  The Chiral Magnetic Effect (CME) is a fundamental prediction of QCD, and
various observables have been proposed in heavy ion collisions to access this
physics. Recently the CMS Collaboration \cite{Khachatryan:2016got} has reported
results from p+Pb collisions at 5.02 TeV on one such observable, the
three-point correlator. The results are strikingly similar to those measured at
the same particle multiplicity in Pb+Pb collisions, which have been attributed
to the CME. This similarity, combined with two key assumptions about the
magnetic field in p+Pb collisions, presents a major challenge to the CME
picture. These two assumptions as stated in the CMS paper are (1) that the
magnetic field in p+Pb collisions is smaller than that in Pb+Pb collisions and
(2) that the magnetic field direction is uncorrelated with the flow angle. We
test these two postulates in the Monte Carlo Glauber framework and find that
the magnetic fields are not significantly smaller in central p+Pb collisions,
however the magnetic field direction and the flow angle are indeed
uncorrelated. The second finding alone gives strong evidence that the
three-point correlator signal in Pb+Pb and p+Pb is not an indication of the
CME. Similar measurements in d+Au over a range of energies accessible at RHIC
would be elucidating. In the same calculational framework, we find that even in
Pb+Pb collisions, where the magnetic field direction and the flow angle are
correlated, there exist large inhomogeneities that are on the size scale of
topological domains. These inhomogeneities need to be incorporated in any
detailed CME calculation.
