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.