Whether composite fermion states with “wrong” chiralities dissolve into cuts

In the possible scaling region for lattice chiral fermions advocated in Nucl. Phys. B486 (1997) 282, 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 ∼ 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). This strongly implies that three-fermion-states with “wrong” chirality are “decoupled” in this limit. October, 1997 PACS 11.15Ha, 11.30.Rd, 11.30.Qc a) E-mail address: [email protected] 1 A possible scaling region of chiral fermions The attempt to get around the “no-go” theorem [1] for the “vector-like” phenomenon of chiral fermions on a lattice is currently a very important issue of theoretical particle physics([2]–[13]). One attempt is the approach of multifermion couplings, which can be traced back from the recent lattice formulation of the Standard Model[14] to the pioneer model suggested in ref.[15] and successive work[16, 17, 18] in the past years. On the other hand, it was pointed out in an crucial paper[19] that the models proposed in ref.[15] fail to give chiral fermions in the continuum limit. The reasons are that an NJL[20] spontaneous symmetry breaking phase separates the strong-coupling symmetric phase from the weak-coupling symmetric phase, and the right-handed Weyl states do not completely disassociate from the left-handed chiral fermions. Further, another crucial paper[21] tried to extent the “no-go” theorem into interacting theories based on the plausible argument of such theories being local. The definite failure of the models so constructed has then been a general belief[2]. To more easily show the possibility and reason of dynamics for such constructed models to work, we further analyze the simple and anomaly-free model of multifermion couplings proposed in the ref.[17]. Note that ψ L (i = 1, 2) is an SUL(2) gauged doublet, χR is an SUL(2) singlet and both are two-component Weyl fermions. χR is treated as a “spectator” fermion. ψ i L and χR fields are dimensionful [a 1 2 ]. The following action for chiral fermions with the SUL(2)⊗UR(1) chiral symmetries on the lattice is suggested: S = Sf + S1 + S2, (1) Sf = 1 2a ∑