# Constraints from orbital motions around the Earth of the environmental fifth-force hypothesis for the OPERA superluminal neutrino phenomenology

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## Abstract

It has been recently suggested by Dvali and Vikman that the superluminal neutrino phenomenology of the OPERA experiment may be due to an environmental feature of the Earth, naturally yielding a long-range fifth force of gravitational origin whose coupling with the neutrino is set by the scale *M*_{*}, in units of reduced Planck mass. Its characteristic length λ should not be smaller than one Earth’s radius *R*_{e}, while its upper bound is expected to be slightly smaller than the Earth-Moon distance (60 *R*_{e}). We analytically work out some orbital effects of a Yukawa-type fifth force for a test particle moving in the modified field of a central body. Our results are quite general since they are not restricted to any particular size of λ; moreover, they are valid for an arbitrary orbital configuration of the particle, i.e. for any value of its eccentricity *e*. We find that the dimensionless strength coupling parameter α is constrained to |α| ≲ 1 × 10^{−10} − 4 × 10^{−9} for 1 *R*_{e} ≤ λ ≤ 10 *R*_{e} by the laser data of the Earth’s artificial satellite LAGEOS II, corresponding to *M*_{*} ≳ 4 × 10^{9} − 1*.*6 × 10^{10}. The Moon perigee allows to obtain |α| ≲ 3 × 10^{−11} for the Earth-Moon pair in the range 15 *R*_{e} ≲ λ ≲ 60 *R*_{e}, which translates as *M*_{*} ≳ 3 × 10^{10} − 4*.*5 × 10^{10}. Our results are neither necessarily limited to the superluminal OPERA scenario nor to the Dvali-Vikman model, in which it is *M*_{*} ~ 10^{−6} at λ ~ 1 *R*_{e}, in contrast with our bounds: they generally extend to any theoretical scenario implying a fifth-force of Yukawa-type.

### Keywords

Neutrino Physics Models of Quantum Gravity### References

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