Particle spectra of parity-violating theories: A less radical approach and an upgrade of the particle spectrum for any tensor Lagrangian framework

Due to computational barriers, parity violation effects have been grossly neglected in gravitational model-building, creating a significant gap in the landscape of existing models. We present a new algorithm for efficiently computing the particle spectrum for any parity-violating tensorial field theory. It allows us to extract conditions for the absence of massive ghosts without resorting to any manipulation of radicals in cases where the particle masses are irrational functions of the Lagrangian coupling coefficients. We test it against several examples, among which is the most general parity-indefinite Einstein-Cartan/Poincaré gravity that propagates two healthy massive scalars (in addition to the massless graviton). Furthermore, we upgrade the er software in the olfram anguage to accommodate parity-violating theories. er is a contribution to the xct project.