Implications of NSI constraints from ANTARES and IceCube on a simplified $Z^\prime$ model

Recently the neutrino experiments ANTARES and IceCube have released new constraints to the non-standard neutrino interaction (NSI) parameter $\epsilon^d_{\mu\tau}$ (flavor off-diagonal). These new constraints are stronger than those obtained from a combination of COHERENT and neutrino oscillation data. In the light of the recent constraints from ANTARES and IceCube data on the NSI parameter $\epsilon^d_{\mu\tau}$, in this work, we study the new physics implications on the parameter space of a simplified $Z^\prime$ model with lepton flavor violating ($\mu\tau$) couplings. For a $Z^\prime$ boson with a mass heavier than the $\tau$ lepton, our results show that ANTARES and IceCube can provide additional constraints to such a new physics scenario with $\mu\tau$ couplings, when compared to bounds from low-energy flavor physics. Moreover, these neutrino experiments can exclude a similar region than ATLAS experiment, showing the potential to provide complementary information to the one obtained from direct searches at the Large Hadron Collider. The impact of the expected sensitivity at DUNE and Belle II experiments is also studied.