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We construct the propagator for a free fermionic unparticle field from basicconsiderations of scale and Lorentz invariance. The propagator is fixed up to anormalization factor which is required to recover the result of a free masslessfermion field in the canonical limit of the scaling dimension. Two new featuresappear compared to the bosonic case. The propagator contains both \gamma andnon-\gamma terms, and there is a relative phase of \pi/2 between the two in thetime-like regime for arbitrary scaling dimension. This should result inadditional interference effects on top of the one known in the bosonic case.The non-\gamma term can mediate chirality flipped transitions that are notsuppressed by a light fermion mass but are enhanced by a large bosonic mass inloops, compared to the pure particle case. We employ this last feature to setstringent bounds on the Yukawa couplings between a fermionic unparticle and anordinary fermion through electromagnetic dipole moments and radiative decays oflight fermions.

Electromagnetic Dipole Moments and Radiative Decays of Particles from Exchange of Fermionic Unparticles