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Pauli Center Blackboard Seminar

On-shell renormalization in the presence of mixing and instability

by Bernd Kniehl (UHH)

Sem. room 2 (DESY Hamburg)

Sem. room 2

DESY Hamburg

We consider a system of unstable spin-1/2 fermions in a general parity-nonconserving theory with intergeneration mixing and explain how to renormalize its propagator matrix to all orders in perturbation theory. We work in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted according to the Lehmann-Symanzik-Zimmermann reduction formalism. Closed analytic expressions for the pole-mass counterterms and WFR matrices in terms of the self-energy functions are derived. In the Dirac case, we identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exploit them. By contrast, the WFR matrices are uniquely fixed in the Majorana case. We demonstrate that, in the presence of instability, the WFR matrices of the in and out states bifurcate in the sense that they are no longer related by pseudo-Hermitian conjugation.