The talk will discuss two prime candidates for exotic hadrons in the
light-meson sector: the hybrid candidate $\pi_1(1600)$ with manifestly
non-$q\bar{q}$ quantum numbers, $J^{PC}=1^{-+}$, and the tetraquark
candidate $a_1(1420)$ located in the vicinity of the $K^*\bar{K}$ threshold.
Based on high-precision data from the COMPASS experiment at CERN, we
observe the $\pi_1(1600)$ hybrid candidate as a resonance in the
$\rho(770)\pi$ and $\eta^\prime\pi$ systems. Moreover, our studies bring
a long-awaited understanding of the seemingly contradictory claims made
in previous analyses of the $\rho(770)\pi\,P$ partial wave.
Studying the tetraquark candidate $a_1(1420)$, we find evidence for a
so-called triangle singularity, a much sought-after effect of the strong
interaction. Our new analysis suggests that the resonance-like signal
seen in the $f_0(980)\pi$ system is produced by such a triangle
singularity, which causes the particles produced in the collision to
change their identities via mutual interaction right at the interaction
point.
I will demonstrate how progress in the understanding of the strong
interaction benefits from a tight collaboration between theory and
experiment on the example of the cooperation of the COMPASS experiment
and the Joint Physics Analysis Center (JPAC).
M. Pepe-Altarelli, P. Silva