Probing the Planck scale with neutrino oscillations

Abstract

Quantum gravity "foam", among its various generic Lorentz non-invariant effects, would cause neutrino mixing. It is shown here that, if the foam is manifested as a nonrenormalizable effect at scale M , the oscillation length generically decreases with energy E as (E/M ) −2 . Neutrino observatories and long-baseline experiments should have therefore already observed foam-induced oscillations, even if M is as high as the Planck energy scale. The null results, which can be further strengthened by better analysis of current data and future experiments, can be taken as experimental evidence that Lorentz invariance is fully preserved at the Planck scale, as is the case in critical string theory.The noisy vacuum of a quantum theory of gravity could _ a priori be imagined to have a variety of effects on the wavefunction of a particle traveling through it. Although unitarity would probably constrain the effects of the vacuum on the wavefunction's amplitude, one could imagine that its phase might be shifted by the local effects of quantum black holes and the like which quickly pop in and out of the vacuum. Also, the type (flavor) of the particle might be affected: for example, a virtual or quantum black hole could as Hawking has suggested [1], erase information by swallowing a neutrino of one type and spit out one of a different type as it evaporates. Thus, possible effects that could be considered include Lorentz invariance violating (LIV) indices of refraction [2,3,4], flavor oscillations of neutral particles [5,6,7,8,9], and corrugations of wavefronts, i.e. Rayleigh scattering [8]. Rayleigh scattering, which would imply momentum non-conservation, appears to be ruled out by the observation that 10 MeV neutrinos propagated without Rayleigh scattering from supernova 1987A [8] (assuming that their scattering cross-section off cells of Planck foam scales as E 2). We conclude that if such "foam" effects exist, they must preserve translation invariance on the Planck distance scale and on larger ones; thus any non-vanishing effects must be cooperative and coherent over space-like distances in this range of scales; it may cause wave dispersion but not opalescence or translucence.

Determination of the atmospheric neutrino flux and searches for new physics with AMANDA-II

“…An L / E À2 energy dependence (n ¼ 2) has been proposed in the context of loop quantum gravity [26] and in the case of nonrenormalizable VLI effects caused by the space-time foam [27]. Both the L / E À1 (n ¼ 1) and the L / E À3 (n ¼ 3) cases have been examined in the context of violations of the equivalence principle [28][29][30].…”

Methods of approaching decoherence in the flavor sector due to space-time foam

“…One of the most sensitive probes of such stochastic quantum-gravity phenomena are neutrinos [7,16,17,18,19,20], in particular high-energy ones [21]. It is the point of this article to present various approaches to gravitationally-induced decoherence of matter and to classify some characteristic experimental predictions that could be falsified in current or near future neutrino experiments.…”

Perturbative Lorentz andCPTviolation for neutrino and antineutrino oscillations

“…A few consider also anisotropic effects [13,[34][35][36][37][38]. Here, we treat the general case, allowing all components of (a L ) α ab and (c L ) αβ ab to be nonzero.…”