  We derive a dynamical field theory for self-propelled particles subjected to
generic torques and forces by explicitly coarse-graining their microscopic
dynamics, described by a many-body Fokker-Planck equation. The model includes
both intrinsic torques inducing self-rotation, as well as interparticle torques
leading to, for instance, the local alignment of particles' orientations.
Within this approach, although the functional form of the pairwise interactions
does not need to be specified, one can directly map the parameters of the field
theory onto the parameters of particle-based models. We perform a linear
stability analysis of the homogeneous solution of the field equations and find
both long-wavelength and short-wavelength instabilities. The former signals the
emergence of a macroscopic structure, which we associate with motility-induced
phase separation, while the second one signals the growth of a finite structure
with a characteristic size. Intrinsic torques hinder phase separation, pushing
the onset of the long-wavelength instability to higher activities. Further,
they generate finite-sized structures with a characteristic size proportional
to both the self-propulsion velocity and the inverse of the self-rotation
frequency. Our results show that a general mechanism might explain why
chirality tends to suppress motility-induced phase separation but instead
promotes the formation of non-equilibrium patterns.
