1. Testing Lorentz Invariance with UHECR Spectrum Li Ye IHEP, CAS, Sep. 26, 2008

2. Outline Lorentz Invariant Violation and UHECR spectrum Theoretical UHECR spectrum UHECR spectrum modified by LIV Constraints on LIV parameter

3. Lorentz Invariant Violation(LIV) GZK cutoff Neutrinos UHE Photon decay Special Relativity Higher theory Lower-energy approximation Sidney Coleman, Sheldon L. Glashow, Phys.Rev. D59 (1999) 116008

4. UHECR spectrum and GZK cutoff Source galactic => extragalactic E(eV)

5. GZK cutoff ? Hires VS. AGASA If Hires, the energy calibration of AGASA is in doubt? If AGASA, Lorentz invariant is violated? E, eV F.W. Stecker, S.T. Scully, Astropart.Phys. 23 (2005) 203-209

6. UHECR spectrum can not be a single power law. Hires: Auger: Thus, LIV can be constrained by the spectrum of UHECRs. Newest Experimental results E, eV

7. Theoretical UHECR Spectrum Propagation The expansion of universe Sources Homogeneous in space Power law spectrum with index V.Berezinsky, A.Z.Gazizov, S.I.Grigorieva Phys.Rev. D74 (2006) 043005

8. Influence of LIV on spectrum The modified inelasticity of interactions Laboratory system Proton rest system Energy loss of proton interactions with CMB UHECR Spectrum

9. Spectrum modified by LIV

10. Cofidence regions

11. Conclusion UHECR spectrum will be modified by LIV Observational data can set constraint on LIV. The result from Hires is Experimental data with higher precision can give better test on Lorentz Invariant This talk is updated on Nov.30 th.