Quenched Chiral Log and Light Quark Mass from Overlap Fermions

We study the quenched chiral behavior of the pion with mass as low as $\approx 180$ MeV. The calculation is done on a quenched lattice of size $16^3\times 28$ and $a = 0.2$ fm with 80 configurations using overlap fermions and an improved gauge action. Using an improved constrained curve fitting technique, we find that the ground state pseudoscalar mass versus bare quark mass behavior is well controlled with small statistical errors; this permits a reliable fit of the quenched chiral log effects, a determination of the chiral log parameter ($\delta = 0.26(3)$), and an estimate of the renormalized mass of the light quark ($m^{\bar{MS}}(\mu=2 {\rm GeV}) = 3.7(3) {\rm MeV}$).