  We explore different branches of the fermion doublers with Wilson fermion in
perturbation theory, in the context of additive mass renormalization and chiral
anomaly, and show that by appropriately averaging over suitably chosen branches
one can reduce cut-off artifacts. Comparing the central branch with all other
branches, we find that the central branch, among all the avatars of the Wilson
fermion, is the most suitable candidate for exploring near conformal lattice
field theories.
