Research: Exotic hadrons

Theoretical interpretations and phenomenological models of multi-quark (in particular four-, five- and six-quark) states are presented.

Quarks and gluons posses a colour charge, analogous to the electric charge of electromagenetismThe interactions between quarks and gluons are described by Quantum Chromodynamics (QCD), the theory of the strong force. Composite particles made of quarks and gluons are collectively referred to as hadrons.Until recently, all known hadrons could be classified as mesons or baryons using the quark model in which mesons are combinations of a quark and anti-quark (qq, where q refers to an antiquark) while baryons, such as the proton, are combinations of three quarks (qqq) or three anti-quarks (qqq). This model has been hugely successful, giving predictions for new states that have subsequently been observed as well as some that remain undiscovered. However, even at the birth of the quark model in the 1960’s it was speculated that other quark combinations can form stable resonances that should be experimentally observed. For example, two quarks and two anti-quarks (qqqq) would form a tetraquark, qqqqq would form a pentaquark, etc. Historically, the successful classification of all known hadrons in terms of combinations mesons and baryons -- and the apparent absence of other possibilities -- was an important inspiration for the development of QCD as the theory of the strong force.


In this picture, hadrons with a larger number of quarks (such as tetraquarks or pentaquarks) are formed from the same quark-level interactions that bind ordinary mesons or baryons. Among the various possible interpretations of exotic hadrons, this is the most "exotic". Due to the technical obstacles in extracting predictions from strong coupling QCD, it is not currently possible to determine from first principles whether or not such states should exist. Inspired by observations of experimental candidates, phenomenological quark models have been used to investigate the mass spectra, and production and decay characteristics, of compact multiquarks. These typically involve quark or effective diquark degrees of freedom, with a long-range confining potential and short-range Coulomb contribution due to one-gluon exchange. Raw mass predictions, with parameters fixed to the spectra of conventional hadrons, have large uncertainties, but the pattern of spin-dependent mass splittings is better controlled.

A generic feature of the compact multiquark picture is that the existence of one such state typically implies a rich spectrum of partner states. A given set of constituents, even restricting to ground states (S-wave), can combine into many possible combinations of spin and isospin, and the multiplicity of states is enlarged further due to the non-trivial "hidden" colour configurations. In the absence of experimental evidence for large families of multiquarks, a challenge for theory is to explain why certain states are special; one possibility is that restrictions on their allowed decays imply that some states are uniquely stable.


A hadronic molecule is a composite of ordinary hadrons, usually bound due to the exchange of pions or other mesons. Whereas compact multiquarks are built from quarks exchanging gluons, molecules are built from hadrons exchanging mesons. The closest analogy is the deuteron, which is well-understood in terms of proton-neutron degrees of freedom -- not as a compact hexaquark. Many of the tools of nuclear physics can be applied to the spectra of hadronic molecules: the only difference is that the proton and neutron are replaced with other (usually heavier) hadrons.

The main contribution to binding in a molecule is typically pion exchange; some models additionally include the exchange of heavier mesons (such as eta's). As with the compact multiquark, it is not possible to determine definitively from theory whether such states should exist: the binding or otherwise tends to be sensitive to a poorly-constrained cut-off parameter in the hadron-hadron potential. Nevertheless, a feature common to most models is that if a state is bound at all, its binding energy is quite small. Thus a key prediction of the molecular approach is that the masses of states are closely aligned to the relevant two-hadron thresholds. Weak binding also implies that hadronic molecules are extended objects, as distinct from "compact" multiquarks.

Another key difference compared to the compact multiquark approach is that the spectra of molecular states is restricted. Assuming the dominance of pion exchange, for example, many combinations of constituents can be ruled out on the basis of simple symmetry arguments, and even among the remaining combinations, only certain channels result in attractive binding potentials. In this sense molecular models are more constrained, and can more readily be falsified by experiment, compared to compact multiquark models, which can typically accommodate experimental candidates with a large variety of constituents and quantum numbers.


Unlike multiquarks and hadronic molecules, whose exotic nature is due to their quark content beyond qq or qqq, the distinguishing feature of hybrids is the manifest role of gluonic degrees of freedom. Quarks bind into hadrons by exchanging gluons, and at large distances this strong coupling is manifest as a gluonic flux tube. In conventional hadrons, the string-like flux tube is in its ground state, and the linear dependence of its energy with distance yields the familiar linear confining potential for quarks. In hybrids, the flux tube is in an excited state, with intrinsic angular momentum; the coupled quark-flux tube system has a wavefunction analogous to a spinning top, with fast and slow rotational degrees of freedom. An alternative picture of hybrids describes the gluonic excitation in terms of a point-like "constituent" gluon.

Although both hybrid mesons and hybrid baryons are possible, it is in the meson sector that they will be most conspicuous, because among their spectra are states which have combinations of spin, parity and charge conjugation quantum numbers which are not possible for conventional mesons. Unlike the other types of exotica discussed above, there are strong predictions from QCD (simulated on the lattice) for the existence of hybrids. Spectra of hybrid mesons (with and without exotic quantum numbers) have been unambiguously observed using lattice QCD (a first-principles method to perform non-perturbative calculations of QCD properties), and the pattern of their quantum numbers confirms model expectations.

This raises the question of why compelling experimental evidence for hybrids remains elusive. A possible explanation is their unusual decay characteristics: both flux tube and constituent gluon models predict that hybrid mesons do not decay into pairs of ground state mesons (where there is most experimental data), but prefer to decay into experimentally more challenging modes involving orbitally-excited final states.

Within QCD even objects with 10^50 quarks  (“quark nuggets”/"Q-balls”/"strangelets”) may exist.