Narrow exotic tetraquark mesons in large- Nc QCD

Abstract

Discussing four-point Green functions of bilinear quark currents in large-Nc QCD, we formulate rigorous criteria for selecting diagrams appropriate for the analysis of potential tetraquark poles. We find that both flavor-exotic and cryptoexotic (i.e., flavor-nonexotic) tetraquarks, if such poles exist, have a width of order O(1/N 2 c ), so they are parametrically narrower compared to the ordinaryqq mesons, which have a width of order O(1/Nc). Moreover, for flavor-exotic states, the consistency of the large-Nc behavior of "direct" and "recombination" Green functions requires two narrow flavorexotic states, each coupling dominantly to one specific meson-meson channel.PACS numbers: 11.15. Pg, 12.38.Lg, 12.39.Mk, 14.40.Rt MOTIVATIONTo provide the theoretical understanding of exotic tetraquark mesons, many candidates for which have been reported in the recent years (see [1,2]), it is conventional to refer to QCD with a large number of colors N c [i.e., SU(N c ) gauge theory for large N c ] with a simultaneously decreasing coupling α s ∼ 1/N c [3,4]: at N c -leading order, large-N c QCD Green functions have only non-interacting mesons as intermediate states; tetraquark bound states may emerge only in N c -subleading diagrams [5]. For many years, this fact was believed to provide the theoretical explanation of the non-existence of exotic tetraquarks. However, as emphasized in [6], even if the exotic tetraquark bound states appear only in subleading diagrams, the crucial question is the width of these objects: if narrow, they might be well observed in nature. The conclusion of [6] was that, if tetraquark states exist, they may be as narrow as the ordinary mesons, i.e., have a width ∼ 1/N c . This issue has been further addressed in [7], discussing the dependence of the width of tetraquark mesons on their flavor structure. Finally, [8] reported for the cryptoexotic tetraquarks an even smaller width of order N −3 c . Before drawing a conclusion about the width of a potential tetraquark pole in large-N c QCD, it is mandatory to formulate rigorous criteria for selecting those QCD diagrams that may lead to the appearance of this pole: the crucial property of such sequence of diagrams is the presence of four-quark intermediate states and the corresponding cuts in the variable s if one expects to observe a tetraquark pole in s [9]. The presence of such a four-particle s-cut should be established on the basis of the Landau equations [10]. It turns out that some of the diagrams attributed to the tetraquark pole in previous analyses are lacking the necessary four-particle cut and thus may not be related to the tetraquark properties. According to our findings, the tetraquark width at large N c does not depend on its flavor structure: both flavor-exotic and flavor-nonexotic tetraquarks have the same width of order 1/N 2 c . We analyse four-point Green functions of bilinear quark currents of various flavor content; any such function depends on six kinematical variables: the four momenta squared of the external currents,, and the two...

Cluster reducibility of multiquark operators

“…12. Properties of possibly existing tetraquarks have been studied for large values of N c in [21][22][23][24][25][26][27][28][29]. General cases of multiquarks have been considered in [30].…”

Tetraquark-adequate formulation of QCD sum rules

“…Before adopting QCD sum-rule techniques for extracting information on the basic properties of multiquark states, such as tetraquarks and pentaquarks, two issues have to be settled: an, or even the most, suitable choice of interpolating operators and the formulation of a selection criterion ensuring an unambiguous identification of all relevant QCD contributions to the correlators considered [6,7].…”

“…The set of all tetraquark-phile Feynman diagrams is straightforwardly characterized [6] by the behaviour of each member as function of the appropriate Mandelstam variable s: any member has to depend nonpolynomially, i.e., nontrivially, on s and to enable one or more proper four-quark intermediate states, by exhibiting branch cuts starting at branch points defined by the sum of the masses of the involved bound-state constituents, i.e., at…”

“…5(b)] cannot support a tetraquark pole: only Feynman diagrams of order O(α 2 s ) [ Fig. 5(c)] or higher may be considered as tetraquark-phile [6,7]. Following this line of argument and implementing the insights gained, one ends up with a novel kind of QCD sum rules, tailored to the requirements of tetraquark analyses, of the generic shape [11] ( fā bcd ) 2 exp(−M 2 τ) = involving the variable τ introduced by Borel transformation, τ-dependent [3][4][5] effective thresholds s eff , and spectral densities ρ p,r in flavour-preserving and flavour-rearranging instances, governed (as perforce also the power corrections) by exclusively tetraquark-phile contributions to the correlators.…”

Tetraquark and two-meson states at large $$N_{\mathrm {c}}$$ N c

“…The internal structure of these tetraquarks, expressed as a quark quadrilinear, would be of the form of a product of two color-singlet bilinears. Part of the results above has been presented in [24]. …”