressed that depend-. [17], O(Nc−1), stems from the fact that color-planar diagrams, with one external quark loop and without internal quark loops, do not have s-channel four-quark singularities This eliminates the potential presence of tetraquark intermediate states in such types of diagram and reduces the magnitude of the tetraquark–two-meson transition amplitudes. For recent reviews on the experimental properties of tetraquark candidates and their theoretical interpretations, we refer the reader to Refs. [25–35]
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