Mixing of fermion fields of opposite parities and baryon resonances

TL;DR

This paper investigates a unique fermion mixing mechanism of opposite parity fields, relevant for baryon resonances, revealing interference effects in partial wave analyses that could improve understanding of resonance structures.

Contribution

It introduces a novel fermion mixing effect of opposite parity fields with potential applications to baryon resonance physics, providing a new framework for analyzing partial wave interference.

Findings

The mixing effect is observable in $ ext{P}_{13}$ and $ ext{D}_{13}$ partial waves.

Interference patterns between resonance and background are clarified.

Potential application to complex resonance structures in $ ext{S}_{11}$ and $ ext{P}_{11}$ waves.

Abstract

We consider a loop mixing of two fermion fields of opposite parities whereas the parity is conserved in a Lagrangian. Such kind of mixing is specific for fermions and has no analogy in boson case. Possible applications of this effect may be related with physics of baryon resonances. The obtained matrix propagator defines a pair of unitary partial amplitudes which describe the production of resonances of spin $J$ and different parity ${1/2}^{\pm}$ or ${3/2}^{\pm}$. The use of our amplitudes for joint description of $\pi N$ partial waves $P_{13}$ and $D_{13}$ shows that the discussed effect is clearly seen in these partial waves as the specific form of interference between resonance and background. Another interesting application of this effect may be a pair of partial waves $S_{11}$ and $P_{11}$ where the picture is more complicated due to presence of several resonance states.