Tetraquark-adequate formulation of QCD sum rules

Abstract

With the experimental observation of several credible candidates for multiquark hadrons, the latter states re-entered the focus of interest of theoretical strong-interaction physics. Proper treatment of hadronic bound states by quantum chromodynamics, QCD, the quantum field theory governing all strong interactions, necessitates a nonperturbative approach. A well-established framework of this kind is provided by QCD sum rules relating hadron features to the parameters of QCD. Conceptual reconsideration, however, reveals that, in order to really match the peculiarities of multiquarks, the long-standing conventional QCD sum-rule techniques evidently must be subjected to considerable modification. The so far overlooked necessity for such adaptations is most easily demonstrated for the case of least complexity, that is, for tetraquarks, bound states of two quarks and two antiquarks.

Tetraquark-adequate QCD sum rules for quark-exchange processes

“…The present work completes the proof provided in [10] for direct-type processes, where the quark flavors are arranged in color-singlet bilinears in the same way in the initial and in the final states.…”

“…These are called T -phile diagrams and are selected according to their singularity structure in the Feynman diagrams of the four-point function, Γ 4j , of quark bilinear color-singlet currents. T -phile diagrams should have a four-quark s-channel cut; such diagrams emerge at order O(α 2 s ) and higher [10]. Obviously, in order to obtain meaningful estimates of the parameters of exotic states, one needs to use the T -adequate QCD sum rule.…”

“…For the case of direct diagrams, the reader is referred to Ref. [10], where a detailed analysis has been presented. In the following, we concentrate on the case of quark-exchange diagrams.…”

“…due to the factorization property of lowest-order QCD diagrams, use was made of conventional SVZ sum rules for correlators of bilinear quark currents to show the cancellation of the non-T-phile diagrams on the OPE side against factorizable two-meson contributions on the hadron side [10]. This transparent procedure is not applicable in the recombination case and therefore one needs to follow a different line of argument, based on the singularity analysis of Feynman diagrams, for the related study.…”

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

“…The notion of multiquark hadrons comprises each bound state composed of a larger number of quarks than any ordinary quark-antiquark meson or ordinary three-quark baryon calls its own. In view of the slowly but steadily increasing evidence for the actual experimental observation, and consequently unambiguous confirmation of the existence, of tetraquarks and pentaquarks, we recently embarked on a rigorous theoretical investigation of multiquarks [1][2][3][4][5][6][7][8]. A standard tool for an extraction of properties of hadronic bound states from the underlying quantum field theory, quantum chromodynamics (QCD), is offered by a technique called QCD sum rules [9].…”