Editing Greisen–Zatsepin–Kuzmin limit (section)

==GZK paradox==
{{update|date=January 2019}}
{{unsolved|physics|Why is it that some cosmic rays appear to possess [[energy|energies]] that are theoretically too high, given that there are no possible near-Earth sources, and that rays from distant sources should have scattered by the cosmic microwave background radiation?}}

A number of observations have been made by the largest cosmic-ray experiments [[Akeno Giant Air Shower Array]] (AGASA), [[High Resolution Fly's Eye Cosmic Ray Detector]], the [[Pierre Auger Observatory]] and [[Telescope Array Project]] that appeared to show cosmic rays with energies above the GZK limit. 
These observations appear to contradict the predictions of [[special relativity]] and [[particle physics]] as they are presently understood. However, there are a number of possible explanations for these observations that may resolve this inconsistency.
* The observed EECR particles can be heavier nuclei instead of protons
* The observations could be due to an instrument error or an incorrect interpretation of the experiment, especially wrong energy assignment.
* The cosmic rays could have local sources within the GZK horizon (although it is unclear what these sources could be).

=== Weakly interacting particles ===
Another suggestion involves ultra-high-energy weakly interacting particles (for instance, [[neutrino]]s), which might be created at great distances and later react locally to give rise to the particles observed. In the proposed Z-burst model, an ultra-high-energy cosmic neutrino collides with a relic anti-neutrino in our galaxy and annihilates to hadrons.<ref>{{cite journal |last1=Fargion |first1=D. |last2=Mele |first2=B. |last3=Salis |first3=A. |title=Ultra–High-Energy Neutrino Scattering onto Relic Light Neutrinos in the Galactic Halo as a Possible Source of the Highest Energy Extragalactic Cosmic Rays |journal=The Astrophysical Journal |date=June 1999 |volume=517 |issue=2 |pages=725–733 |doi=10.1086/307203 |arxiv=astro-ph/9710029 |bibcode=1999ApJ...517..725F |s2cid=118916318 }}</ref> This process proceeds through a (virtual) Z-boson:
: <math>\nu + \bar{\nu} \to \text{Z} \to \text{hadrons}.</math>

The cross-section for this process becomes large if the center-of-mass energy of the neutrino antineutrino pair is equal to the Z-boson mass (such a peak in the cross-section is called "resonance"). Assuming that the relic anti-neutrino is at rest, the energy of the incident cosmic neutrino has to be
: <math>E = \frac{{m_\text{Z}}^2}{2 m_\nu} = 4.2 \times 10^{21} \left(\frac{\text{eV}}{m_\nu}\right)~\text{eV},</math>
where <math>m_\text{Z}</math> is the mass of the Z-boson, and <math>m_\nu</math> the mass of the neutrino.