Tetraquarks back in the spotlight

The existence of particles with fractional charges and fractional baryon numbers was a hard sell in 1964 when Gell-Mann and Zweig independently proposed the quark model. Physicists remained sceptical until the discovery of the J/ψ meson 10 years later. Heavier than anything previously seen and extremely narrow, with a width of just 0.1 MeV and a mass of 3097 MeV, the J/ψ pointed to the existence of a new quark with its own quantum number. This confirmed Glashow, Iliopoulos and Maiani’s 1970 hypothesis, which they cooked up to explain peculiarities in rare kaon decays. Any doubt as to the existence of a charm–anticharm system was eliminated by observing narrow excitations of the J/ψ, which lined up as expected in non-relativistic quantum mechanics. The spectrum of charmonium mesons soon became populated by states with widths up to hundreds of MeV as their masses surpassed the threshold for decaying to a pair of “open-charm” mesons with a single charm quark each.

Hadron spectroscopy continues to be a rich area of fundamental exploration today, with results from collider experiments over the past two decades revealing the existence of multi-quark states more exotic than the familiar mesons and baryons (CERN Courier April 2017 p31). The LHCb experiment at CERN is at the forefront of this work. Now, a structure in the J/ψ-pair mass spectrum consistent with a tetraquark state made up of two charm quarks and two charm antiquarks has been observed by the collaboration. With doubly hidden charm, the new cccc state is the most significant evidence so far for the existence of tightly bound tetraquarks composed of a pair of colour-charged “diquarks”, and sheds light on a difficult-to-model regime of quantum chromodynamics (QCD).

Multi-quark states

Gell-Mann and Zweig both acknowledged that the symmetries which led to the quark hypothesis allowed for more complicated quark configurations than just mesons (qq) and baryons (qqq). Tetraquarks (qqqq), pentaquarks (qqqqq) and hexaquarks (qqqqqq or qqqqqq) were all suggested. In the early 1970s, a deepening understanding of the dynamics of strong interactions brought about by QCD only furthered the motivation for seeking new multi-quark states. QCD not only predicted attractive forces between a quark and an antiquark, and between three quarks, but also between two quarks.

The attraction between two quarks can easily be proven when they are close together and the strong coupling constant is small enough to allow perturbative calculations. Similar interactions also likely occur in the non-perturbative regime. Such systems, known as diquarks, have the colour charge of an antiquark. (For example, red and blue combine to make an anti-green diquark.) As coloured objects, they can be confined in hadrons by partnering with other coloured constituents. A diquark can attract a quark to create a simple baryon. Alternatively, a diquark and an antidiquark can attract each other to create a tetraquark. As a result of their direct colour couplings, such compact tetraquarks can have binding energies of several hundreds of MeV.

Compact two-diquark tetraquarks stand in stark contrast to the alternative “molecular” model for tetraquarks, which was named by loose analogy with the exchange of electrons between atoms in molecules. In this picture, the tetraquark is arranged as a pair of mesons that attract each other by exchanging colour-neutral objects, such as light mesons and glueballs – an idea first proposed in 1935 by Hideki Yukawa, in the context of interactions between nucleons. Such exchanges only provide a binding energy of a few MeV per nucleon.

Molecular tetraquarks are therefore expected to be only loosely bound, with masses near the sum of the masses of their constituent mesons, however they could have rather narrow widths if their mass lies below the “fall-apart” threshold. As such states are most likely to be created without angular momentum between the mesons, the spin-parity combinations available to them are highly restricted. In contrast, a rich spectrum of radial and angular momentum excitations between the coloured constituents is predicted for diquark tetraquarks. The widths of these states could be large, as they can easily fall apart into lighter hadrons, with their binding energy transformed into a light quark–antiquark pair.

Unfortunately, it is difficult to rigorously apply QCD in the confining regime of multi-quark states. It is therefore up to experiments to discover which multi-quark states actually exist in nature. There have been some hints of tetraquark states built out of light quarks, though without definite proof. This is largely because additional light quark pairs can easily be created in the decay process of simple mesons and baryons, and the highly relativistic nature of such states makes model predictions for their excitations unreliable. Hidden charm states have proved helpful again, however, as the charmonium spectrum and the properties of such states are well predicted.

Experiments to the fore

Molecular tetraquark proposals were fuelled in 2003 by the unexpected discovery by the Belle collaboration, at the KEKB electron–positron collider in Tsukuba, Japan, of a new narrow state, right at the sum of the masses of a charmed-meson pair. Unlike other charmonium states near its mass, the state is surprisingly narrow, with a width of the order of just 1 MeV. Originally named X(3872), it is now conventionally referred to as χ_c1(3872), reflecting its nature as a possible triplet P-wave state with hidden charm and one unit of total angular momentum. Despite subsequent results from collider experiments around the world, there is no consensus about its exact nature, as it variously exhibits features of simple charmonium or a loosely bound molecule.

It is up to experiments to discover which multi-quark states actually exist in nature

Stronger evidence for the loose meson–meson binding of multi-quark states was provided by observations in 2013 of a hidden-charm tetraquark candidate Z_c(3900) by the BES III collaboration at the BEPC II electron–positron collider in Beijing, China, and by Belle, and of the Z_c(4020), also by BES III. Since they have electrically charged forms, they cannot be counted as charmonium states. They are both relatively narrow states near meson–meson thresholds for open charm, with widths of the order of tens of MeV. They are definitely tetraquarks, though it is still a moot point if they are genuinely bound states or merely manifestations of non-binding hadron–hadron forces that manifest in complicated forms. The molecular interpretation had also been reinforced in 2012 by Belle’s observations of the hidden-beauty Z_b(10610) and Z_b(10650) tetraquarks. These states also have relatively narrow widths of the order of tens of MeV and masses near the threshold for falling apart, in this case to “open-beauty” mesons.

Pentaquark observations have also weighed in on the debate. Last year’s observation of three narrow hidden-charm pentaquarks by the LHCb collaboration, with widths below tens of MeV and masses close to the charm meson-baryon threshold (CERN Courier May/June 2019 p15), also points to loose hadron–hadron binding, in this case between a meson and a baryon.

Bucking the trend

Yukawa-style bindings cannot, however, explain a large number of broader tetraquark-like structures with hidden charm, with widths of hundreds of MeV, which are not near any hadron–hadron threshold. Such states include the charged Z_c(4430) observed by Belle in 2008 and later confirmed by LHCb in 2014, and a family of states that decay to a J/ψ φ final state, including X(4140) and X(4274), which were observed by the CDF collaboration at Fermilab in 2009 and later by CMS and LHCb at CERN. These states could be either manifestations of diquark interactions or kinematic effects near the fall-apart threshold. No single simple model can account for all of them.

Reaching states with hidden double charm (cccc) now promises new insights into multi-quark dynamics, as all the quarks are non-relativistic. Furthermore, there is no known mechanism for two charmonium mesons to be loosely bound, according to a molecular model, as no light valence quarks are available to be exchanged. Compact diquark-type tetraquarks have been predicted for such quark combinations, but it is not clear whether they might lead to experimentally detectable signatures – the tetraquarks could be too broad or their production rate too small. While collisions at the LHC provide enough energy to simultaneously produce pairs of charm–anticharm quark combinations, getting them close enough together to form diquarks is a tall order. Additionally, while observations of beauty-charm mesons such as B_c and doubly charmed baryons such as Ξ_cc showed that LHCb has reached the sensitivity to detect the interactions of two heavy quarks, it was unclear until recently if the interactions of diquark-model tetraquarks could be detected. The observation, reported in July, by LHCb, of a highly significant J/ψ-pair mass structure is therefore an exciting moment for the study of multi-quark dynamics.

Introducing the X(6900)

Exploiting the full data set collected from 2011 to 2018, LHCb investigated the J/ψ-pair invariant mass spectrum, where J/ψ meson candidates are reconstructed from the dimuon decay mode. A narrow peaking structure at 6900 MeV and a broader structure at approximately twice the J/ψ mass threshold was observed. The structure of X(6900) is consistent with the signature of a resonance (see figure), suggesting a four-charm-quark state.

While the peaking X(6900) structure is close to the χ_c0 χ_c1 meson-pair threshold, its width, of the order of a hundred MeV, seems too large to fit into the loose-binding scheme, wherein decay modes other than the “fall-apart” topology are expected to be strongly suppressed, and in any case, there is no known loose binding mechanism between two charmonium states. Charmonium-pair re-scattering effects are also disfavoured due to the requirements of such interactions. This observation is therefore the most intriguing experimental indication so far for hadrons made out of diquarks.

It is less clear if the observed structure is made of one state, or several that may or may not interfere with each other. There is no information on the spin-parity of the observed structure. Neither do we yet know if mass structures also appear in the invariant mass spectra of other charmonium or doubly charmed baryon pairs.

This observation is the most intriguing experimental indication so far for hadrons made out of diquarks

The first LHCb upgrade is currently in progress and data taking will recommence at the beginning of LHC Run 3 in 2022, with a second upgrade phase planned to collect a much larger data set by 2030. The ATLAS and CMS experiments have highly performing muon detectors too, and could also make significant contributions to the study of the new X(6900) structure, with both existing and future data. A key contribution may also be made by Belle’s successor, Belle II, currently in its start-up phase, which observes electron–positron collisions at the SuperKEKB collider at energies above the observed J/ψ-pair mass structure. It is unclear, however, if the collision energy, luminosity and electromagnetic production cross sections will be high enough to achieve the required sensitivity.

Research is already moving forward quickly, with further evidence for diquark tetraquarks coming from an even more recent discovery by LHCb of two “X(2900)” states with widths between 57 and 110 MeV. As they decay to a D⁺K^– final state, they are both openly charming and openly strange. Their most likely composition is that of a (cs)(ud) diquark tetraquark. While the X(2900) states decay strongly, similar heavy-light diquark systems, such as (cc)(ud), (bc)(ud) and (bb)(ud), have been studied theoretically, resulting in varying degrees of confidence that some may be stable with respect to strong interactions, and instead decay weakly, with measurable lifetimes. Hunting for such states is an exciting prospect for the upgraded LHCb experiment.

LHCb’s new tetraquark observations have once again thrown open the debate on the nature of multi-quark states. With the theory still mired in non-perturbative calculations, experimental observations will be decisive in leading the development of this subject. The community is waiting eagerly to see if other experiments confirm the LHCb observation, and shed light on its nature.