A bestiary of exotic hadrons – CERN Courier

Seventy-six new particles have been discovered at the Large Hadron Collider (LHC) so far: the Higgs boson, 52 conventional hadrons and a bestiary of 23 exotic hadrons whose structure cannot reliably be explained or their existence predicted.

The exotic states are varied and complex, displaying little discernible pattern at first glance. They represent a fascinating detective story: an experimentally driven quest to understand the exotic offspring of the strong interaction, motivating rival schools of thought among theorists.

This surge in new hadrons has been one of the least expected outcomes of the LHC (see “Unexpected” figure). With a tenfold increase in data at the High-Luminosity LHC (HL-LHC) on the horizon, and further new states also likely to emerge at the Belle II experiment in Japan, the BESIII experiment in China, and perhaps at a super charm–tau factory in the same country, their story is in its infancy, with twists and turns still to come.

Building blocks

Just as electric charges arrange themselves in neutral atoms, the colour charges that carry the strong interaction arrange themselves into colourless composite states. As fundamental particles with colour charge, quarks (q) and gluons (g) therefore cannot exist independently, but only in colour-neutral composite states called hadrons. Since the discovery of the pion in 1947, a rich phenomenology of mesons (qq) and baryons (qqq) inspired the quark model and eventually the theory of quantum chromodynamics (QCD), which serves as an impeccable description of the strong interaction to this day.

But why should nature not also contain exotic colour-neutral combinations such as tetraquarks (qqqq), pentaquarks (qqqqq), hexaquarks (qqqqqq or qqqqqq), hybrid hadrons (qqg or qqgg) and glueballs (gg or ggg)?

The existence of exotic hadrons was debated without consensus for decades, with interest growing in the early 2000s, when new states with unexpected features were observed. In 2003, the BaBar experiment at SLAC discovered the D^*_s0(2317)⁺ meson, with a mass close to the sum of the masses of a D meson and a kaon. A few months later that year, Belle discovered the χ_c1(3872) meson, then called X(3872) (see “What’s in a name?” panel), with a mass close to the sum of the masses of a D⁰ meson and a D^*0 meson. As well as their striking closeness to meson–meson thresholds, the “width” of their signals was much narrower than expected. (Measured in units of energy, such widths are reciprocal to particle lifetimes.)

Soon afterwards, in 2007, a number of other charmonium-like and bottomonium-like states were observed. Belle’s observation in 2007 of the electrically charged charmonium-like state Z(4430)⁺ (now called T_cc1(4430)⁺) was a pathfinder in theorising the existence of QCD exotics. Though these states exhibited the telltale signs of being excitations of a charm–anticharm (cc) system (see “The new particles”), their net electric charge indicated a system that could not be composed of only a quark–antiquark pair, as particles and antiparticles have opposite electric charges. Two additional quarks had to be present.

Exotic states at the LHC

The start-up of the LHC opened up the trail, with 23 new exotic hadrons observed there so far (see “The 23 exotic hadrons discovered at the LHC” table). The harvest of new states began in autumn 2013 with the CMS experiment at the LHC reporting the observation of the χ_c1(4140) state in the J/ψφ mass spectrum in B⁺ → J/ψφK⁺ decays, confirming a hint from the CDF experiment at Fermilab. Its minimal quark content is likely ccss. CMS also reported evidence for a state at a higher mass, observed by the LHCb experiment at the LHC in 2016 as the χ_c1(4274), alongside two more states at masses of 4500 and 4700 MeV.

In a 2021 analysis of the same B⁺ → J/ψφK⁺ decay mode including LHC Run 2 data, LHCb reported two more neutral states, χ_c1(4685) and X(4630), that do not correspond to cc states expected from the quark model. The analysis also reported two more resonances seen in the J/ψK⁺ mass spectrum, T_ccs1(4000)⁺ and T_ccs1(4220)⁺. Carrying charge and strangeness, these charmonia-like states are manifestly exotic, with a minimal quark content ccus.

For T_ccs1(4000)⁺, LHCb had sufficient data to produce an Argand diagram with the distinct signature of a resonance (see “Round resonances” panel). A possible isospin partner, T_ccs1(4000)⁰ was later found in B⁰ → J/ψφK⁰_s decays, lending further evidence that it is a resonance and not a kinematical feature. (According to an approximate symmetry of QCD, the strong interaction should treat a ccus state almost exactly like a ccds. state, as up and down quarks have the same colour charges and similar masses.) Other charmonium-like tetraquarks were later seen by LHCb in the decays χ_c0(3960) → D⁺_sD^–_s and χ_c1(4010) → D^*+D^–.

The world’s first pentaquarks were discovered by LHCb in 2015. Two pentaquarks appeared in the J/ψp spectrum by studying Λ⁰_b → J/ψpK^– decays: P_cc(4380)⁺, a rather broad resonance with a width of 200 MeV; and P_cc(4450)⁺, which is narrower at 40 MeV. The observed decay mode implied a minimal quark content ccuud, excluding any conventional interpretation.

These states were hiding in plain sight: they were spotted independently by several LHCb physicists, including a CERN summer student. In a 2019 analysis using more data, the heavier state was identified as the sum of two overlapping pentaquarks now called P_cc(4440)⁺ and P_cc(4457)⁺. Another narrow state was also seen at a mass of 4312 MeV. LHCb observed the first strange pentaquark in B^– → J/ψΛp decays in 2022, with a quark content ccuds.

Other manifestly exotic hadrons followed, with two exotic hadrons T_cccc(6600) and T_cccc(6900) observed by LHCb, CMS and ATLAS in the J/ψJ/ψ spectrum. They can be interpreted as a tetraquark made of two charm and two anti-charm quarks – a fully charmed tetraquark. When both J/ψ mesons decay to a muon pair, the final state consists of four muons, allowing the LHCb, ATLAS and CMS experiments to study the final spectrum in multiple acceptance regions and transverse momentum ranges. These states do not contain any light quarks, which eases their theoretical study and also implies a state with four bottom quarks that could be long-lived.

Doubly charming

The world’s first double-open-charm meson was discovered by LHCb in 2021: the T_cc(3875)⁺. With a charm of two, it cannot be accommodated in the conventional qq scheme. There is an intriguing similarity between the exotic T_cc(3875)⁺(ccud) and the charmonium-like (cc-like) χ_c1(3872) meson discovered by Belle in 2003, whose nature is still controversial. Both have similar masses and remarkably narrow widths. The jury is still out on their interpretation (see “Inside pentaquarks and tetraquarks“).

The discovery of a T_cc(3875)⁺ (ccud) meson also implies the existence of a T_bb state, with a bbud quark content, that should be stable except with regard to weak decays. The observation of the first long-lived exotic state, with a sizable flight distance, is an intriguing goal for future experiments. At the HL-LHC, the search for B⁺_c mesons displaced from the interaction point, could return the first evidence for a T_bb tetraquark given that the decays of weakly decaying double-beauty hadrons such as Ξ_bbq and T_bb are their only known sources.

Round resonances

Particles are most likely to be created in collisions when the centre-of-mass energy matches their mass. The longer the mean lifetime of the new particle, the greater the uncertainty on its decay time and, via Heisenberg’s uncertainty principle, the smaller the uncertainty on their energy. Such particles have narrow peaks in their energy spectra. Fast-decaying particles have broad peaks. Searching for such “resonances” can reveal new particles – but bumps can be deceiving. A more revealing analysis fits differential decay rates to measure the complex quantum amplitude A(s) describing the production of the particle. As the energy (√s) increases, the amplitude traces a circle counterclockwise in the complex plane, with the magnitude of the amplitude tracing the classic resonant peak observed in energy spectra (see figure above left).

Demonstrating this behaviour, as LHCb did in 2021 for theT_ccs1(4000)⁺ meson (above, centre) is a significant experimental achievement, which the collaboration also performed in 2018 for the pathfinding Z(4430)⁺ (T_cc1(4430)⁺) meson discovered by Belle in 2007 (black points, above right). The LHCb measurement confirmed its resonant character and resolved any controversy over whether it was a true exotic state. The simulated blue measurement illustrates the improvement such measurements stand to accrue with upgraded detectors and increased statistics at the HL-LHC.

There are also other exotic states predicted by QCD that are still missing in the particle zoo, such as meson–gluon hybrids and glueballs. Hybrid mesons could be identified by exotic spin-parity (J^P) quantum numbers not allowed in the qq scheme. Glueballs could be observed in gluon-enriched heavy-ion collisions. A potential candidate has recently been observed by the BESIII collaboration, which is another major player in exotic spectroscopy.

Exotic hadrons might even have been observed in the light quark sector without having been searched for. The scalar mesons are too numerous to fit in the conventional quark model, and some of them, for instance the f₀(980) and a₀(980) mesons, might be tetraquarks. Exotic light pentaquarks may also exist. Twenty years ago, the θ⁺ baryon caused quite some excitement, being apparently openly exotic, with a positive strangeness and a minimal quark content uudds. No fewer than 10 different experiments presented evidence for it, including several quoting 5σ significance, before it disappeared in blind analyses of larger data samples with better background subtraction (CERN Courier April 2004 p29). Its story is now material for historians of science, but its interpretation triggered many theory papers that are still useful today.

The challenge of understanding how quarks are bound inside exotic hadrons is the greatest outstanding question in hadron spectroscopy. Models include a cloud of light quarks and gluons bound to a heavy qq core by van-der-Waals-like forces (hadro-quarkonium); colour-singlet hadrons bound by residual nuclear forces (hadronic molecules); and compact tetraquarks [qq] [qq] and pentaquarks [qq][qq]q composed of diquarks [qq] and antidiquarks [qq], which masquerade as antiquarks and quarks, respectively.

Some exotic hadrons may also have been misinterpreted as resonant states when they are actually “threshold cusps” – enhancements caused by rescattering. For instance, the P_cc(4457)⁺ pentaquark seen in Λ⁰_b → J/ψpK^– decays could in fact be rescattering between the D⁰ and Λ_c(2595)⁺ decay products in Λ⁰ _b→ Λ_c(2595)⁺D⁰K^– to exchange a charm quark and form a J/ψp system. This hypothesis can be tested by searching for additional decay modes and isospin partners, or via detailed amplitude analyses – a process already completed for many of the aforementioned states, but not yet all.

Establishing the nature of the exotic hadrons will be challenging, and a comprehensive organisation of exotic hadrons in flavour multiples is still missing. Establishing whether exotic hadrons obey the same flavour symmetries as conventional hadrons will be an important step forward in understanding their composition.

Effective predictions

The dynamics of quarks and gluons can be described perturbatively in hard processes thanks to the smallness of the strong coupling constant at short distances, but the spectrum of stable hadrons is affected by non-perturbative effects and cannot be computed from the fundamental theory. Though lattice QCD attempts this by discretising space–time in a cubic lattice, the results are time consuming and limited in precision by computational power. Predictions rely on approximate analytical methods such as effective field theories.

The challenge of understanding how quarks are bound inside exotic hadrons is the greatest outstanding question in hadron spectroscopy

Hadron physics is therefore driven by empirical data, and hadron spectroscopy plays a pivotal role in testing the predictions of lattice QCD, which is itself an increasingly important tool in precision electroweak physics and searches for physics beyond the Standard Model.

Like Mendeleev and Gell-Mann, we are at the beginning of a new field, in the taxonomy stage, discovering, studying and classifying exotic hadrons. The deeper challenge is to explain and anticipate them. Though the underlying principles are fully known, we are still far from being able to do the chemistry of quantum chromodynamics.