Probing CPT violation in neutrino oscillation: A three flavor analysis

We have studied $CPT$ violation in neutrino oscillation considering three flavor framework with matter effect. We have constructed a new way to find the oscillation probability incorporating $CPT$ violating terms without any approximation. Then $CPT$ violation with atmospheric neutrinos for a magnetized iron calorimeter detector considering the muons (directly measurable with high resolution) of the charge current events has been studied for zero and nonzero $\theta_{13}$ values. It is found that a potential bound of $\delta b_{32} \lapp 6\times 10^{-24}$ GeV at 99% CL can be obtained with 1 Mton.year exposure of this detector; and unlike neutrino beam experiments, there is no possibility to generate `fake' $CPT$ violation due to matter effect with atmospheric neutrinos. The advantages of atmospheric neutrinos to discriminate $CPT$ violation from CP violation and nonstandard interactions are also discussed.