Tetraquark-Adequate 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.

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

“…We arrive at an identical conclusion [5,6,8]: Within a perturbative expansion in powers of ) (c) of the strong coupling α s (corresponding to the internal exchanges of no, one or two gluons, respectively, indicated by curly lines) to a flavour-preserving Green function T j ab j cd j † ab j † cd of four quark-bilinear currents j ( †) (left), and the contraction to the correlator T θ abcd θ † abcd of two tetraquark operators θ ( †) abcd (right) [5,6].…”

“…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].…”

“…Given the above general recipe, it is, in principle, straightforward to derive QCD sum rules from n-point Green functions of (appropriately defined) hadron interpolating operators. In the case of all multiquark hadrons, however, due care has to be paid to the proper disentanglement of those contributions to any such correlation function that may involve the kind of multiquark states of interest and those contributions that are definitely not related to the states under study since, for instance, they affect exclusively ordinary hadrons [5,6,8]. More precisely, from our point of view all the latter contributions should be unambiguously identified, stripped off from any QCD sum rule found in the first step by naïve application of the formalism, and discarded.…”

“…Any contribution of the first kind, i.e., presumably capable of providing information about tetraquarks in the focus of interest, is termed tetraquark-phile [2,4]: retaining exclusively that sort of contributions entails QCD sum rules enjoying the wanted tetraquark adequacy [5,6,8]. Phrased, a little bit more technically, in terms of Feynman diagrams, in order to be regarded as tetraquark-phile a Feynman diagram should depend on the appropriate Mandelstam variable s in a non-polynomial manner and must develop a branch cut starting at a branch pointŝ defined by the square of the sum of the masses m a , m b , m c , m d of all involved (anti)quarks q a , q b , q c , q d acting as constituents of the envisaged tetraquark bound state [1]:ŝ = (m a +m b +m c +m d ) 2 .…”

“…Dealing with flavour-exotic tetraquarks, we must discriminate between two quark-flavour topologies characterized by whether the quark-flavour distributions in initial and final state are the same or different and, unsurprisingly, analyze separately [5,6,8] two disjoint categories of processes: those that do not undergo quark rearrangement (Sect. 2) and those that do (Sect.…”