Two-detector flavor sensitivity to ultra-high-energy cosmic neutrinos

Ultra-high-energy (UHE) cosmic neutrinos, with energies above 100 PeV, could be finally discovered in the near future. Measuring their flavor composition would reveal information about their production and propagation, but new techniques are needed for UHE neutrino telescopes to have the capabilities to do it. We address this by proposing a new way to measure the UHE neutrino flavor composition that does not rely on individual telescopes having flavor-identification capabilities. We manufacture flavor sensitivity from the joint detection by one telescope sensitive to all flavors -- the radio array of IceCube-Gen2 -- and one mostly sensitive to $\nu_\tau$ -- GRAND. From this limited flavor sensitivity, predominantly to $\nu_\tau$, and even under conservative choices of neutrino flux and detector size, we extract important insight. For astrophysics, we forecast meaningful constraints on the neutrino production mechanism; for fundamental physics, vastly improved constraints on Lorentz-invariance violation. These are the first measurement forecasts of the UHE $\nu_\tau$ content.