Cascade Appearance Signatures of Sterile Neutrinos at 1-100 TeV

Neutrino telescopes provide strong sensitivity to sterile neutrino oscillations through matter-enhanced oscillation, occurring in the few TeV energy range for eV$^{2}$-scale neutrino mass-squared splittings. Prior searches have focused on $\nu_\mu$ disappearance, which has a particularly strong sensitivity to the mixing angle $\theta_{24}$ via $\nu_\mu\rightarrow\nu_s$ transitions. Nowadays, the $\nu_\mu\rightarrow\nu_e$ and $\nu_\mu\rightarrow\nu_\tau$ appearance channels have been considered less promising at neutrino telescopes, due in part to the much smaller target volume for cascades relative to tracks. This work explores the detectability of these signatures at neutrino telescopes given present constraints on sterile neutrino mixing, and as an example, forecasts the sensitivity of the IceCube Neutrino Observatory to the mixing angles $\theta_{14}$, $\theta_{24}$, and $\theta_{34}$ in the 3+1 sterile neutrino model using the cascade channel with ten years of data. We find that $\nu_\tau$ appearance signatures consistent with the existing IceCube $\nu_\mu$ disappearance best-fit point are discoverable for values of $\theta_{34}$ consistent with world constraints, and that the sterile neutrino parameters favored by the BEST and gallium anomalies are expected to be testable at the 95\% confidence level.