In neutrino oscillation with non-standard interactions (NSI) the system is enriched with
CP violation caused by phases due to NSI in addition to the standard lepton
Kobayashi-Maskawa phase $¥delta$. In this paper we show that it is possible to
disentangle the two CP violating effects by measurement of muon neutrino appearance
by a near-far two detector setting in neutrino factory experiments.
Prior to the quantitative analysis we investigate in detail the various features of
the neutrino oscillations with NSI, but under the assumption that only one of the NSI elements,
$¥varepsilon_{e ¥mu}$ or $¥varepsilon_{e ¥tau}$, is present.
They include synergy between the near and the far detectors, the characteristic
differences between the $¥varepsilon_{e ¥mu}$ and $¥varepsilon_{e ¥tau}$ systems,
and in particular, the parameter degeneracy.
Finally, we use a concrete setting of muon energy 50 GeV and two magnetized iron
detectors at the two baselines, one at $L=3000$ km and the other at $L=7000$ km,
each having a fiducial mass of 50 kton to study the discovery potential of NSI and its
CP violation effects.
We demonstrate by assuming $4 ¥times 10^{21}$ useful muon decay
for both polarities that one can identify non-standard CP violation down to
$¥vert ¥varepsilon_{e ¥mu} ¥vert ¥simeq ¥text{a few} ¥times 10^{-3}$,
% $¥vert ¥varepsilon_{e ¥mu} ¥vert ¥simeq ¥text{ several} ¥times 10^{-4}$,
and $¥vert ¥varepsilon_{e ¥tau} ¥vert ¥simeq 10^{-2}$ at 3$¥sigma$ CL
for $¥theta_{13}$ down to $¥sin^2 2¥theta_{13} = 10^{-4}$ in most of the
region of $¥delta$. The impact of existence of NSI on measurement of
$¥delta$ and the mass hierarchy is also worked out.