View source for Greisen–Zatsepin–Kuzmin limit

{{short description|Theoretical upper limit on the energy of cosmic ray protons}}
The '''Greisen–Zatsepin–Kuzmin limit''' ('''GZK limit''' or '''GZK cutoff''') is a theoretical upper limit on the energy of [[cosmic ray]] [[proton]]s traveling from other galaxies through the intergalactic medium to our galaxy. The limit is {{val|5|e=19|ul=eV}} (50 EeV), or about 8&nbsp;[[joule]]s (the energy of a proton travelling at ≈&nbsp;{{val|99.99999999999999999998}}% the speed of light). The limit is set by the slowing effect of interactions of the protons with the [[Cosmic microwave background radiation|microwave background radiation]] over long distances (≈&nbsp;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|Oh-My-God Particle]], which has been found to possess a record-breaking {{val|3.12|e=20|u=eV}} (50 joules)<ref>{{Cite web|url=http://www.cosmic-ray.org/reading/flyseye.html#SEC10|title=HiRes – The High Resolution Fly's Eye Ultra High Energy Cosmic Ray Observatory|website=www.cosmic-ray.org|access-date=2019-06-13}}</ref><ref>{{Cite web|url=https://phys.org/news/2011-06-oh-my-god-particles.html|title=Oh-My-God Particles|website=phys.org|language=en-us|access-date=2019-06-13}}</ref> of energy (about the same as the kinetic energy of a 95&nbsp;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 [[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.

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]],<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> [[Georgiy 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.

==Cosmic-ray 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]], [[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 ray]]s, or EECRs). The observation of these particles was the so-called '''GZK paradox''' or '''cosmic-ray paradox'''.

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 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_Z^2}{2 m_\nu} = 4.2 \times 10^{21} \left(\frac{\text{eV}}{m_\nu}\right)~\text{eV},</math>

where <math>m_Z</math> is the mass of the Z-boson, and <math>m_\nu</math> the mass of the neutrino.

===Other theories===
A number of exotic theories have been advanced to explain the AGASA observations, including [[doubly special relativity]]. However, it is now established that standard doubly special relativity does not predict any GZK suppression (or GZK cutoff), contrary to models of Lorentz symmetry violation involving an absolute rest frame.{{citation needed|date=October 2014}} Other possible theories involve [[Ultra-high-energy cosmic ray#Relation with dark matter|a relation with dark matter]], or decays of exotic super-heavy particles beyond those known in the [[Standard Model]].

==Controversy about cosmic rays above the GZK limit==
A suppression of the cosmic-ray flux that can be explained with the GZK limit has been confirmed by the latest generation of cosmic-ray observatories. A former claim by the [[AGASA]] experiment that there is no suppression was overruled. It remains controversial whether the suppression is due to the GZK effect. The GZK limit only applies if ultra-high-energy cosmic rays are mostly protons.

In July 2007, during the 30th International Cosmic Ray Conference in Mérida, Yucatán, México, the [[High Resolution Fly's Eye Cosmic Ray Detector|High Resolution Fly's Eye Experiment]] (HiRes) and the Pierre Auger Observatory (Auger) presented their results on ultra-high-energy cosmic rays. HiRes observed a suppression in the UHECR spectrum at just the right energy, observing only 13 events with an energy above the threshold, while expecting 43 with no suppression. This was interpreted as the first observation of the GZK limit.<ref name="Abbasi2008">{{cite journal |last=Abbasi |first=R. U. |display-authors=etal |date=2008 |title=First Observation of the Greisen-Zatsepin-Kuzmin Suppression |journal=Physical Review Letters |volume=100 |issue= 10|pages=101101 |doi=10.1103/PhysRevLett.100.101101 |pmid=18352170 |arxiv=astro-ph/0703099 |bibcode=2008PhRvL.100j1101A|s2cid=118960558 }}</ref> Auger confirmed the flux suppression, but did not claim it to be the GZK limit: instead of the 30 events necessary to confirm the AGASA results, Auger saw only two, which are believed to be heavy-nuclei events.<ref name="Abraham2008">{{cite journal |last=Abraham |first=J. |display-authors=etal |date=2008 | title=Observation of the suppression of the flux of cosmic rays above 4×10<sup>19</sup> eV |journal=Physical Review Letters |volume=101 |issue=6 |pages=061101–1–061101–7 |doi=10.1103/PhysRevLett.101.061101 |pmid=18764444 |arxiv=0806.4302 |bibcode=2008PhRvL.101f1101A|s2cid=118478479 }}</ref> The flux suppression was previously brought into question when the AGASA experiment found no suppression in their spectrum{{citation needed|date=December 2017}}. According to [[Alan Andrew Watson|Alan Watson]], former spokesperson for the Auger Collaboration, AGASA results have been shown to be incorrect, possibly due to the systematic shift in energy assignment.

In 2010 and the following years, both the Pierre Auger Observatory and HiRes confirmed again a flux suppression,<ref>{{cite journal |date=2010 |title=Measurement of the energy spectrum of cosmic rays above {{val|e=18|u=eV}} using the Pierre Auger Observatory |journal=Phys. Lett. B |volume=685 |issue=4–5 |pages=239–246 |arxiv=1002.1975 |bibcode=2010PhLB..685..239A |doi=10.1016/j.physletb.2010.02.013 |author=The Pierre Auger Collaboration }}</ref><ref>{{cite journal |arxiv=1010.2690 |author1=Sokolsky |author2=for the HiRes Collaboration |title=Final Results from the High Resolution Fly's Eye (HiRes) Experiment |journal=Nuclear Physics B: Proceedings Supplements |volume=212–213 |pages=74–78 |date=2010 |doi=10.1016/j.nuclphysbps.2011.03.010 |bibcode=2011NuPhS.212...74S|s2cid=108291051 }}</ref> in case of the Pierre Auger Observatory the effect is statistically significant at the level of 20 standard deviations.

After the flux suppression was established, a heated debate ensued whether cosmic rays that violate the GZK limit are protons. The Pierre Auger Observatory, the world's largest observatory, found with high statistical significance that ultra-high-energy cosmic rays are not purely protons, but a mixture of elements, which is getting heavier with increasing energy.<ref name="Aab2017"/>
The [[Telescope Array Project]], a joint effort from members of the HiRes and AGASA collaborations, agrees with the former HiRes result that these cosmic rays look like protons.<ref name="Hanlon2017">{{cite journal |last1=Hanlon |first1=William |last2=others |title=Telescope Array Composition Summary |journal=PoS |date=2017 |volume=301 |issue=536 |pages=536 |doi=10.22323/1.301.0536 |url=https://pos.sissa.it/301/536/pdf|bibcode=2017ICRC...35..536H |doi-access=free }}</ref> The claim is based on data with lower statistical significance, however. The area covered by Telescope Array is about one third of the area covered by the Pierre Auger Observatory, and the latter has been running for a longer time.

The controversy was partially resolved in 2017, when a joint working group formed by members of both experiments presented a report at the 35th International Cosmic Ray Conference.<ref name="deSouza2017">{{cite journal |last1=de Souza |first1=Vitor |last2=others |title=Testing the agreement between the Xmax distributions measured by the Pierre Auger and Telescope Array Observatories |journal=PoS |date=2017 |volume=301 |issue=522 |url=https://pos.sissa.it/301/522/pdf}}</ref> According to the report, the raw experimental results are not in contradiction with each other. The different interpretations are mainly based on the use of different theoretical models and the fact that Telescope Array has not collected enough events yet to distinguish the pure-proton hypothesis from the mixed-nuclei hypothesis.

===Extreme Universe Space Observatory on Japanese Experiment Module (JEM-EUSO)===
[[Extreme Universe Space Observatory|EUSO]], which was scheduled to fly on the [[International Space Station]] (ISS) in 2009, was designed to use the atmospheric-[[fluorescence]] technique to monitor a huge area and boost the statistics of UHECRs considerably. EUSO is to make a deep survey of UHECR-induced extensive air showers (EASs) from space, extending the measured energy spectrum well beyond the GZK cutoff. It is to search for the origin of UHECRs, determine the nature of the origin of UHECRs, make an all-sky survey of the arrival direction of UHECRs, and seek to open the astronomical window on the extreme-energy universe with neutrinos. The fate of the EUSO Observatory is still unclear, since NASA is considering early retirement of the ISS.

===The Fermi Gamma-ray Space Telescope to resolve inconsistencies===
Launched in June 2008, the [[Fermi Gamma-ray Space Telescope]] (formerly GLAST) will also provide data that will help resolve these inconsistencies.
* With the Fermi Gamma-ray Space Telescope, one has the possibility of detecting gamma rays from the freshly accelerated cosmic-ray nuclei at their acceleration site (the source of the UHECRs).<ref>{{cite journal |last=Ormes |first=Jonathan F. |display-authors=etal |date=2000 |title=The origin of cosmic rays: What can the Fermi Gamma-ray Telescope say? |journal=AIP Conference Proceedings |volume=528 |pages=445–448 |doi=10.1063/1.1324357 |arxiv=astro-ph/0003270|s2cid=7461124 }}</ref>
* UHECR protons accelerated (see also [[Centrifugal mechanism of acceleration]]) in astrophysical objects produce ''secondary electromagnetic cascades'' during propagation in the cosmic microwave and infrared backgrounds, of which the GZK process of pion production is one of the contributors. Such cascades can contribute between about 1% and 50% of the GeV–TeV diffuse photon flux measured by the [[EGRET]] experiment. The Fermi Gamma-ray Space Telescope may discover this flux.<ref name="Kalashev2007">{{cite journal |last=Kalashev |first=Oleg E. |author2=Semikoz, Dmitry V. |author3=Sigl, Guenter |year=2009 |title=Ultra-High Energy Cosmic Rays and the GeV–TeV Diffuse Gamma-Ray Flux |journal=Physical Review D |volume=79 |issue=6 |pages=063005 |arxiv=0704.2463 |bibcode=2009PhRvD..79f3005K|doi=10.1103/PhysRevD.79.063005|s2cid=119154125 }}</ref>

==Possible sources of UHECRs==
In November 2007, researchers at the Pierre Auger Observatory announced that they had evidence that UHECRs appear to come from the [[Active galactic nucleus|active galactic nuclei]] (AGNs) of energetic galaxies powered by matter swirling onto a supermassive black hole. The cosmic rays were detected and traced back to the AGNs using the [[Philippe Véron|Véron–Cetty–Véron]] catalog. These results are reported in the journal ''[[Science (journal)|Science]]''.<ref>{{cite journal |author=The Pierre Auger Collaboration |date=2007 |title=Correlation of the Highest-Energy Cosmic Rays with Nearby Extragalactic Objects |journal=Science |volume=318 |issue=5852 |pages=938&ndash;943 |doi=10.1126/science.1151124 |arxiv=0711.2256 |pmid=17991855 |bibcode = 2007Sci...318..938P |s2cid=118376969 }}</ref> Nevertheless, the strength of the correlation with AGNs from this particular catalog for the Auger data recorded after 2007 has been slowly diminishing.<ref>{{cite journal |author=The Pierre Auger Collaboration |date=2010 |title=Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter |journal=Astropart. Phys. |volume=34 |issue=5 |pages=314&ndash;326 |doi=10.1016/j.astropartphys.2010.08.010 |arxiv=1009.1855 |bibcode = 2010APh....34..314A|s2cid=56362511 }}</ref>

==See also==
* {{annotated link|Ultra-high-energy cosmic ray}}

==References==
{{reflist|25em}}

==External links==
*[http://www.physics.rutgers.edu/hex/HIRES.html Rutgers University experimental high energy physics HIRES research page]
*[http://www.auger.org Pierre Auger Observatory page]
*[http://www.cosmic-ray.org/ Cosmic-ray.org]
*[http://www.p-ng.si/public/pao/history.php History of Cosmic Ray Research] {{Webarchive|url=https://web.archive.org/web/20120305185007/http://www.p-ng.si/public/pao/history.php |date=2012-03-05 }}

{{DEFAULTSORT:Greisen-Zatsepin-Kuzmin Limit}}
[[Category:Cosmic rays]]
[[Category:Physical paradoxes]]
[[Category:Energy]]
[[Category:Special relativity]]
[[Category:Astroparticle physics]]
[[Category:Unsolved problems in physics]]
[[Category:Unsolved problems in astronomy]]