## Details

**Abstract: **In this talk, I will present recent advances in the understanding of mesonic bound states in 2d QCD, obtained by employing synergy integrability techniques and the S-Matrix bootstrap. This talk will be based on **2406.11078**, **2312.15598** (with S. Komatsu), and some work in progress with P. Vieira and G. Lefundes.I will mainly focus on the 't Hooft model: 2D QCD in the large Nc limit, coupled to fundamental quarks. Here, the spectrum of mesons can be encoded as a solution of a TQ-Baxter equation, which is typical of integrable models. This reveals a rich analytical structure in the complex plane of quark masses and allows for systematic expansions. Furthermore, I will present some preliminary results on how the S-Matrix for the scattering of two bound states into two bound states can be *bootstrapped, *using as a minimal input the integrability spectrum, unitarity, and crossing. Remarkably, this integrability structure persists in generalized YM theories coupled to fundamental quarks, where the dynamics of gluons is enriched by a BF coupling to an adjoint scalar field. We formulate the spectral problem for mesons as TQ-system for any generic potential for the scalar field. This integrability structure makes possible to study systematically phases and critical points of the theory, in the space of potentials and quark masses.