In a BRST-symmetric theory with non-Hermitian fermion mass matrix, the one-loop contribution to the φ†φ two-point function becomes real for real external momentum after removing the i factor from the e^{iS} normalization, due to conjugate pole pairing.
Non-Hermitian extension of gauge theories and implications for neutrino physics
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abstract
An extension of QED is considered in which the Dirac fermion has both Hermitian and anti-Hermitian mass terms, as well as both vector and axial-vector couplings to the gauge field. Gauge invariance is restored when the Hermitian and anti-Hermitian masses are of equal magnitude, and the theory reduces to that of a single massless Weyl fermion. An analogous non-Hermitian Yukawa theory is considered, and it is shown that this model can explain the smallness of the light-neutrino masses and provide an additional source of leptonic CP violation.
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Pathways to Real Composite Operators from Non-Hermitian Fermions
In a BRST-symmetric theory with non-Hermitian fermion mass matrix, the one-loop contribution to the φ†φ two-point function becomes real for real external momentum after removing the i factor from the e^{iS} normalization, due to conjugate pole pairing.