A systematic method is presented for determining the conditions on the parameters in the action of a parity-preserving gauge theory of gravity for it to contain no ghost or tachyon particles. The technique naturally accommodates critical cases in which the parameter values lead to additional gauge invariances. The method is implemented as a computer program, and is used here to investigate the particle content of parity-conserving Poincaré gauge theory, which we compare with previous results in the literature. We find 450 critical cases that are free of ghosts and tachyons, and we further identify 10 of these that are also power-counting renormalizable, of which four have only massless tordion propagating particles and the remaining six have only a massive tordion propagating mode.

We present 48 further examples, in addition to the 10 identified in [1], of ghost-and-tachyon-free critical cases of parity-conserving Poincaré gauge theories of gravity (PGT + ) that are also powercounting renormalizable (PCR). This is achieved by extending the range of critical cases considered. Of the new PCR theories, 7 have 2 massless degrees of freedom (d.o.f.) in propagating modes and a massive 0 − or 2 − mode, 8 have only 2 massless d.o.f., and 33 have only massive mode(s). We also clarify the treatment of non-propagating modes in determining whether a theory is PCR. *

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