Multiquark-Adequate QCD Sum Rules: the Case of Flavour-Exotic Tetraquarks

Abstract

Frequently, theoretical discussions of multiquark hadron states prove to be contaminated or even dominated by contributions of conventional hadrons. For the approach to QCD bound states in terms of QCD sum rules, we show how to get rid of all unwanted ordinary-hadron ballast by boiling down the traditional QCD sum-rule formalism to the nonconventional aspects in the focus of interest.

Cluster reducibility of multiquark operators and tetraquark-adequate QCD sum rules

“…Recently, we worked out [1][2][3][4][5][6][7][8][9][10][11] for a popular approach to hadrons called QCD sum rules a, from our point of view, kind of improvement tailored to the peculiarities of exotic hadrons.…”

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

“…Recently, we worked out [1][2][3][4][5][6][7][8][9][10][11] for a popular approach to hadrons called QCD sum rules a, from our point of view, kind of improvement tailored to the peculiarities of exotic hadrons.…”

“…In our search for multiquark adequacy of any tool utilized for the investigation of exotic hadrons, an (evidently) decisive move is to find a means both to discard all those contributions that definitely won't have an impact on the multiquarks under , and α 2 s (c) to flavour-preserving correlation functions of four quark-bilinear currents j and the latters' configuration-space vertex contractions to correlation functions of either two tetraquark interpolating operators θ (1) (left) [6,9], or one tetraquark interpolating operator θ (1) plus two quark-bilinear currents (right) [6].…”

“…FIGURE 1. Exemplary perturbative contributions of lowest conceivable strong-coupling orders α 0 s (a), αs (b), and α 2 s (c) to flavour-preserving correlation functions of four quark-bilinear currents j and the latters' configuration-space vertex contractions to correlation functions of either two tetraquark interpolating operators θ(1) (left)[6,9], or one tetraquark interpolating operator θ(1) plus two quark-bilinear currents (right)[6].…”

“…FIGURE 3. Disentanglement of the QCD sum-rule output of flavour-preserving correlation functions of two tetraquark interpolating operators θ, generating pairs of ordinary-meson QCD sum rules reflecting the nature of the factorizable contributions (top row, separated by dash-dotted lines) as well as the requested tetraquark-adequate QCD sum rules embodying the totality of nonfactorizable contributions (bottom row)[6,9].…”