Detector Requirements for Model-Independent Measurements of Ultrahigh Energy Neutrino Cross Sections

The ultrahigh energy range of neutrino physics (above $\sim 10^{7} \, \mathrm{GeV}$), as yet devoid of detections, is an open landscape with challenges to be met and discoveries to be made. Neutrino-nucleon cross sections in that range - with center-of-momentum energies $\sqrt{s} \gtrsim 4 \, \mathrm{TeV}$ - are powerful probes of unexplored phenomena. We present a simple and accurate model-independent framework to evaluate how well these cross sections can be measured for an unknown flux and generic detectors. We also demonstrate how to characterize and compare detector sensitivity. We show that cross sections can be measured to $\simeq ^{+65}_{-30}$% precision over $\sqrt{s} \simeq$ 4-140 TeV ($E_\nu = 10^7$-$10^{10}$ GeV) with modest energy and angular resolution and $\simeq 10$ events per energy decade. Many allowed novel-physics models (extra dimensions, leptoquarks, etc.) produce much larger effects. In the distant future, with $\simeq 100$ events at the highest energies, the precision would be $\simeq 15\%$, probing even QCD saturation effects.