Spacetime noncommutativity and ultra-high energy cosmic ray experiments

Abstract: If new physics were capable to push the neutrino-nucleon inelastic cross section three orders of magnitude beyond the standard-model (SM) prediction, then ultra-high energy (UHE) neutrinos would have already been observed at neutrino observatories. We use such a constraint to reveal information on the scale of noncommutativity (NC) Lambda_NC in noncommutative gauge field theories (NCGFT) where neutrinos possess a tree-level coupling to photons in a generation-independent manner. In the energy range of interest (10^10 to 10^11 GeV) the theta-expansion (|theta| ~ 1/Lambda_NC^2) and therefore the perturbative expansion in terms of Lambda_NC retains no longer its meaningful character, forcing us to resort to those NC field-theoretical frameworks involving the full theta-resummation. Our numerical analysis of the contribution to the process coming from the photon exchange, pins impeccably down a lower bound on Lambda_NC to be as high as around up to 900 (450) TeV, depending on the estimates for the cosmogenic neutrino flux. If, on the other hand, one considers a surprising recent result occurred in Pierre Auger Observatory (PAO) data, that UHE cosmic rays are mainly composed of highly-ionized Fe nuclei, then our bounds get weaker, due to the diminished cosmic neutrino flux. Nevertheless, we show that even for the very high fraction of heavy nuclei in primary UHE cosmic rays, our method may still yield remarkable bounds on Lambda_NC, typically always above 200 TeV. Albeit, in this case one encounters a maximal value for the Fe fraction from which any useful information on Lambda_NC can be drawn, delimiting thus the applicability of our method.