The main goal of the spectroscopy program at COMPASS is to explore the light-meson spectrum below about $2\,\text{GeV}/c^2$ in diffractive production. Our flagship channel is the decay into three charged pions: $p + \pi^-\to \pi^-\pi^-\pi^+ + p_\text{recoil}$, 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 resonance parameters of the $\pi_J$ and $a_J$ states that appear in the $\pi^-\pi^-\pi^+$ system, we performed the so far largest resonance-model fit, using Breit-Wigner resonances and non-resonant contributions.

This method in combination with the high statistical precision of our measurement allows us to study ground and excited states.
We have found an evidence of the $a_1(1640)$ and $a_2(1700)$ in our data, which are the first excitations of the $a_1(1260)$ and $a_2(1320)$, respectively. The relative strength of the excited states with respect to the corresponding ground state is larger in the $f_2(1270)\,\pi$ decay mode compared to the $\rho(770)\,\pi$ decay mode.
We also study the spectrum of $\pi_2$ states in our data. Therefore, we simultaneously describe four $J^{PC}=2^{-+}$ waves in the resonance-model fit by using three $\pi_2$ resonances, the $\pi_2(1670)$, the $\pi_2(1880)$, and the $\pi_2(2005)$. Within the limits of our model, we can conclude that the $\pi_2(2005)$ is required to describe all four $2^{-+}$ waves properly.