Link to Fulltext

¡ ¢¡ £
At yet higher energies (greater than GeV for and greater than GeV for [9, 10,
¡
11]) atmospheric neutrinos are produced mainly as prompt decay products of charmed particles
with very short life times.
For primaries in the lower part of the cosmic ray energy spectrum, yielding leptons of a few
GeV at most, a ratio value of 1/2 is expected for . However, this is not reflected in measurements
made by some experiments – the so-called ’atmospheric anomaly’ [7]. Measurements
made by IMB [12], SOUDAN2 [13] and Kamiokande [14] yielded a value closer to 1, whereas
NUSEX [15] and Frejus [16] get results more in agreement with the predicted ratio of 1/2 [10].
¢
When is greater than several GeV and production from muon decay can be neglected,
the muon neutrino spectrum via pion and kaon decay is approximately given by [7]:
¥¤ £
¢ ¤§¦ £
¨¢©¤
£¤
¤ ¢ ¤
¡
¡ ¡
4
£¤
¤ ¢ ¤ (4)
¡
£ ¤ ¡
, ¤
¦ ¡ where and is a constant that depends
on the spectral index and on nucleon and pion attenuation lengths. The first term inside the
¦
parentheses represents neutrinos from the decay of pions. At energies ¢ ¤ , all the
¢
pions
©
,
decay and the neutrino spectrum from pions follows the primary cosmic ray spectrum
whereas at higher energies, pions can interact before decaying and the spectrum steepens to
© ¢
. For cascade development in the
Earth’s
atmosphere .
¡
Similar considerations apply for kaons, but since , kaon induced neutrinos
will dominate over pion induced ones at high energies. Further terms can be added to Eq. 4 for
charmed particles (see [10]) which, due to their high critical energy, will dominate for ¢ ¤ greater
than 100 TeV.
Since the contribution from muon decay to the production of atmospheric electron-
(anti)neutrinos is inhibited by muon interaction, they have an energy spectrum steeper by one
power (with a maximum around 30-40 MeV).
The declination distribution of neutrinos is given by Eq. 4, i.e. is
fundamentally
¡
. For
low energies however, the flux is strongly suppressed towards the horizon, since the slant depth
then becomes large and interactions of parent particles are more likely [11].
As for cosmic neutrinos, they can be produced with the spectral index of the source if produced
there, or with that of the diffusive cosmic ray spectrum if produced by particle collision
with ISM (interstellar matter). They will retain their original spectrum in both cases, if we suppose
that the matter densities they travel through are low.
Atmospheric neutrinos have an energy distribution suppressed at energies high enough for
their parent particles to interact with the atmosphere. Thus, sources of cosmic neutrinos should
be detectable above the atmospheric background, given that their flux is large enough.
Cosmic rays interacting with ISM will produce a flux of neutrinos which can be estimated
to be ¢¡ © of the cosmic-ray flux in the PeV range [10]. It would be a diffuse flux, but originating
mainly from regions with higher matter densities such as the spiral arms of our galaxy and
molecular clouds and thus concentrated to the galactic plane (yielding some 5 events/year above
10 TeV in a ¡ detector, well below the atmospheric
neutrino
background
[10]). Another
source is the Sun ¥
which has a critical energy TeV, i.e. much higher than in the Earth’s atmosphere,
and is more efficient at neutrino production. However, due to the limited
angular
size
¢¡
of the Sun, the predicted rates are very low (less than 2 events/year above 10 GeV in a
detector [10]).