Whether composite fermion states with ``wrong'' chiralities dissolve into cuts

TL;DR

This paper investigates the behavior of composite fermion states with incorrect chiralities in lattice models, showing they effectively decouple at low energies due to vanishing propagators, which supports the consistency of certain lattice chiral fermion formulations.

Contribution

It demonstrates that composite fermion states with wrong chiralities decouple in the low-energy limit, providing insight into lattice chiral fermion behavior without spontaneous symmetry breaking.

Findings

Wrong-chirality three-fermion-states vanish at low energy

No spontaneous symmetry breaking occurs in the considered regime

Decoupling of wrong-chirality states supports lattice chiral fermion models

Abstract

In the possible scaling region for lattice chiral fermions advocated in hep-lat/9609037, no hard spontaneous symmetry breaking occurs and doublers are gauge-invariantly decoupled via mixing with composite three-fermion-states. However the strong coupling expansion breaks down due to no ``static limit'' for the low-energy limit ($p\sim 0$). We further analyze relevant Green functions of three-fermion-operators. It is shown that in the low-energy limit, the propagators of three-fermion-states with the ``wrong'' chiralities positively vanish due to the generalized form factors (the wave-function renormalizations) of these composite states vanishing as $O(p^4)$. This strongly implies that three-fermion-states with ``wrong'' chirality are ``decoupled'' in this limit.