Triangle Singularity as the Origin of the a_{1}(1420)

The COMPASS Collaboration experiment recently discovered a new isovector resonancelike signal with axial-vector quantum numbers, the a_{1}(1420), decaying to f_{0}(980)π. With a mass too close to and a width smaller than the axial-vector ground state a_{1}(1260), it was immediately interpreted as a new light exotic meson, similar to the X, Y, Z states in the hidden-charm sector. We show that a resonancelike signal fully matching the experimental data is produced by the decay of the a_{1}(1260) resonance into K^{*}(→Kπ)K[over ¯] and subsequent rescattering through a triangle singularity into the coupled f_{0}(980)π channel. The amplitude for this process is calculated using a new approach based on dispersion relations. The triangle-singularity model is fitted to the partial-wave data of the COMPASS experiment. Despite having fewer parameters, this fit shows a slightly better quality than the one using a resonance hypothesis and thus eliminates the need for an additional resonance in order to describe the data. We thereby demonstrate for the first time in the light-meson sector that a resonancelike structure in the experimental data can be described by rescattering through a triangle singularity, providing evidence for a genuine three-body effect.

Exploring Possible Triangle Singularities in the Ξ b − → K − J / ψ Λ Decay

We analyze possible singularities in the J/ψΛ invariant mass distribution of the Ξb−→K−J/ψΛ process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop diagrams. Among those with Ξ*-charmonium-Λ intermediate states, the one from the χc1Ξ(2120)Λ loop, which is located around 4628 MeV, is found the most likely to cause observable effects. One needs S- and P-waves in χc1Λ and J/ψΛ systems, respectively, when the quantum numbers of these systems are 1/2+ or 3/2+. When the quantum numbers of the Ξ(2120) are JP=1/2+, 1/2− or 3/2+, the peak structure should be sharper than the other JP choices. This suggests that although the whole strength is unknown, we should pay attention to the contributions from the Ξ*-charmonium-Λ triangle diagram if structures are observed in the J/ψΛ invariant mass spectrum experimentally. In addition, a few triangle diagrams with the Ds1*(2700) as one of the intermediate particles can also produce singularities in the J/ψΛ distribution, but at higher energies above 4.9 GeV.

Triangle singularity in the γp → pπ0η reaction ??

The γp → pπ0η reaction has been studied with the CBELSA/TAPS detector system to search for experimental evidence for triangle singularities. Kinematically these singularities exist in the decay chain Δ* → ηΔ(1232) → ηπ0 p but do not show an experimental effect because of the weakness of the π0 − η interaction at low \sqrt s near threshold far below the a0(980) resonance.