The astrophysical models discussed present difficulties in providing a completely satisfactory explanation of the super-GZK events, if there are any. This may simply reflect our present lack of statistics, our present ignorance of the true conditions of processes in some highly energetic regions of the universe, or, perhaps, may imply that exotic mechanisms are at play. Physics from the most favored theories beyond the standard model (SM) like string/M theory, supersymmetry (SUSY), grand unified theories (GUTs), and TeV-scale gravity have been invoked to explain the possible flux above the GZK energy limit. This review is not mainly concerned with beyond-SM scenarios (for more comprehensive surveys see e.g. [1, 70, 380, 381, 382]), but for the sake of completeness, we provide here a brief account of some of the most relevant exotic explanations.
The most economical among hybrid proposals involves a familiar extension of
the SM, namely, neutrino masses. It was noted many years ago that
's
arriving at Earth from cosmologically distant sources have an annihilation
probability on the relic neutrino background of roughly
3 h65-1%
[383].
Inspired on this analysis, Weiler
[384]
and Fargion et al.
[385]
noted that neutrinos within a few Z widths of the right energy,
![]() |
(65) |
to annihilate with the relic neutrinos at the Z-pole with large cross section,
![]() |
(66) |
may produce a "local" flux of nucleons and photons.
(35)
Remarkably, the energy of the
neutrino annihilating at the peak of the Z-pole has to be well
above the GZK limit. The mean energies of the ~ 2 nucleons and ~ 20
-rays in
each process can be estimated by
distributing the resonant energy among the mean multiplicity of 30
secondaries. The proton energy is given by
![]() |
(67) |
whereas the
-ray energy
is given by
![]() |
(68) |
The latter is a factor of 2 smaller to account for the photon origin in two
body 0 decay. This
implies that the highly boosted decay products of the Z could be
observed as super-GZK primaries.
(36)
However, to reproduce
the observed spectrum, the Z-burst mechanism requires very luminous
sources of extremely high energy neutrinos throughout the universe
[387,
388,
389].
The present limits on these sources are near the threshold of
sensitivity to the required flux
[390].
In 1931, Georges Lemaître [391] - a forerunner of the Big Bang hypothesis - introduced the idea that the entire material filling the universe, as well as the universe's expansion, originated in the super-radioactive disintegration of a "Primeval Atom", which progressively decayed into atoms of smaller and smaller atomic weight. The CRs were introduced in this picture as the energetic particles emitted in intermediate stages of the decay-chain. Echoing Lemaître, in the so-called "top-down models", charged and neutral primaries arise in the quantum mechanical decay of supermassive elementary X particles [392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406].
To maintain an appreciable decay rate today, it is necessary to tune the X lifetime to be longer (but not too much longer) than the age of the universe, or else "store" short-lived X particles in topological vestiges of early universe phase transitions (such as magnetic monopoles, superconducting cosmic strings, vortons, cosmic necklaces, etc.). Discrete gauged symmetries [407, 408, 409] or hidden sectors [410, 411] are generally introduced to stabilize the X particles. Higher dimensional operators, wormholes, and instantons are then invoked to break the new symmetry super-soflty to mantain the long lifetime [399, 400] (collissional annihilation has been considered too [412]). Arguably, these metastable super-heavy relics (MSRs) may constitute (a fraction of) the dark matter in galactic haloes.
Of course, the precise decay modes of the X's and the detailed
dynamics of the first generation of secondaries depend on the
exact nature of the X particles under consideration. However, in
minimal extensions of the SM, where there are no new mass scales
between MSUSY ~ 1 TeV and mX, the
squark and sleptons would behave like their corresponding supersymmetric
partners, enabling one to infer from the "known" evolution of
quarks and leptons the gross features of the X particle decay:
the strongly interacting quarks would fragment into jets of hadrons
containing mainly pions together with a 3% admixture of nucleons
[413,
414,
415].
(37) This implies
that the injection spectrum is a rather hard fragmentation-type
shape (with an upper limit usually fixed by the GUT scale) and
dominated by
-rays and
neutrinos produced via pion decay.
Therefore, the photon/proton ratio can be used as a diagnostic
tool in determining the CR origin
[418].
In light of the mounting evidence that UHECRs are not
-rays,
one may try to force a proton dominance at ultrahigh energies by
postulating efficient absorption of the dominant ultrahigh energy
photon flux on the universal and/or galactic radio background.
(38)
However, the neutrino flux
accompanying a normalized proton flux is inevitably increased to a
level where it should be within reach of operating experiments
[420].
It is clear that because of the wide variety of top down models
the ratio of the volume density of the X-particle to its decay
time is model dependent. However, if a top down scenario is to
explain the origin of UHECRs, the injection spectrum should be
normalized to account for the super-GZK events without violating
any observational flux measurements or limits at higher or lower energies
[421].
In particular, neutrino and
-ray fluxes
depend on the energy released integrated over
redshift, and thus on the specific top down model. Note that the
electromagnetic energy injected into the Universe above the pair
production threshold on the CMB is recycled into a generic cascade
spectrum below this threshold on a short time scale compared with
the Hubble time. Therefore, it can have several potential
observable effects, such as modified light element abundances due
to 4He photodisintegration, or induce spectral distortions of
universal
-ray and
neutrino backgrounds
[422,
423].
Additionally, measurements of the diffuse GeV
-ray flux
[424],
to which the generic cascade
spectrum would contribute directly, limit significantly the
parameter space in which X's can generate the flux of the UHECRs
[425,
426,
427],
especially if there is already a significant contribution to this
background from conventional sources such as unresolved
-ray
blazars. Recently, a possible lower extragalactic contribution to the
diffuse
-ray
background measured by EGRET has been pointed out
[428,
429].
The ~ 50% smaller EGRET flux practically rules out extragalactic
top down and Z-burst scenarios
[430].
If MSRs are the progenitors of the observable UHECRs, then the
flux will be dominated by the decay or annihilation products of
X's in the Galactic halo, i.e., by sources at distances smaller
than all relevant interaction lengths. A clean signal of this
scenario is the predicted anisotropy due to the non-central
position of the Sun in our galaxy
[431,
432].
Although it was noted that the predicted anisotropy is consistent with
AGASA and Haverah Park data
[59],
recent analyses
[433,
434]
of SUGAR data excludes the MSR hypothesis at the
5 level if all events
above 1019.6 eV are due to metastable X clustered in the
halo. (For the extreme case where the population of MSRs is
responsible only for CRs with energies
1019.8
eV, the annihilation scenario is disfavored at least at the 99% CL,
whereas decaying MSRs still have a probability ~ 10% to
reproduce SUGAR data.)
A more exotic explanation postulates that the X's themselves constitute the primaries: magnetic monopoles easily pick up energy from the magnetic fields permeating the universe and can traverse unscathed through the primeval radiation, providing an interesting candidate to generate extensive air showers [435]. In particular, a baryonic monopole encountering the atmosphere will diffuse like a proton, producing a composite heavy-particle-like cascade after the first interaction [436] with a great number of muons among all the charged particles [437]. Although this feature was observed in a poorly understood super-GZK event [438, 439], it seems unlikely that a complete explanation for the UHECR data sample would be in terms of magnetic monopoles alone. Moreover, any confirmed directional pairing of events would appear difficult to achieve with the monopole hypothesis.
A novel beyond-SM-model proposal to break the GZK barrier is to
assume that UHECRs are not known particles but rather a new
species, generally referred to as the uhecron, U
[440,
441,
442].
The meager information we have about super-GZK particles allows a
naïve description of the properties of the U. The muonic
content in the atmospheric cascades suggests U's should interact
strongly. At the same time, if U's are produced at cosmological
distances, they must be stable, or at least remarkably long lived,
with mean-lifetime
106 (mU / 3 GeV) (d / Gpc) s,
where d is the distance to the source and
mU, the uhecron's mass. Additionally, since the threshold
energy increases linearly with mU, to avoid photopion
production on the CMB mU
1.5 GeV. In
recent years, direct searches of supersymmetric hadrons
[443,
444,
445,
446]
have severely eroded the attractiveness of the U scenario.
However, adequate fine-tunings leave a small window still open
[447,
448].
On a similar track, it was recently put forward [449] that strangelets (stable lumps of quark matter with roughly equal numbers of up, down, and strange quarks) can circumvent the acceleration problem in a natural way (due to a high mass and charged, but low charge-to-mass ratio) and move the expected cutoff to much higher energies.
Another possibility in which super-GZK CRs can reach us from very distance sources may arise out of photons that mix with light axions in extragalactic magnetic fields [450]. These axions would be sufficiently weakly coupled to travel large distances unhindered through space, and so they can convert back into high energy photons close to the Earth. An even more radical proposal postulates a tiny violation of local Lorentz invariance, such that some processes become kinematically forbidden [451]. In particular, photon-photon pair production and photopion production may be affected by Lorentz invariance violation. Hence, the absence of the GZK-cutoff would result from the fact that the threshold for photopion production "disappears" and the process becomes kinematically not allowed. This implies that future PAO observations of faraway sources could provide constraints on, or even a measurement of, the violation of Lorentz symmetry, yielding essential insights into the nature of gravity-induced wave dispersion in the vacuum [452, 453, 454, 455, 456, 457, 458, 459, 460, 461].
In summary, future UHECR data may not only provide clues to the particle sources, but could enhance our understanding of fundamental particle physics. We are entering this new High Energy Physics era with the Pierre Auger Observatory [462, 463, 464].
35 GF = 1.16639(1) × 10-5 GeV-2 is the Fermi coupling constant. Back.
36 Similarly, gravi-burst fragmentation jets can contribute to the super-GZK spectrum [386]. Back.
37 In light of this, the sensitivity of future CR experiments to test the SUSY parameter space has been estimated [416, 417]. Back.
38 Of course, this is not the case in
traditional scenarios (for an exception see
[419])
of decaying massive dark matter in the
Galactic halo, which due to the lack of absorption, predict
compositions directly given by the fragmentation function, i.e.,
domination by
-rays.
Back.