Speaker
Description
Our current understanding of the rich spectrum of hadrons is governed by quantum chromodynamics (QCD). The universal parameters of hadronic resonances are encoded theoretically in the poles of the relevant $S$-matrix. And experimentally, hadronic resonances can appear as peaks in the invariant mass distributions. However, not all experimentally observed peaks in invariant mass distributions correspond to genuine hadronic resonances. Kinematic effects, such as triangle singularities governed by Landau equations, can also produce prominent enhancements. A notable example is the narrow enhancement, then called the $a_1(1420)$, in the three-pion energy spectrum at $\sqrt{s} \approx 1.42$~GeV with the $a_1$ quantum numbers observed at the COMPASS experiment. While this peak has been attributed to a one-loop triangle singularity involving intermediate on-shell $K^*(892)$, $K$ and $\bar{K}$ states producing an $f_0(980)$, this mechanism forms only part of a non-diagonal transition within a larger coupled-channel framework. Building on previous toy-model studies, we demonstrate the feasibility of embedding these one-loop triangle-singularity calculations into a comprehensive unitary three-body formalism (IVU). By combining up to $P$-wave isobars and all sub-channel isospins, we construct a nine-channel production amplitude that consistently incorporates final-state interactions. This amplitude is fitted to COMPASS lineshapes across different momentum transfers. Our model successfully reproduces the narrow enhancement in the $(f_0(980)\pi)_P$ channel, demonstrating that the triangle singularity mechanism sufficiently explains the COMPASS observations without requiring an additional, genuine $a_1(1420)$ pole. Incidentally, we also extract the parameters of the $a_1(1260)$ from the data. The techniques used in this analysis improves our understanding of triangle singularities, and is of relevance to a general audience.