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Testing Lorentz Invariance with UHECR Spectrum
Li Ye
IHEP, CAS, Sep. 26, 2008
Outline
Lorentz Invariant Violation and UHECR spectrum
Theoretical UHECR spectrum UHECR spectrum modified by LIV Constraints on LIV parameter
Lorentz Invariant Violation(LIV)
GZK cutoff
Neutrinos
UHE
Photon decay
Special Relativity Higher theoryLower-energy approximation
Sidney Coleman, Sheldon L. Glashow, Phys.Rev. D59 (1999) 116008
2 2 2 2E m p p
UHECR spectrum and GZK cutoff
Source galactic => extragalactic
E(eV)
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
UHECR spectrum can not be a single power law.
Hires:
Auger:
Thus, LIV can be constrained by the spectrum of UHECRs .
5
6
Newest Experimental results
E, eV
Theoretical UHECR Spectrum
CMBp p e e
CMBp p
Propagation The expansion of universe
CMBp p e e
CMBp p
Sources Homogeneous in space Power law spectrum
with index
V.Berezinsky, A.Z.Gazizov, S.I.Grigorieva Phys.Rev. D74 (2006) 043005
Influence of LIV on spectrum The modified inelasticity of interactions
Laboratory system
Proton rest system
Energy loss of proton interactions with CMB
UHECR Spectrum
Spectrum modified by LIV
Cofidence regions
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.30th.
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