We use the background field method to extract the "connected" piece of the
neutron electric polarizability. We present results for quenched simulations
using both clover and Wilson fermions and discuss our experience in extracting
the mass shifts and the challenges we encountered when we lowered the quark
mass. For the neutron we find that as the pion mass is lowered below 500\MeV,
the polarizability starts rising in agreement with predictions from chiral
perturbation theory. For our lowest pion mass, m_\pi=320\MeV, we find that
\alpha_n = 3.8(1.3)\times 10^{-4}\fm^3, which is still only one third of the
experimental value. We also present results for the neutral pion; we find that
its polarizability turns negative for pion masses smaller than 500\MeV which
is puzzling.Comment: 11 pages, 8 figures, presented at the XXVII International Symposium
on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, Chin