Can INO be sensitive to flavor-dependent long-range forces?

Flavor-dependent long-range leptonic forces mediated by the ultra-light and neutral bosons associated with gauged $L_e-L_{\mu }$ or $L_e-L_{\tau }$ symmetry constitute a minimal extension of the Standard Model. In presence of these new anomaly free abelian symmetries, the SM remains invariant and renormalizable, and can lead to interesting phenomenological consequences. For an example, the electrons inside the Sun can generate a flavor-dependent long-range potential at the Earth surface, which can enhance ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ survival probabilities over a wide range of energies and baselines in atmospheric neutrino experiments. In this paper, we explore in detail the possible impacts of these long-range flavor-diagonal neutral current interactions due to $L_e-L_{\mu }$ and $L_e-L_{\tau }$ symmetries (one at-a-time) in the context of proposed 50 kt magnetized ICAL detector at INO. Combining the information on muon momentum and hadron energy on an event-by-event basis, ICAL will be sensitive to long-range forces at 90$\%$ (3$\sigma$) C.L. with 500 kt$\cdot$yr exposure if the effective gauge coupling ${\alpha }_{e\mu /e\tau }>1.2\times {10}^{-53}$ ($1.75\times {10}^{-53}$). The sensitivity of ICAL towards ${\alpha }_{e\mu }$ (${\alpha }_{e\tau }$) is $\sim 46$ (53) times better than the existing bound from the Super-Kamiokande experiment at 90$\%$ C.L., and at 3$\sigma$, the sensitivity of ICAL is comparable to the bounds obtained from the combined solar and KamLAND data.