- "why is the limit imposed by pion pair production as opposed
to electron pair production? the energies required for electron
pair production is /significantly/ less than pion pair
production." I recently came across the figure below, which
depicts the energy loss of a proton times 1/E (the relative
energy loss per year), due to electron-positron pair production,
and - at higher energies - pion production: [Fig 1 (a) from
V.Berezinsky, A.Z.Gazizov, S.I.Grigorieva "On astrophysical
solution to ultra high energy cosmic rays", Phys.Rev. D74 (2006)
043005, arXiv:hep-ph/0204357] As one sees, the electron-positron
pair production leads to a loss and is the dominant contribution
at energies below ≈ 1019 eV, but at higher energies pion
production takes over, increasing the energy loss by a factor of
~ 100 which is the effect responsible for the cut-off in the
spectrum. Essentially the same is depicted differently in the
figure below from Roberto Aloisio's talk, slide 2. I didn't hear
the talk but a good guess is tha