From oscillation dip to oscillation valley in atmospheric neutrino experiments

Atmospheric neutrino experiments can show the "oscillation dip" feature in data, due to their sensitivity over a large $L/E$ range. In experiments that can distinguish between neutrinos and antineutrinos, like INO, oscillation dips can be observed in both these channels separately. We present a data-driven approach -- that uses the asymmetry in the up and down events, binned in the reconstructed $L/E$ of muons – to demonstrate the dip, thereby confirming the oscillation hypothesis. We further propose, for the first time, the identification of an "oscillation valley" in the ($E_{\mu} - \cos\theta_{\mu}$) plane, feasible for detectors like INO having excellent muon energy and direction resolutions. We illustrate how this two-dimensional valley offers a clear visual representation and test of the $L/E$ dependence, the alignment of the valley quantifying the atmospheric mass-squared difference.