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Resolving the NO$ν$A and T2K tension in the presence of Neutrino Non-Standard interactions

The current data of the two long-baseline accelerator experiments NO$ν$A and T2K, shows a tension at more than 90$\%$ C.L. for 2 degrees of freedom, in the determination of the standard CP-phase $δ_{\mathrm {CP}}$ in case of neutrino normal ordering (NO). NO$ν$A measures the value close to $δ_{\mathrm {CP}} \sim 0.8 π$, while T2K prefers the value of $δ_{\mathrm {CP}} \sim 1.4 π$. We show that such a tension can be resolved if one hypothesizes the existence of neutral-current non-standard interactions (NSI) of neutrinos involving the flavor changing type $e-μ$ or the $e-τ$ sectors with couplings $|\varepsilon_{eμ}| \sim |\varepsilon_{eτ}|\sim 0.2$. Remarkably, our analyses show that in the presence of such NSI, both the experiments point towards the same common value of the standard CP-phase $δ_{\mathrm {CP}} \sim 3π/2$, thereby indicating towards the maximal CP-violation in the standard $3ν$ framework. We also show that the best fit values of the new CP-phases $ϕ_{eμ}$ or $ ϕ_{eτ}$ are close to $\sim 3π/2$, hence pointing towards the maximal CP-violation in the NSI sector.