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Several air shower observatories have established that the number of muonsproduced in UHE air showers is significantly larger than that predicted bymodels. We argue that the only solution to this muon deficit, compatible withthe observed Xmax distributions, is to reduce the transfer of energy from thehadronic shower into the EM shower, by reducing the production or decay ofpi0s. We present four different models of new physics, each with a theoreticalrationale, which can accomplish this. One has a pure proton composition andthree have mixed composition. Two entail new particle physics and suppress pi0production or decay above LHC energies. The other two are less radical butnonetheless require significant modifications to existing hadron productionmodels -- in one the changes are only above LHC energies and in the other thechanges extend to much lower energies. We show that the models havedistinctively different predictions for the correlation between the number ofmuons at ground and Xmax in hybrid events, so that with future hybrid data itshould be possible to discriminate between models of new physics anddisentangle the particle physics from composition.

Testing models of new physics with UHE air shower observations