Constraining the violation of the equivalence principle with IceCube atmospheric neutrino data

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Abstract

The recent high-statistics high-energy atmospheric neutrino data collected by IceCube open a new window to probe new physics scenarios that are suppressed in lower-energy neutrino experiments. In this paper we analyze the IceCube atmospheric neutrino data to constrain the violation of equivalence principle (VEP) in the framework of three neutrinos with nonuniversal gravitational couplings. In this scenario the effect of the VEP on neutrino oscillation probabilities can be parametrized by two parameters, $\mathrm{\ensuremath{\Delta}}{\ensuremath{\gamma}}_{21}\ensuremath{\equiv}{\ensuremath{\gamma}}_{2}\ensuremath{-}{\ensuremath{\gamma}}_{1}$ and $\mathrm{\ensuremath{\Delta}}{\ensuremath{\gamma}}_{31}\ensuremath{\equiv}{\ensuremath{\gamma}}_{3}\ensuremath{-}{\ensuremath{\gamma}}_{1}$, where ${\ensuremath{\gamma}}_{i}$'s denote the coupling of neutrino mass eigenstates to the gravitational field. By analyzing the latest muon-tracks data sets of IceCube-40 and IceCube-79, besides providing the two-dimensional allowed regions in the $(\ensuremath{\phi}\mathrm{\ensuremath{\Delta}}{\ensuremath{\gamma}}_{21},\ensuremath{\phi}\mathrm{\ensuremath{\Delta}}{\ensuremath{\gamma}}_{31})$ plane, we obtain the upper limits $|\ensuremath{\phi}\mathrm{\ensuremath{\Delta}}{\ensuremath{\gamma}}_{21}|<9.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}$ (at 90% C.L.), which improves the previous limit by $\ensuremath{\sim}4$ orders of magnitude, and $|\ensuremath{\phi}\mathrm{\ensuremath{\Delta}}{\ensuremath{\gamma}}_{31}|\ensuremath{\lesssim}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}$ (at 90% C.L.), which improves the current limit by $\ensuremath{\sim}1$ order of magnitude. Also we discuss in detail and analytically the effect of the VEP on neutrino oscillation probabilities.

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