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Gamma ray burst (GRB) fireballs provide one of very few astrophysicalenvironments where one can contemplate the acceleration of cosmic rays toenergies that exceed 10^20 eV. The assumption that GRBs are the sources of theobserved cosmic rays generates a calculable flux of neutrinos produced when theprotons interact with fireball photons. With data taken during constructionIceCube has already reached a sensitivity to observe neutrinos produced intemporal coincidence with individual GRBs provided that they are the sources ofthe observed extragalactic cosmic rays. We here point out that the GRB originof cosmic rays is also challenged by the IceCube upper limit on a possiblediffuse flux of cosmic neutrinos which should not be exceeded by the fluxproduced by all GRB over Hubble time. Our alternative approach has theadvantage of directly relating the diffuse flux produced by all GRBs tomeasurements of the cosmic ray flux. It also generates both the neutrino fluxproduced by the sources and the associated cosmogenic neutrino flux in asynergetic way.

GRBs on probation: testing the UHE CR paradigm with IceCube