The L? structure of gauge theories with matter

In this work we present an algebraic approach to the dynamics and perturbation theory at tree-level for gauge theories coupled matter. The field will consider are: Chern-Simons-Matter, Quantum Chromodynamics, scalar Chromodynamics. Starting with construction of master action in classical Batalin-Vilkovisky formalism, extract $L_{\infty}$-algebra that allow us recursively calculate perturbiner expansion from its minimal model. Maurer-Cartan obtained procedure then motivate a generating function all scattering amplitudes. There are two interesting outcomes construction: generator fully-flavoured amplitudes via localisation on Dyck words; closed expressions fermion lines attached $n$-gluons arbitrary polarisations.