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n u
d
W
Hadrons
Figure 4: Charged current neutrino-quark deep inelastic scattering.
0.2 GeV/m, a minimum muon energy (and hence neutrino energy) of at least a few GeV can be
deduced. With a mass of just 105.7 ¡
, this means that a detected muon in that type of de-
tector is highly relativistic Furthermore, the mean deviation between the neutrino and the muon
¢ £ ¢
is
with ¢ ¤
and
¤¥¤
in TeV and yielding about at 3 TeV [7].
12
¢ ¤§¦
(16)
¡©¨
These two facts imply that the path of the muon is a straight track prolonging the neutrino
track with a deviation of a few degrees, decreasing with energy.
The inaccuracy due to recoiling effects and to multiple scattering have been estimated for
water to be less than after the half mean range of an initial 50 GeV muon and decreasing with
energy (see [26], also [27]).
That the minimum energy of a detectable and reconstructible neutrino is of the order of GeV’s
does not mean that it is the threshold of the detector. Other considerations have to be taken into
account in its determination, such as what kind of physics one wants to achieve; what effective
area, energy resolution or signal-to-noise is aimed at; if the array is to be used as a telescope or
as a particle-detector, etc.
Cross section
The cross-section for the reaction
¡ ¥ ¡
¢¢ is given by [28]:
£ ¤
¢
¡ ¦
(17)
£ ¦
§ £§ ¡
where is the invariant momentum transfer between the incident neutrino and outgoing
muon,
and are the nucleon and W-boson masses, is the Fermi constant and and
are quark and antiquark distribution functions.
Introduced here also are the Bjorken scaling variables
¦
¦ ¢ ¤ ¢ (18)