  We present an exploratory study of the electromagnetic corrections to meson
masses and the hadronic vacuum polarization using $N_f=2+1$ Domain Wall
fermions. These corrections are estimated with two different approaches, a
stochastic approach using $U(1)$ gauge configurations for the photon fields,
and a perturbative approach through a QED perturbative expansion of the QCD+QED
path integral. We compare results and statistical errors from both methods.
