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 (TSs), 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. * fkguo@itp.ac.cn † xiaohai.liu@tju.edu.cn ‡ shsakai@itp.ac.cn 1 The X(3872) is named χ c1 (3872) according to its quantum numbers I G (J P C ) = 0 + (1 ++ ) by the PDG [10]. Similarly, the vector charmonium-like states Y (4260) and Y (4660) mentioned below are called ψ(4260) and ψ(4660), respectively. This naming scheme does not mean that the PDG assumes them to be normal cc charmonium states. Here we follow the XY Z naming scheme that is still used in most of the relevant publications.2 A conventional explanation of the observed peaks was given in Refs. [26,27].3 region Z c (4430) [30], Z c (3900) [31,32] and Z c (4020) [33], the charged bottomonium-like structures Z b (10610) and Z b (10650) [34], and the pentaquark candidates with hidden charm P c (4312), P c (4440) and P c (4457) [35,36]. Most of these new structures were observed in the heavy-flavor sector. In particular, the heavy quarkonium-like ones are often called XY Z states in the literature due to the undetermined internal structure. On the one hand, these discoveries enlarged the known QCD spectrum to a large extent; on the other hand, they became a nice showcase of the intricate nonperturbative nature of QCD at low energies 3 : most of them fall off the expectations from quark model, which despite being just a model had provided useful guidance in classifying a large amount of hadrons into various multiplets. Therefore, they are regarded as prominent candidates of exotic hadrons. However, how the spectrum of exotic hadrons should be organized and even what types of exotic hadrons can be well defined are still unclear. Partly because of this, the observation of each of these new structures leads to different models such as compact tetraquarks (or pentaquarks), hadronic molecules, hybrid states, hadro-charmonia, and kinematic effects, etc. Nevertheless, a deeper understanding of how the hadron spectrum, in particular that of the excited hadrons above (or at least close to) strong decay thresholds, is organized can shed light on the color confinement problem of QCD. For th...

Resonant $$a_0(980)$$ state in triangle rescattering $$D_s^+\rightarrow \pi ^+\pi ^0\eta $$ decays

“…Despite the fact that B(D + s → ρ + η ) is a few times smaller than B(D + s → ρ + η) [10], they give similar contributions to B(D + s → a 0 π) and B(D + s → π(a 0 →)ηπ ). Since ρ η ( ) ,π , the ρ meson decay width is not negligible, which causes the width effect [21,25,26]. As a test, we also treat the ρ meson as a stable particle.…”

Triangle singularity appearing as an X(3872) -like peak in B→(J/ψπNakamura1 2020Phys. Rev. D16180View full textAdd to dashboardCite

“…[34]. Attempts have been made to interpret some XYZ exotic candidates as bumps due to TSs [35][36][37][38][39][40][41][42][43][44][45].…”

Analytic Properties of Triangle Feynman Diagrams in Quantum Field Theory

“…I have presented a detailed analysis of dispersion representations for the triangle diagram, laying main emphasis on the appearance of the anomalous contributions in these representations. These anomalous singularities play an important role in the analysis of physical processes, see, e.g., [21][22][23][24][25][26] and a recent review [27] for details. In some kinematic regions, the properties of the triangle diagram and the amplitudes of the corresponding processes are mainly determined by the anomalous contributions.…”