Renormalizability of a lattice chiral fermion in the overlap formulation

Renormalizability of a lattice chiral fermion is studied at one loop level in the overlap formulation in four dimensions. The fermion chirality is examined including the self-energy corrections due to gauge interactions. Divergent terms breaking the chiral symmetry do not appear and the chiral fermion is renormalized, preserving the correct chiral properties without adding new counter-terms or tuning the parameters involved. The divergent part of the wave function renormalization factor agrees with that of the continuum theory. The overlap formulation of a lattice chiral fermion has passed the important test, the renormalizability, at one loop level.