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

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.