The atmospheric neutrino data collected by the Super-Kamiokande experiment span about four decades in neutrino energy E , and are thus appropriate to probe the energy dependence of the oscillation wavelength \lambda associated to \nu _ { \mu } \leftrightarrow \nu _ { \tau } flavor transitions , when these are assumed to explain the data .
Such dependence takes the form \lambda ^ { -1 } \propto E ^ { n } in a wide class of theoretical models , including “ standard ” oscillations due to neutrino mass and mixing ( n = -1 ) , energy-independent oscillations ( n = 0 ) , and violations of the equivalence principle or of Lorentz invariance ( n = 1 ) .
We study first how the theoretical zenith distributions of sub-GeV , multi-GeV , and upward-going muon events change for different integer values of n .
Then we perform a detailed analysis of the Super-Kamiokande data by treating the energy exponent n as a free parameter , with unconstrained scale factors for both the amplitude and the phase of \nu _ { \mu } \leftrightarrow \nu _ { \tau } oscillations .
We find a best-fit range n = -0.9 \pm 0.4 at 90 % C.L. , which confirms the standard scenario ( n = -1 ) as the dominant oscillation mechanism , and strongly constrains possible concurrent exotic processes ( n \neq - 1 ) .
In particular , we work out the interesting case of leading standard oscillations plus subleading terms induced by violations of special or general relativity principles , and obtain extremely stringent upper bounds on the amplitude of such violations in the ( \nu _ { \mu } , \nu _ { \tau } ) sector .