GZK cutoff and constraints on the Lorentz invariance violation

1. GZK cutoff and constraints on the Lorentz invariance violation Bi Xiao-Jun (IHEP) 2011/5/9

2. GZK cutoff • We know that the UHECRs (E > 1018 eV) are originated from the extragalactic sources. When propagate in the intergalactic space they interact with CMB photons, which results in energy and flux depletion. In particular, the photomeson process (pγ->pπ) will induce a suppression in the spectrum above (3–6) ×1019 eV and lead to the well-known Greisen-Zatsepin-Kuzmin (GZK) cutoff. • The spectrum of UHECRs can be calculated by assuming the source distribution and injection energy spectrum at the sources.

3. Introduction of LIV • To account for the AGASA data beyond the GZK cutoff, LIV has been introduced by Coleman and Glashow, • Even a LIV parameter as small as ~3 × 10-23 may lead to the removal of the GZK cutoff

4. Cutoff confirmed by HiRes and Auger • The HiRes Collaboration confirms the GZK cutoff with a 5σ standard deviation • The Pierre Auger Collaboration gives results consistent with HiRes and rejects a single power-law spectrum above 1019 eV at the 6 σ confidence level • The two sets of data can set constraints on the LIV parameters introduced by Coleman and Glashow

5. Propagation of UHECRs • We assume the composition of UHECRs is pure proton • In the propagation we consider the adiabatic energy loss by the universe expansion and photopion production and e+e- pair production when interacting with CMB • At z=0, • σ is the interaction cross section, K is the average fraction of energy loss We have the threshold

6. At z, • We employ two assumptions: (1) proton sources are distributed homogeneously in the Universe without the evolution effect; (2) the source spectrum is a power law with index γg

7. The observed spectrum • Solving the above equation with the initial condition E(z=0)=E0, we get the observed spectrum is [Berezinsky 06] • J(E0 )ΔE0= F(Eg) Δ Eg, this means (Eg, Eg + dEg) at redshift z contribute to the detected energy interval (E0 , E0 + d E0); the sum of all redshifts gives the total flux • L0 is the total luminosity of UHE protons and is determined by matching the calculated spectrum to the observational data.

8. Predicted spectrum and fit of γg GZK is due to photopion production Angle is explained by e+e- pair

9. LIV takes effects • The inelasticity K=Eπ/Ep, is given [Alfaro 2003] • The equation is solved numerically and averaged over the scattering angle.

10. Inelasticity with(out) the LIV • ξ = +-1 ×10-23 • Generally the LIV surpress the inelasticity at high energies.

11. After considering the LIV • For very high energies or for large magnitudes of LIV parameters, the source spectra tend not to be distorted

12. Fit power index and LIV parameter • For the HiRes monocular spectra and the Auger combined spectrum, respectively We see

13. For iron component • Auger shows that the UHECR are iron-like particles, we can also set constraints on the LIV • To have the cutoff the reaction 56Fe+CMB-> 55Mn+p is only possible for ξ > -2 ×10-25. On the other hand, spontaneous fragmentation 56Fe->55Mn+p should be forbidden for iron energy less than 3×1020eV, this gives ξ < 1.2 × 1023 • Finally we get -2 ×10-25 < ξ < 1.2 × 1023

14. Summary • HiRes and Auger observed the GZK cutoff. • This observation give constraints on the LIV effect. • Calculate the UHECR propagation in the intergalactic space and the interaction with CMB, we give a global fit to the UHECR power index and the LIV parameter ξ