Determination of the neutrino mass ordering (NMO) is one of the biggest priorities in the intensity frontier of high energy particle physics. To accomplish that goal a lot of efforts are being put together with the atmospheric, solar, reactor, and accelerator neutrinos. In the standard 3-flavor framework, NMO is defined to be normal if $m_1<m_2<m_3$, and inverted if $m_3<m_1<m_2$, where $m_1$, $m_2$, and $m_3$ are the masses of the three neutrino mass eigenstates $ u_1$, $ u_2$, and $ u_3$ respectively. Interestingly, two long-baseline experiments T2K and NO$ u$A are playing a leading role in this direction and provide a $sim2.4sigma$ indication in favor of normal ordering (NO) which we find in this work. In addition, we examine how the situation looks like in presence of non-standard interactions (NSI) of neutrinos with a special focus on the non-diagonal flavor changing type $varepsilon_{etau}$ and $varepsilon_{emu}$. We find that the present indication of NO in the standard 3-flavor framework gets completely vanished in the presence of NSI of the flavor changing type involving the $e-tau$ flavors.
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