A detection of the ultra-high energy neutrino flux
might establish an experimental lower limit on r and thus
allow important insights into new fundamental physics near the
grand unification scale. Even a non-detection with more stringent upper limits
would also be useful since it
could eliminate large classes of top down models of ultra-high
energy cosmic ray origin. For example, failing to detect
neutrinos above 10 EeV with an exposure A x t would rule out such
scenarios of the type shown in the figure above for r > [100
km**3 x 2pi x sr x yr/(A x t)].
The figure on the left shows a top down scenario with special focus
on the expected neutrino flux, as compared to contributions from
other potential sources.
Shown are predictions for the differential fluxes of muon
neutrinos and anti-neutrinos (solid blue lines) from the atmospheric
background for different zenith angles (hatched
region marked "atmospheric"), from proton blazars that are
photon optically thick to nucleons and are therefore not subject
to the "Waxman Bahcall bound", but contribute to the diffuse
gamma-ray flux (``proton blazar''), from ultra-high energy cosmic
ray interactions with the cosmic microwave background
("cosmogenic"), and for the same top down model (marked "SLBY98a",
for details see
as discussed overleaf
for the "visible" gamma ray and nucleon fluxes that are
shown again as dashed red line and dotted black line, respectively.
The data shown for the cosmic ray flux and the diffuse gamma ray flux
EGRET are as overleaf.
Points with arrows represent approximate upper limits on the
diffuse neutrino flux from the Frejus, the
EAS-TOP, and the
Fly's Eye experiments, as indicated. The projected
limit for the proposed
Auger Project is for non-detection
over a five year period, and similarly for the
Orbiting Wide-angle Light collectors (OWL).
The neutrino flux prediction from this
TD scenario produces an integral flux of about 0.15 events per year
above 10 EeV in a 2 pi km**3 sr size detector, which is close
to the model independent upper limit discussed above.
One of the major unresolved questions in particle physics is
whether neutrinos have mass. If they have masses m of several
electron volts, the relic neutrino background would constitute a
significant fraction of
the energy density of the present day universe in the form of
As an example, the figure on the left shows resulting neutrino fluxes
in a TD scenario (marked "SLBY98b", for details see
where heavy X particles of mass 10**14 GeV
decay into two neutrinos, using the same line key
as above. The neutrino fluxes are maximal in the sense that the
secondary cascade gamma rays produced mostly by neutrino
interactions with the uniform relic neutrino background is
compatible with the EGRET limit. All neutrinos have been assumed
to have a mass of 1 eV. The secondary gamma-rays and nucleons
at ultra high energies are mostly produced on the local
clustered (hot dark matter) component of massive neutrinos
and can account for the highest energy events if the product
of the clustering length scale and the overdensity over this
scale is larger than 150 Mpc. On a Supercluster scale of about
5 Mpc, this would correspond to an overdensity of 30, not
inconceivable values. As can be seen, the neutrino fluxes are
even comparable with predictions by more conventional models
of active galactic nuclei down to 1 PeV, and would give rise
to event rates of 0.64 above 10 EeV, and 2.8 above 1 PeV
per year in a 2 pi km**3 sr size detector.
As a further example (for details, see
this paper), the figure on the left shows
fluxes from a homogeneous distribution of AGNs exclusively
emitting neutrinos with an E**(-1) spectrum up to 10**(22) eV
and a redshift of 3 (assuming a bright phase exponent of 3).
The neutrinos of mass 1 eV were assumed to have an
overdensity of 20 on the scale of the local Supercluster.
Again, the gamma ray and nucleon fluxes are all secondaries of the
neutrino interactions. See also
Physical Review Focus 2, story 33 for a popular
account of this scenario.
The detection of ultra-high energy neutrinos not only depends on the astrophysical fluxes but also on the neutrino-nucleon cross section which is not measured above 100 TeV. For example, radiative corrections can have an important influence on the character of the air showers created by ultra-high energy neutrinos interacting in ice, water, or the atmosphere; I have discussed Standard Model predictions in this paper.
In addition, new interactions beyond the electroweak scale could significantly modify cross sections which in turn can be probed by astrophysical ultra-high energy neutrinos.
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