Nucleon axial charge from quenched lattice QCD with domain wall fermions

We present a quenched lattice calculation of the nucleon isovector vector and axial-vector charges $g_V$ and $g_A.$ The chiral symmetry of domain wall fermions makes the calculation of the nucleon axial charge particularly easy since the Ward-Takahashi identity requires the vector and axial-vector currents to have the same renormalization, up to lattice spacing errors of order ${O(a}^2).\mathrm{}$ The doubly blocked Wilson 2 (DBW2) gauge action provides enhancement of the good chiral symmetry properties of domain wall fermions at larger lattice spacing than the conventional Wilson gauge action. Taking advantage of these methods and performing a high statistics simulation, we find a significant finite volume effect between the nucleon axial charges calculated on lattices with (1.2 ${\mathrm{f}\mathrm{m})}^3$ and (2.4 ${\mathrm{f}\mathrm{m})}^3$ volumes $\left(a\approx 0.15\mathrm{fm}\right).\mathrm{}$ On the large volume we find $g_A=1.212\mathrm{}\pm 0.027\left(\mathrm{stat}\right)\pm 0.024\left(\mathrm{norm}\right).\mathrm{}$ The quoted systematic error is the dominant (known) one, corresponding to current renormalization. We discuss other possible remaining sources of error. This theoretical first principles calculation, which does not yet include isospin breaking effects, yields a value of $g_A$ only a little bit below the experimental one, $1.2670\pm \mathrm{0.0030.}$