Uncovering Secret Neutrino Interactions at Tau Neutrino Experiments

We investigate the potential of future tau neutrino experiments for identifying the $\nu_\tau$ appearance in probing secret neutrino interactions. The reference experiments include the DUNE far detector utilizing the atmospheric data, which is for the first time in probing the secret interactions, the Forward Liquid Argon Experiment (FLArE100) detector at the Forward Physics Facility (FPF), and emulsion detector experiments such as SND@LHC, AdvSND, FASER$\nu$2, and SND@SHiP. For concreteness, we consider a reference scenario in which the hidden interactions among the neutrinos are mediated by a single light gauge boson $Z'$ with a mass at most below the sub-GeV scale and an interaction strength $g_{\alpha \beta}$ between the active neutrinos. We confirm that these experiments have the capability to significantly enhance the current sensitivities on $g_{\alpha \beta }$ for $m_{Z'} \lesssim 500$ MeV due to the production of high energy neutrinos and excellent ability to detect tau neutrinos. Our analysis highlights the crucial role of downward-going DUNE atmospheric data in the search for secret neutrino interactions because of the rejection of backgrounds dominated in the upward-going events. Specifically, 10 years of DUNE atmospheric data can provide the best sensitivities on $g_{\alpha \beta}$ which is about two orders of magnitude improvement. In addition, the beam-based experiments such as FLArE100 and FASER$\nu$2 can improve the current constraint on $g_{e\tau}$ and $g_{\mu\tau}$ by more than an order of magnitude after the full running of the high luminosity LHC with the integrated luminosity of 3 ab$^{-1}$. For $g_{e\mu}$ and $g_{ee}$ the SHiP experiment can play the most important role in the high energy region of $E> few~100$ MeV.