Cluster Reducibility of Multiquark Operators and Tetraquark-Adequate QCD Sum Rules

Abstract

If connecting properties of a multiquark hadron with those exhibited by its constituents, QCD sum rules inferred along the routes of traditional wisdom necessarily involve contributions not related at all to and thus not presenting information about multiquarks. Realizing this deficiency, we propose to increase, for the example of tetraquarks, the predictive power of the QCD sum-rule formalism by disposal of all of the unwanted contributions from the very beginning; this move is easily accomplished by subjecting the contributions to our perspicuous selection criterion.

Multiquark-Oriented QCD Sum Rules

“…Armed with our rigorous criterion [14,15] above, for every two-or three-point correlation function it is then a straightforward task to identify the tetraquark-phile [16,17] contributions: Flavour-retaining ones [6,[8][9][10] with no or at most a single gluon exchange [Fig. 1(a,b)] are spatially separable and vanish at all or involve s in merely polynomial form, implying that just ones with two or more relevant gluon exchanges do affect tetraquarks [Fig.…”

“…2(a)]. [6][7][8][9][10] are not spatially separable and will support tetraquarks only if resorting to two or more gluon exchanges, as revealed by the Landau equations [Fig. 2(b,c)].…”

“…• Every flavour-preserving relation (Fig. 3) consists of two kinds of QCD sum rules [6,[8][9][10]; the first of these provides two unconnected QCD sum rules for conventional mesons (Fig. 4) and the second one the required tetraquark-adequate QCD sum rule (Fig.…”

“…• By investing a little bit more efforts, every flavour-rearranging relation may be unscrambled [6][7][8][9][10] and systematically reorganized as two relationships, one that does not [Fig. 6 In addition to the perturbative contributions to the QCD sum rules aimed at, various power corrections have to be considered, too.…”

“…In this context QCD accounts for both perturbative contributions, given by integrals over spectral densities, and nonperturbative power corrections (that involve vacuum condensates multiplied by powers of Borel variables).The colour-singlet bound states governed by QCD encompass not just all quark-antiquark mesons and three-quark baryons, labelled conventional hadrons, but also multiquark hadrons: tetraquarks, pentaquarks, hexaquarks, etc. For attempts to take hold of such exotic hadrons by QCD sum rules, a systematic scrutiny [6][7][8][9][10] points to the necessity of adapting the traditional wisdom to the peculiarities of multiquarks: Retaining just contributions potentially capable of providing information on multiquark features by getting rid of all contributions not related to multiquarks yields the novel sort of multiquark-adequate QCD sum rules; for some tetraquark categories [11], all of the latter involve, at least, two gluon exchanges of appropriate topology.…”