New test of Lorentz symmetry using ultrahigh-energy cosmic rays

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We propose an innovative test of Lorentz symmetry by observing pairs of simultaneous parallel extensive air showers produced by the fragments of ultrahigh-energy cosmic ray nuclei which disintegrated in collisions with solar photons.

• We show that the search for a cross-correlation of showers in arrival time and direction becomes background free for an angular scale < 3^\circ and a time window {\cal O}(10 s).
• We also show that if the solar photo-disintegration probability of helium is {\cal O} (10^{-5.5}) then the hunt for spatiotemporal coincident showers could be within range of existing cosmic ray facilities, such as the Pierre Auger Observatory.
• We demonstrate that the actual observation of a few events can be used to constrain Lorentz violating dispersion relations of the nucleon.