Abstract.We suggest the most model-independent and simple description of the γγ → ππ

We obtain in analytical form the dressed propagator of the massive RaritaSchwinger field taking into account all spin components. We found that the nearest analogy for dressing the Rarita-Schwinger field in spin-1/2 sector is dressing the two Dirac fermions of opposite parity with presence of mutual transitions. The calculation of the self-energy contributions confirms that besides the leading spin-3/2 component the Rarita-Schwinger field contains also two spin-1/2 components of different parity.

We suggest the description of the dressed fermion propagator with parity non-conservation in the form with separated positive and negative energy poles. We found general form of the γ-matrix off-shell projectors and corresponding resonance factors. The parity violation leads to deviation of resonance factors from the naive Breit-Wigner form and to appearance of non-trivial spin corrections. However, for top quark with SM vertex the resonance factor returns to the standard one due to Γ/m ≪ 1.

We develop the spectral representation of propagator for $n$ mixing fermion fields in the case of $\mathsf{P}$-parity violation. The approach based on the eigenvalue problem for inverse matrix propagator makes possible to build the system of orthogonal projectors and to represent the matrix propagator as a sum of poles with positive and negative energies. The procedure of multiplicative renormalization in terms of spectral representation is investigated and the renormalization matrices are obtained in a closed form without the use of perturbation theory. Since in theory with $\mathsf{P}$-parity violation the standard spin projectors do not commute with the dressed propagator, they should be modified. The developed approach allows us to build the modified (dressed) spin projectors for a single fermion and for a system of fermions.Comment: 22 pages, this is refreshed and extended versio

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