Neutrino induced muons The straight part of the depth intensity curve at about 10-13 is that of atmospheric neutrino induced muons in vertical and horizontal direction.
Types of detected neutrino events: 1) events interacting inside the detector 2) upward going muons There is no other particle then neutrinos that can penetrate through the Earth and enter the detector from below. These muons must be a result of muon neutrino charge current interactions below the detector that produce muons that enter it from below.
Advantages of studies of upward going neutrino induced muons: much increased effective detector volume Disadvantages: neutrino energy is not known, can only be statistically estimated for a large experimental sample V' = A (h + R eff )
Neutrino cross section There are generally two types of neutrino interactions: 1) charge current (CC) interactions l + N = l + X, produce the corresponding lepton of energy (1 y) E and the rest goes to hadrons Neutrino energy has to be higher than the lepton mass for this interaction to happen. So for electron neutrinos the threshold is above 0.511 MeV and for muon neutrinos it is abobe 105 MeV. 2) neutral current (NC) interactions + N = + X, neutrino loses a part y of its energy to hadrons.
The differential CC neutrino cross section is
Where x and y are the Bjorken variables: y is the fractional energy loss of the neutrino (lepton) x is the ratio of the transferred impulse to quark momentum. u, d, s, c, b, t are the structure functions of respective quarks At low energy the antineutrino cross section is about 1/3 of the neutrino cross section while at the highest energy they are the same. The second set of curves shows the NC cross section.
Is the term we want to consider here It is the W propagator where Q 2 is the momentum transfer and m W is the W boson mass of 80.4 GeV. At energies below m W 2 the cross section grows linearly with the neutrino energy and then growth starts to slow down.
One can calculate the rate of upward going muons by folding the neutrino flux with the probability for a neutrino to generate a muon above certain energy. Where the probability P depends on d /dy and on the muon effective range, i.e. on the distance that the muon can penetrate
At relatively low muon energy the flux of neutrino induced upward going muons declines slowly with the muon energy because 1) the neutrino cross section is proportional to the neutrino energy 2) the muon range R is proportional to the muon energy (only ionization energy loss) which adds E 2 to the neutrino energy spectrum. At higher energy the neutrino cross section grows more slowly and the muon energy loss increases, thus the muon energy spectrum decreases faster.
Probability P for production of muons with energy above 1 GeV and 1 TeV.
Expected and detected flux of upward going neutrino produced muons from atmospheric neutrinos. Points are from the MACRO experiment in Gan Sasso, Italy. Difference with expectations are because of neutrino oscillations (next week).
Neutrino induced muons is what IceCube uses for detection of extraterrestrial neutrinos. Only neutrinos from the Northern hemisphere can be detected at South Pole. The assumption is that neutrinos from powerful astrophysical objects will have much flatter spectra than atmospheric neutrinos. In astrophysical environments all pions (and other mesons) decay and so do the muons to generate neutrino spectra with the same spectral index as the accelerated cosmic rays (E -2?). Such flat spectra would clearly be visible above the atmospheric neutrino background. The response to atmospheric neutrinos peaks at about 300 GeV and that to flat neutrino spectra peaks at about 10 TeV. This is the energy range (1 to 10 TeV) for which IceCube is designed.
With the growth of the neutrino cross section the Earth is not anymore transparent for neutrinos of energy 10 5 GeV that propagate along the its diameter. Above 10 7 GeV the Earth is not transparent to neutrinos in any direction. Neutrino telescopes have to look for downward going neutrinos with huge energy, which makes the search more difficult.
IceCube made the BBC news today after a paper on the limits on neutrino fluxes from GRB was published in Nature yesterday. The neutrino telescope looked for neutrinos around gamma ray bursts observed by satellite detectors first in the Northern hemisphere and in both. Presented are the limits from IC40 and IC59 versions of the detector, before the completeion of the whole detector which now consists of 86 strings. Different ways of analyzing the data were presented.
IC40+IC59