COMPASS points to triangle singularity

23 August 2021

The COMPASS experiment at CERN has reported the first direct evidence for a long-hypothesised interplay between hadron decays which can masquerade as a resonance. The analysis, which was published last week in Physical Review Letters, suggests that the “a1(1420)” signal observed by the collaboration in 2015 is not a new exotic hadron after all, but the first sighting of a so-called triangle singularity.

“Triangle singularities are a mechanism for generating a bump in the decay spectrum that does not correspond to a resonance,” explains analyst Mikhail Mikhasenko of the ORIGINS Cluster in Munich. “One gets a peak that has all features of a new hadron, but whose true nature is a virtual loop with known particles.” 

“This is a prime example of an aphorism which is commonly attributed to Dick Dalitz,” agrees fellow analyst Bernhard Ketzer, of the University of Bonn: “Not every bump is a resonance, and not every resonance is a bump!”

Triangle singularities take their name from the triangle in a Feynman diagram when a secondary decay product fuses with a primary decay product. If the particle masses line up such that the process can proceed as a cascade of on-mass-shell hadron decays, the matrix element is enhanced by a so-called logarithmic singularity which can easily be mistaken for a resonance. But the effect is usually rather small, requiring a record 50 million πp→ππ+πp events, and painstaking work by the COMPASS collaboration to make certain that the a1(1420) signal, which makes up less than 1% of the three-pion sample, wasn’t an artefact of the analysis procedure.

Hadron experiments are reaching the precision needed to see one of the most peculiar multi-body features of QCD

Mikhail Mikhasenko

“The correspondence of this small signal with a triangle singularity is noteworthy because it shows that hadron experiments are finally reaching the precision and statistics needed to see one of the most peculiar features of the multi-body non-perturbative regime of quantum chromodynamics,” says Mikhasenko.

Triangle singularities were dreamt up independently by Lev Landau and Richard Cutkosky in 1959. After five decades of calculations and speculations, physicists at the Institute for High-Energy Physics in Beijing in 2012 used a triangle singularity to explain why intermediate f0(980) mesons in J/ψ meson decays at the BESIII experiment at the Beijing Electron–Positron Collider II were unusually long-lived. In 2019, the LHCb collaboration ruled out triangle singularities as the origin of the pentaquark states they discovered that year. The new COMPASS analysis is the first time that a “bump” in a decay spectrum has been convincingly explained as more likely due to a triangle singularity than a resonance.

Triangle singularity

COMPASS collides a secondary beam of charged pions from CERN’s Super Proton Synchrotron with a hydrogen target in the laboratory’s North Area. In this analysis, gluons emitted by protons in the target excite the incident pions, producing the final state of three charged pions which is observed by the COMPASS spectrometer. Intermediate resonances display a variety of angular momentum, spin and parity configurations. In 2015, the collaboration observed a small but unmistakable “P-wave” (L=1) component of the f0(980)π system with a peak at 1420 MeV and JPC=1++. Dubbed a1(1420), the apparent resonance was suspected to be exotic, as it was narrower, and hence more stable, than the ground-state meson with the same quantum numbers, a1(1260). It was also surprisingly light, with a mass just above the K*K threshold of 1.39 GeV. A tempting interpretation was that a1(1420) might be a dsūs̄ tetraquark, and thus the first exotic hadronic state with no charm quarks, and a charged cousin of the famous exotic X(3872) at the D*D threshold to boot, explains Mikhasenko.

According to the new COMPASS analysis, however, the bump at 1420 MeV can more simply be explained by a triangle singularity, whereby an a1(1260) decays to a K*K pair, and the kaon from the resulting K*→Kπ decay annihilates with the initial anti-kaon to create a light unflavoured f0(980) meson which decays to a pair of charged pions. Crucially, the mass of f0(980) is just above the KK threshold, and the roughly 300 MeV width of the conventional a1(1260) meson is wide enough for the particle to be said to decay to K*K on-mass-shell.

A new resonance is not required. That is phenomenologically significant.

Ian Aitchison

“The COMPASS collaboration have obviously done a very thorough job, being in possession of a complete partial-wave analysis,” says Ian Aitchison, emeritus professor at the University of Oxford, who in 1964 was among the first to propose that triangle graphs with an unstable internal line (in this case the K*) could lead to observable effects. This enables the whole process to occur nearly on-shell for all particles, which in turn means that the singularities of the amplitude will be near the physical region, and hence observable, explains Aitchison. “This is not unambiguous evidence for the observation of a triangle singularity, but the paper shows pretty convincingly that it is sufficient to explain the data, and that a new resonance is not required. That is phenomenologically significant.”

The collaboration now plans further studies of this new phenomenon, including its interference with the direct decay of the a1(1260). Meanwhile, observation by Belle II of the a1(1420) phenomenon in decays of the tau meson to three pions should confirm our understanding and provide an even cleaner signal, says Mikhasenko.

Further reading

G. D. Alexeev et al. (COMPASS Collaboration) 2021 Phys. Rev. Lett. 127 082501

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