Quantum Field Theory and the Standard Model by Schwartz M.D. z-lib.org · Problem 2.3
Lorentz invariance and second quantization — Schwartz M.D. z-lib.org
Physics — QFT · gzk-bound
Problem
The GZK bound. In 1966 Greisen, Zatsepin and Kuzmin argued that we should not see cosmic rays (high-energy protons hitting the atmosphere from outer space) above a certain energy, due to interactions of these rays with the cosmic microwave background.
(a) The universe is a blackbody at 2.73 K. What is the average energy of the photons in outer space (in electronvolts)?
(b) How much energy would a proton (p+) need to collide with a photon (γ) in outer space to convert it to a 135 MeV pion (π0)? That is, what is the energy threshold for p++γ→p++π0?
(c) How much energy does the outgoing proton have after this reaction?
This GZK bound was finally confirmed experimentally 40 years after it was conjectured [Abbasi et al., 2008].