The main goal of the spectroscopy program at COMPASS is to explore the light-meson spectrum in the mass range below about $2\,\text{GeV}/c^2$ using diffractive dissociation reactions. Our flagship channel is the production of three charged pions in the reaction: $\pi^- + p \to \pi^-\pi^-\pi^+ + p_\text{recoil}$, for which COMPASS has acquired the so far world's largest dataset of roughly $50\,\text{M}$ exclusive events using an $190\,\text{GeV}/c$ $\pi^-$ beam.

Based on this dataset, we performed an extensive partial-wave analysis.

In order to extract the parameters of the $\pi_J$ and $a_J$ resonances that appear in the $\pi^-\pi^-\pi^+$ system, we performed the so far most comprehensive resonance-model fit, using Breit-Wigner parametrizations.

This method in combination with the high statistical precision of our data allows us to study ground and excited states.

We study the $a_4(2040)$ resonance in the $\rho(770)\pi G$ and $f_2(1270)\pi F$ decays.

In addition to the ground state resonance $a_1(1260)$, we have found evidence for the $a_1(1640)$, which is the first excitations of the $a_1(1260)$, in our data.

We also study the spectrum of $\pi_2$ states by simultaneously describing four $J^{PC}=2^{-+}$ waves using three $\pi_2$ resonances, the $\pi_2(1670)$, the $\pi_2(1880)$, and the $\pi_2(2005)$.

Using a novel analysis approach, where the resonance-model fit is performed simultaneously in narrow bins of the squared four-momentum transfer $t'$ between the beam pion and the target proton, allows us to study the $t'$ dependence of resonant and non-resonant components included in our model.

We observe that for most of the partial waves, the non-resonant components show a steeper $t'$ spectrum compared to the resonances and that the $t'$ spectrum of most of the resonances becomes shallower with increasing resonance mass.

We also study the $t'$ dependence of the relative phases between resonance components. The pattern we observe is consistent with a common production mechanism of these states.