The chiral fermion model with local multifermion interactions proposed in
Nucl. Phys. B486 (1997) 282 and Phys. Rev. D61 (2000) 054502 processes an exact
SU_L(2) chiral gauge symmetry and SU_L(2) by U_R(1) chiral flavour symmetry on
a lattice and a plausible scaling region for the target chiral gauge theory in
the continuum limit. Following the previous analysis of massive and massless
fermion spectra in the scaling region, we compute the coupling vertices between
gauge field and fermions by the strong multifermion coupling expansion and
analytical continuation of these vertex functions in the energy-momentum space.
We show a peculiar scenario that a massless fermion is SU_L(2)-chirally gauged
in the low energy and 15 non-degenerate massive Dirac fermions are
SU_L(2)-vectorially gauged at the lattice scale O(1/a). The Ward identities
associated to the chiral gauge symmetry are realized by both the massless
chiral fermion and massive Dirac fermions. These Ward identities protect the
perturbative calculations in the small gauge coupling from hard gauge-symmetry
breakings and lead to the normal gauge-invariant renormalization prescription.
The vacuum functional is perturbatively computed by a continuum regularization
scheme in 16 edges of Brillouin zones. We achieve the correct form of the gauge
anomaly and U_L(1) fermion-flavour singlet anomaly with the soft chiral
symmetry breaking scale that is much smaller than the lattice scale. The
residual breakings of chiral gauge symmetry after the gauge anomaly
cancellation are eliminated in the normal gauge-invarinant renormalization
prescription. We discuss the consistency of the scenario and the reasons for it
to work for perturbative and non-perturbative gauge field.Comment: 40 pages, RevTeX, revised version to appear in Nucl. Phys.
