  We present a valence calculation of the electric polarizability of the
neutron, neutral pion, and neutral kaon on two dynamically generated
nHYP-clover ensembles. The pion masses for these ensembles are 227(2) MeV and
306(1) MeV, which are the lowest ones used in polarizability studies. This is
part of a program geared towards determining these parameters at the physical
point. We carry out a high statistics calculation that allows us to: (1)
perform an extrapolation of the kaon polarizability to the physical point; we
find $\alpha_K =0.269(43)\times10^{-4}$fm$^{3}$, (2) quantitatively compare our
neutron polarizability results with predictions from $\chi$PT, and (3) analyze
the dependence on both the valence and sea quark masses. The kaon
polarizability varies slowly with the light quark mass and the extrapolation
can be done with high confidence.
