Astrophysical Limits on Lorentz Violation For All Charged Species

If Lorentz violation exists, it will affect the thresholds for pair creation processes. Lorentz-violating operators that change the maximum velocities of charged particles may increase or decrease the extinction rate of γ-rays moving through space. If the emissions from high-energy astrophysical sources do not show any signs of anomalous absorption, this allows us to place bounds on the Lorentz-violating c coefficients for multiple species of charged particles. The bounds for a species of mass mX based on observing photons at an energy Eγ can be O(m 2 X/E 2 γ), which corresponds to limits at the 10 (mX/m 2 e) level for the most energetic photons. 1 [email protected] There is growing interest in the possibility that Lorentz symmetry may not be exact in nature. Many candidate theories of quantum gravity predict Lorentz violation in some regimes. For example, Lorentz violation may arise spontaneously in string theory [1, 2] or elsewhere [3]. There could also be Lorentz-violating physics in loop quantum gravity [4, 5] and non-commutative spacetime [6, 7] theories, Lorentz violation through spacetimevarying couplings [8], or anomalous breaking of Lorentz and CPT symmetries [9] in certain spacetimes. If Lorentz violation were uncovered experimentally, it would be a discovery of tremendous importance, telling us a great deal about the structure of new physics. To date, there is no significant evidence for Lorentz violation, although there have been many highprecision searches. The experimental tests have included studies of matter-antimatter asymmetries for trapped charged particles [10, 11, 12] and bound state systems [13, 14], determinations of muon properties [15, 16], analyses of the behavior of spin-polarized matter [17, 18], frequency standard comparisons [19, 20, 21, 22], Michelson-Morley experiments with cryogenic resonators [23, 24, 25], Doppler effect measurements [26, 27], measurements of neutral mesons [28, 29, 30, 31, 32, 33], polarization measurements on the light from distant galaxies [34, 35, 36], high-energy astrophysical tests [37, 38, 39, 40] and others. In this paper, we shall look at some further astrophysical bounds, based on observations of high-energy γ-rays; what is especially interesting about these bounds is that some of them apply to all charged particle species—including those of the second and third fermion generations and the charged intermediate vector bosons. Possible violations of Lorentz invariance are described theoretically by the standard model extension (SME). The SME contains local Lorentz-violating operators built from known standard model fields (including gravity) and constant background tensors [41, 42, 43]. Constraints on various Lorentz-violating effects can be translated into bounds on the renormalizable coefficients of the SME. We shall consider a form of Lorentz violation that can exist for any type of particle. This type of Lorentz violation is very simple, and it also happens that if the Lorentzviolating coefficients are Plank scale suppressed, their effects will become important just at the very highest observable energy scales. The Lagrange density for free fermions with this form of Lorentz violation is Lψ = ψ̄[i(γ μ + cγν)∂μ −mψ]ψ. (1) The coefficients c form a traceless tensor, and at leading order, only the symmetric part of the tensor is physical. For spinless charged particles, the equivalent form of Lorentz violation is Lφ = (∂ φ)(∂μφ) + k μν φ (∂νφ ∗)(∂μφ)−m 2 φ |φ| 2 , (2) and for a gauge field LA = − 1 4 F Fμν − 1 4 (kF ) α ναμ (F Fρ ν + F F ν ρ) . (3)