Threshold cusps and triangle singularities in hadronic reactions

Abstract: The spectrum of hadrons is the manifestation of color confinement of quantum chromodynamics. Hadronic resonances correspond to poles of the S-matrix. Since 2003, lots of new hadron resonant structures were discovered in the mass regions from light mesons to hadrons containing a pair of a heavy quark and an antiquark. Many of them are candidates of exotic hadrons, and they are usually observed as peaks in invariant mass distributions. However, the S-matrix also has kinematical singularities due to the on-shellness of intermediate particles for a process, such as two-body thresholds and triangle singularities, and they can produce peaks as well. On the one hand, such singularities may be misidentified as resonances; on the other hand, they can be used as tools for precision measurements. In this paper, we review the threshold cusps and various triangle singularities in hadronic reactions, paying attention to their manifestations in phenomena related to exotic hadron candidates.

• The paper demonstrates that threshold cusps and triangle singularities can mimic genuine resonances in QCD processes.
• It details how two-body thresholds and three-particle on-shell conditions distort invariant mass distributions in heavy quarkonium and hadron spectroscopy.
• The study emphasizes using refined amplitude analyses to distinguish kinematical effects from authentic exotic states in experimental data.

Analysis of Threshold Cusps and Triangle Singularities in Hadronic Reactions

The paper, "Threshold cusps and triangle singularities in hadronic reactions," provides a comprehensive review of kinematical singularities in quantum chromodynamics (QCD) and their manifestations in heavy quarkonium and hadron spectroscopy. The central focus is on threshold cusps and triangle singularities (TSs), which are kinematical phenomena arising from the on-shell conditions of intermediate particles in a reaction. These singularities can lead to observable effects in invariant mass distributions, often mimicking the signals of genuine resonances, and present in both theoretical studies and experimental data.

Threshold Cusps

Threshold cusps appear at two-body thresholds and are square root branch points of the $S$-matrix. These cusps can significantly distort the energy distributions of hadronic decays or scatterings. An illustrative example is the cusp observed in the $K^\pm \to \pi^\pm \pi^0 \pi^0$ decay by the NA48/2 collaboration, which enabled the precise measurement of $\pi\pi$ scattering lengths. The paper suggests that other processes, such as $\eta \to 3\pi$ or $\eta' \to \eta\pi\pi$, might also exhibit such cusp effects, providing further opportunities to extract low-energy hadronic interaction parameters.

Triangle Singularities

TSs arise from three on-shell intermediate particles, leading to logarithmic branch points. The manifestation of TSs in hadronic processes has gained renewed interest due to their potential to produce peaks in energy distributions analogous to resonance signals. The paper discusses several compelling cases:

• The $Z_c(3900)$ and $Z_b(10610)$, prominent candidates for exotic states, might be influenced by TSs rather than being attributed solely to resonances.
• Light meson states like $\eta(1405/1475)$ and $a_1(1420)$ show unexpected isospin behaviors that can be explained by TS contributions from $K^* \bar K K$ loops.
• The observed peaks in $J/\psi p$ and $\Lambda_b^0 \to J/\psi K^- p$ decays, interpreted as pentaquarks, could potentially be TS manifestations rather than genuine exotic baryonic states.

Implications and Future Directions

The implications of these findings are profound for both the theoretical understanding of QCD and the practical analysis of data from high-energy physics experiments. The ability to distinguish between genuine resonances and TS or cusp effects is crucial for accurately mapping the hadron spectrum and identifying exotic states. As experimental facilities like LHCb, Belle II, and BESIII continue to gather data, sophisticated amplitude analyses incorporating these kinematical effects are essential.

The paper hints at an exciting future direction: using TS to measure hadronic scattering lengths and enhance molecule production. What's more, detecting the variation of TS peaks by changing kinematic configurations presents a viable strategy to distinguish these singularities from authentic particle states.

In conclusion, the paper underscores the importance of accounting for and understanding threshold cusps and triangle singularities in QCD processes. Doing so not only aids in correctly interpreting experimental data but also enriches our comprehension of the non-perturbative regime of QCD, offering insights into the complex interactions underlying hadronic matter.