The –Zatsepin–Greisen–Zatsepin–Kuzmin limit (GZK limit or GZK cutoff) is a theoretical upper limit on the energy of cosmic ray protons traveling from other galaxies through the intergalactic medium to our galaxy. The limit is (50 EeV), or about 8 joules (the energy of a proton travelling at ≈ % the speed of light). The limit is set by the slowing effect of interactions of the protons with the microwave background radiation over long distances (≈ 160 million light-years). The limit is at the same order of magnitude as the upper limit for energy at which cosmic rays have experimentally been detected, although indeed some detections appear to have exceeded the limit, as noted below. For example, one extreme-energy cosmic ray, the Oh-My-God Particle, which has been found to possess a record-breaking (50 joules) of energy (about the same as the kinetic energy of a 95 km/h baseball).
The precise GZK limit is derived under the assumption that ultra-high energy cosmic rays are protons. Measurements by the largest cosmic-ray observatory, the Pierre Auger Observatory, suggest that most ultra-high energy cosmic rays are heavier elements known as HZE ions. 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 also occurs roughly in this energy range (at 10 EeV/nucleon) and similarly restricts very long distance propagation.
In the past, the apparent violation of the GZK limit has inspired cosmologists and theoretical physicists to suggest other ways that circumvent the limit. These theories propose that ultra-high energy cosmic rays are produced near our galaxy or that Lorentz covariance is violated in such a way that protons do not lose energy on their way to our galaxy.
Computation
The limit was independently computed in 1966 by Kenneth Greisen, Georgiy Zatsepin, and Vadim Kuzmin based on interactions between cosmic rays and the photons of the cosmic microwave background radiation (CMB). They predicted that cosmic rays with energies over the threshold energy of would interact with cosmic microwave background photons relatively blueshifted by the speed of the cosmic rays, to produce pions through the resonance,
or
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 . 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 comes from two causes: The pion has a mass only about ~130 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 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 () and with energies greater than the threshold should never be observed on Earth. This distance is also known as GZK horizon.
Cosmic-ray paradox
A number of observations have been made by the largest cosmic-ray experiments Akeno Giant Air Shower Array, 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 this limit (called extreme-energy cosmic rays, or EECRs). The observation of these particles was the so-called GZK paradox or cosmic-ray paradox.