Enhancing Sensitivity to Non-Standard Neutrino Interactions at INO combining muon and hadron information

The neutral current non-standard interactions (NSI's) of neutrino with matter fermions while propagating through long distances inside the Earth matter can give rise to the extra matter potentials apart from the standard MSW potential due to the $W$-mediated interactions in matter. In this paper, we explore the impact of flavor violating neutral current NSI parameter $\varepsilon_{\mu\tau}$ in the oscillation of atmospheric neutrino and antineutrino using the 50 kt magnetized ICAL detector at INO. We find that due to non-zero $\varepsilon_{\mu\tau}$, $\nu_\mu\rightarrow\nu_\mu$ and $\bar\nu_\mu\rightarrow\bar\nu_\mu$ transition probabilities get modified substantially at higher energies and longer baselines, where vacuum oscillation dominates. We estimate the sensitivity of the ICAL detector for various choices of binning schemes and observables. The most optimistic bound on $\varepsilon_{\mu\tau}$ that we obtain is $-0.01 < \varepsilon_{\mu\tau} < 0.01$ at 90$\%$ C.L. using 500 kt$\cdot$yr exposure and considering $E_\mu,\, \cos\theta_\mu,\,E'_{\rm had}$ as observables in their ranges [1, 21] GeV, [-1, 1], and [0, 25] GeV respectively. For the first time we show that the charge identification capability of the ICAL detector is crucial to set stringent constraints on $\varepsilon_{\mu\tau}$. We also show that when we marginalize over $\varepsilon_{\mu\tau}$ in fit in its range of -0.1 to 0.1, the mass hierarchy sensitivity deteriorates by 10$\%$ to 20$\%$ depending on the analysis mode, and the precision measurements of atmospheric parameters remain quite robust at the ICAL detector.