Nucleon axial charge from quenched lattice QCD with domain wall fermions and improved gauge action

In our previous DWF calculation with the Wilson gauge action at $\beta=6.0$ ($a^{-1}\simeq$ 1.9 GeV) on a $16^3 \times 32 \times 16$ lattice, we found that $\Ga$ had a fairly strong dependence on the quark mass. A simple linear extrapolation of $\Ga$ to the chiral limit yielded a value that was almost a factor of two smaller than the experimental one. Here we report our recent study of this issue. In particular, we investigate possible errors arising from finite lattice volume, especially in the lighter quark mass region. We employ a RG-improved gauge action (DBW2), which maintains very good chiral behavior even on a coarse lattice ($a^{-1}\simeq$ 1.3 GeV), in order to perform simulations at large physical volume ($> (2{\rm fm})^3$). Our preliminary results suggest that the finite volume effect is significant.