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.

Zooming in on Multiquark Hadrons within QCD Sum-Rule Approaches

“…Given the insights established generally for the four-point correlation functions (11), identical conclusions about nature of tetraquark-phile contributions (Fig. 5), decomposition of deduced quark-hadron relations and tetraquark-fitting QCD sum rules will hold for the contraction (7).…”

“…Then, as indicated by Fig. 2, the contraction (6) of a correlation function (11) decomposes into a pair of ordinary-meson QCD sum rules (Fig. 3), and a tetraquark-friendlier QCD sum rule (Fig.…”

“…Our present intention is to lift the standard QCD sum-rule formalism encoded in the above prescription -in particular, the theoretical starting point, viz., the QCD input to the correlation function -to a level better matching the group-theoretically induced peculiarities of the exotic multiquark hadrons that strikingly distinguish them from the class of ordinary hadrons [6][7][8][9][10][11]. Specifically, for well-defined categories of tetraquarks [12], we are led to suspect that this goal necessitates a QCD contribution to involve two or more gluon exchanges of suitable topology.…”

“…The analysis of the flavour-preserving case is comparatively easy [6]: Figure 1 exemplifies the lower-order perturbative QCD-level contributions to the four-point correlation functions (11).…”

Mission Target: Exotic Multiquark Hadrons—Sharpened Blades

“…(These tools' transfer to other cases seems evident.) In particular, a brief glance at the related present experimental situation [4][5][6][7][8][9][10][11] (Section 2) will be followed by a recapitulation of insights gained upon basing the strong interactions' gauge symmetry tentatively on special unitary groups of higher dimension [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] (Section 4) and a sketch of the advantages of trimming a popular technique for the nonperturbative analytical discussion of QCD bound states to fit to the needs of multiquark hadrons [27][28][29][30][31][32][33][34][35][36][37][38][39] (Section 5).…”