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Register a new userLorentz Violation and Ultrahigh-Energy Photons
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Matteo Galaverni
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The propagation of photons, electrons and positrons at ultra-high energies above 10^{19} eV can be changed considerably if the dispersion relations of these particles are modified by terms suppressed by powers of the Planck scale. We recently pointed out that the current non-observation of photons in the ultra-high energy cosmic ray flux at such energies can put strong constraints on such modified dispersion relations. In the present work we generalize these constraints to all three Lorentz invariance breaking parameters that can occur in the dispersion relations for photons, electrons and positrons at first and second order suppression with the Planck scale. We also show how the excluded regions in these three-dimensional parameter ranges would be extended if ultra-high energy photons were detected in the future.
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Lorentz symmetry breaking at very high energies may lead to photon dispersion relations of the form omega^2=k^2+xi_n k^2(k/M_Pl)^n with new terms suppressed by a power n of the Planck mass M_Pl. We show that first and second order terms of size xi_1 > 10^(-14) and xi_2 < -10^(-6), respectively, would lead to a photon component in cosmic rays above 10^(19) eV that should already have been detected, if corresponding terms for electrons and positrons are significantly smaller. This suggests that Lorentz invariance breakings suppressed up to second order in the Planck scale are unlikely to be phenomenologically viable for photons.
There has been much interest in possible violations of Lorentz invariance, particularly motivated by quantum gravity theories. It has been suggested that a small amount of Lorentz invariance violation (LIV) could turn off photomeson interactions of ultrahigh energy cosmic rays (UHECRs) with photons of the cosmic background radiation and thereby eliminate the resulting sharp steepening in the spectrum of the highest energy CRs predicted by Greisen Zatsepin and Kuzmin (GZK). Recent measurements of the UHECR spectrum reported by the HiRes and Auger collaborations, however, indicate the presence of the GZK effect. We present the results of a detailed calculation of the modification of the UHECR spectrum caused by LIV using the formalism of Coleman and Glashow. We then compare these results with the experimental UHECR data from Auger and HiRes. Based on these data, we find a best fit amount of LIV of $4.5^{+1.5}_{-4.5} times 10^{-23}$,consistent with an upper limit of $6 times 10^{-23}$. This possible amount of LIV can lead to a recovery of the cosmic ray spectrum at higher energies than presently observed. Such an LIV recovery effect can be tested observationally using future detectors.
The Large High Altitude Air Shower Observatory~(LHAASO) is one of the most sensitive gamma-ray detector arrays currently operating at TeV and PeV energies. Recently the LHAASO experiment detected ultra-high-energy~(UHE; $E_{gamma}gtrsim 100~mathrm{TeV}$) photon emissions up to $1.4~mathrm{PeV}$ from twelve astrophysical gamma-ray sources. We point out that the detection of cosmic photons at such energies can constrain the photon self-decay motivated by superluminal Lorentz symmetry violation~(LV) to a higher level, thus can put strong constraints to certain LV frameworks. Meanwhile, we suggest that the current observation of the PeV-scale photon with LHAASO may provide hints to permit a subluminal type of Lorentz violation in the proximity of the Planckian regime, and may be compatible with the light speed variation at the scale of $3.6times 10^{17}~mathrm{GeV}$ recently suggested from gamma-ray burst~(GRB) time delays. We further propose detecting PeV photons coming from extragalactic sources with future experiments, based on LV-induced threshold anomalies of $e^{+}e^{-}$ pair-production, as a crucial test of subluminal Lorentz violation. We comment that these observations are consistent with a D-brane/string-inspired quantum-gravity framework, the space-time foam model.
A general framework for tests of Lorentz invariance with electromagnetic waves is presented, allowing for operators of arbitrary mass dimension. Signatures of Lorentz violations include vacuum birefringence, vacuum dispersion, and anisotropies. Sensitive searches for violations using sources such as active galaxies, gamma-ray bursts, and the cosmic microwave background are discussed. Direction-dependent dispersion constraints are obtained on operators of dimension 6 and 8 using gamma-ray bursts and the blazar Markarian 501. Stringent constraints on operators of dimension 3 are found using 5-year data from the Wilkinson Microwave Anisotropy Probe. No evidence appears for isotropic Lorentz violation, while some support at one sigma is found for anisotropic violation.
All quadratic translation- and gauge-invariant photon operators for Lorentz breakdown are included into the Stueckelberg Lagrangian for massive photons in a generalized xi-gauge. The corresponding dispersion relation and tree-level propagator are determined exactly, and some leading-order results are derived. The question of how to include such Lorentz-violating effects into a perturbative quantum-field expansion is addressed. Applications of these results within Lorentz-breaking quantum field theories include the regularization of infrared divergences as well as the free propagation of massive vector bosons.
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