Virial coefficients of trapped and untrapped three-component fermions with three-body forces in arbitrary spatial dimensions

Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in d spatial dimensions, both in homogeneous space and in a harmonic trapping potential of frequency ?. Using the three-body problem to renormalize, we report analytic results for the change in the fourth- and fifth-order virial coefficients ?b4 and ?b5 as functions of ?b3. Additionally, we argue that in the 0 limit the relationship bnT=n-d/2bn holds between the trapped (T) and the homogeneous coefficients for arbitrary temperature and coupling strength (not merely in scale-invariant regimes). Finally, we point out an exact, universal (coupling- and frequency-independent) relationship between ?b3T in one dimension with three-body forces and ?b2T in two dimensions with two-body forces