A field theory in $3+1$ dimensions contains two fermions, two Abelian gauge fields, and one complex scalar, with dynamics fixed by a Becchi-Rouet-Stora-Tyutin (BRST) symmetry. For a specific parameter configuration, the fermion mass matrix becomes non-Hermitian, and the propagators exhibit complex-conjugate poles. We evaluate the one-loop fermion contribution to the scalar two-point function. Once the factor $i$ of the $e^{iS}$ normalization is removed, the contribution is real for real external momentum below the threshold $(m+m^{*}{)}^2$ of the two constituents, which follows from the pairing of complex-conjugate terms in the loop integral. The thresholds of the equal-mass pairs sit at complex $p^2$ and generate no cut on the real axis, while the mixed pair, whose constituent masses add up to the real number $m+m^{*}$, opens a cut. Across this cut, the upper and lower boundary values are related by complex conjugation, so that the associated spectral density is real. Its positivity is not established here. The BRST construction of the action provides the starting point for an algebraic renormalization analysis.

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