Testing violations of Lorentz invariance with cosmic rays

Abstract

Cosmic rays are the highest energy particles available for our study, and as such serve as excellent probes of the effects of Lorentz invariance violations which are expected to increase with energy. This general paradigm is investigated in this paper by studying the effects of such violations within the Coleman-Glashow model in which each particle species may have its own maximum attainable velocity, even exceeding that of light in vacuo. The particular focus here is that the muon neutrino may have the maximum speed exceeding that of light. We show that such an assumption leads to the elongation of the decay lifetime of the pion which increases with energy over and above the time dilation effects. We provide a transparent analytical derivation of the spectral intensities of muon neutrinos and muons generated in the Earth's atmosphere by cosmic rays. In this derivation we not only account for elongation of the pion lifetime, but also for the loss of energy by the neutrinos by radiation of the electron-positron pairs through the Cohen-Glashow process during their propagation. We then compare the theoretical spectra with observations of neutrinos and muons from large instruments like IceCube and BUST to set a limit of $10 À13 on the fractional excess speed of neutrinos over that of light. We also show that the ratio of the spectral intensities of downward and upward moving neutrinos at various angles constitute an exclusive diagnostic for the Cohen-Glashow process, which may be searched for in the IceCube data set. We conclude the paper with several comments, including those related to improvements of these tests when definite signals of Griesen-Zatsepin-Kuzmin neutrinos will be observed.

Limiting superluminal electron and neutrino velocities using the 2010 Crab Nebula flare and the IceCube PeV neutrino events

“…Superluminal Neutrino Velocity Constraint Assuming δ e ≥ 0 Since eq. (6) implies that δ νe ≫ δ e , we find that δ ν ≃ δ νe ∼ 5.6 × 10 −19 , almost ten orders of magnitude better than the time-of-flight constraint from the SN1987A neutrino burst [20] and more than five orders of magnitude better than the constraint obtained from the study of atmospheric neutrino spectra [21]. Our new constraints apply directly to the dimension-4 operators in the SME; c e T T ≡ −δ e andc (4) ≡ −δ ν (see tables D6 and D19 of Ref.…”

“…In ad-dition, time-of-flight constraints from the detection of a multi-MeV neutrino burst from supernova 1987A [18,19] yielded the constraint δ ν ≤ 2×10 −9 [20]. A comparison of atmospheric neutrino spectra with theoretical spectra expected from the change in the pion decay rate if neutrinos are superluminal has yielded the indirect constraint δ ν ≤ O(10 −13 ) [21]. New IceCube observations, together with new constraints on superluminal electron velocities derived from γ-ray observations of the September, 2010 Crab Nebula flare using the Large Area Telescope on the Fermi Gamma Ray Space Telescope, now allow one to place stronger constraints on LIV in both the electron and the neutrino sectors.…”

Olber's paradox for superluminal neutrinos: constraining extreme neutrino speeds at TeV–ZeV energies with the diffuse neutrino background

“…Such limits have previously been derived for protons [5] and photons [6]. Recent limits of this kind for neutrinos include those from e + e − pair production [7][8][9][10], neutrino splitting [11], and suppression of pion decay [10,12]. These limits rule out the OPERA results in standard Lorentz invariance theories, and they become stronger at high energy.…”

“…I assume that expected astrophysical neutrino backgrounds from pion production processes actually exist; if pions do not decay or neutrinos decay en route [7,10,12,19], the limits will not apply.…”

Use of energy loss mechanisms to constrain Lorentz invariance violations

“…If the energy loss increases with the amount of Lorentz invariance violation, the observations of high energy particles may be used to place limits on the size of the Lorentz invariant violating parameters (see Refs. [18][19][20][21][22][23][24]). Reactions of this sort include: photon and neutrino splitting (γ → 3γ and ν l → ν l ν l ν l ), photon production by charged leptons and neutrinos (e ± → e ± γ and ν l → ν l γ), and pair production by neutrinos (ν l → ν l e + e − ), which will be the one we will use hereafter when specific information is needed; we refer the reader to Ref.…”