Stronger Neutrino Interactions at Extremely High Energies and the Muon Anomalous Magnetic Moment

A specific model of parity-conserving lepton substructure is considered. We show that a positive-definite contribution to the muon $(g-2)/2$ at the possible level of about $4\times 10^{-9}$, can be related to a significant increase in the interaction cross section for cosmic-ray neutrinos with energies above about $10^{19}$ eV. The additional cross section at $\sim 10^{20}$ eV is calculated to be $\sim 10^{-29}$ cm$^2$, which is about 100 times the standard weak-interaction cross section. The model involves an extremely massive, neutral lepton, with $m_L\cong 2\times 10^6$ GeV fixed by the new contribution to $(g-2)/2$.