Editing Greisen–Zatsepin–Kuzmin limit (section)

==Computation==
The limit was independently computed in 1966 by [[Kenneth Greisen]],<ref name=Greisen1966>{{cite journal |last=Greisen |first=Kenneth |date=1966 |title=End to the cosmic-ray spectrum? |journal=Physical Review Letters |volume=16 |issue=17 |pages=748–750 |doi=10.1103/PhysRevLett.16.748 |bibcode=1966PhRvL..16..748G}}</ref> [[Georgy Zatsepin]], and [[Vadim Kuzmin (physicist)|Vadim Kuzmin]]<ref name=Zatsepin>{{cite journal |last1=Zatsepin |first1=G.T. |author1-link=Georgiy Zatsepin |last2=Kuz'min |first2=V.A. |author2-link=Vadim Kuzmin (physicist) |year=1966 |title=Upper limit of the spectrum of cosmic rays |journal=Journal of Experimental and Theoretical Physics Letters |volume=4 |pages=78–80 |bibcode=1966JETPL...4...78Z |url=http://www.jetpletters.ac.ru/ps/1624/article_24846.pdf }}</ref> based on interactions between [[cosmic ray]]s and the photons of the [[cosmic microwave background radiation]] (CMB). They predicted that cosmic rays with energies over the threshold energy of {{val|5|e=19|ul=eV}} would interact with cosmic microwave background photons <math>\gamma_{\rm CMB}\;,</math> relatively [[blueshift]]ed by the speed of the cosmic rays, to produce [[pion]]s through the [[Delta baryon|<math>\Delta</math> resonance]],

: <math>p + \gamma_\text{CMB} \to \Delta^+ \to p + \pi^0 \;,</math>

or

: <math>p + \gamma_\text{CMB} \to \Delta^+ \to n + \pi^+ ~.</math>

Pions produced in this manner proceed to decay in the standard pion channels – ultimately to photons for neutral pions, and photons, positrons, and various neutrinos for positive pions. Neutrons also decay to similar products, so that ultimately the energy of any cosmic ray proton is drained off by production of high-energy photons plus (in some cases) high-energy electron–positron pairs and neutrino pairs.

The pion production process begins at a higher energy than ordinary electron-positron [[pair production]] (lepton production) from protons impacting the CMB, which starts at cosmic-ray proton energies of only about {{val|e=17|ul=eV}}. However, pion production events drain 20% of the energy of a cosmic-ray proton, as compared with only 0.1% of its energy for electron–positron pair production.

This factor {{nobr|of 200 {{=}} {{sfrac| 20% | 0.1% }} }} comes from two causes: The pion has a mass only about ~130&nbsp;times the leptons, but the extra energy appears as different kinetic energies of the pion or leptons, and results in relatively more kinetic energy transferred to a heavier product pion, in order to [[conservation of linear momentum|conserve momentum]]. The much larger total energy losses from pion production result in pion production becoming the process limiting high-energy cosmic-ray travel, rather than the lower-energy process of light-lepton production.

The pion production process continues until the cosmic ray energy falls below the threshold for pion production. Due to the mean path associated with this interaction, [[extragalactic cosmic ray]] protons traveling over distances larger than {{val|50|ul=Mpc}} ({{val|163|ul=Mly}}) and with energies greater than the threshold should never be observed on Earth. This distance is also known as GZK horizon.

The precise GZK limit is derived under the assumption that [[ultra-high energy cosmic rays]], those with energies above {{val|1|e=18|ul=eV}}, are protons. Measurements by the largest [[cosmic-ray observatory]], the [[Pierre Auger Observatory]], suggest that most ultra-high energy cosmic rays are [[HZE ions|heavier elements known as HZE ions]].<ref name="Aab2017">{{cite arXiv |eprint=1710.07249|author1=The Pierre Auger Collaboration|title=Inferences on Mass Composition and Tests of Hadronic Interactions from 0.3 to 100 EeV using the water-Cherenkov Detectors of the Pierre Auger Observatory |class=astro-ph.HE|year=2017}}</ref> In this case, the argument behind the GZK limit does not apply in the originally simple form: however, as Greisen noted, the [[Giant Dipole Resonance|giant dipole resonance]] also occurs roughly in this energy range (at 10 EeV/nucleon) and similarly restricts very long-distance propagation.