- Open Access
Atmospheric neutrinos in the context of muon and neutrino radiography
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB 2010
- Received: 19 December 2008
- Accepted: 5 June 2009
- Published: 22 February 2010
Using the atmospheric neutrinos to probe the density profile of the Earth depends on knowing the angular distribution of the neutrinos at production and the neutrino cross section. This paper reviews the essential features of the angular distribution with emphasis on the relative contributions of pions, kaons and charm.
- cosmic rays
In principle atmospheric neutrinos can be used to measure the density profile of the Earth (integrated along a chord) by comparing the observed rate of upward-moving neutrino-induced muons as a function of zenith angle with what is produced in the atmosphere. The measurement depends on several factors: the zenith angle dependence of neutrino production in the atmosphere, the differential neutrino cross section as a function of energy, properties of muon propagation in the medium surrounding the detector and the angular and energy resolution of the detector. Gonzalez-Garcia et al. (2008) show that it may be possible to measure some aspects of the core-mantle transition region with the IceCube detector currently under construction at the South Pole (Karle et al., 2007). A data accumulation of order ten years or more would be needed.
The critical energy range for such a measurement is 10 ≤ E v ≤ 100 TeV where the absorption of the Earth becomes important, first for neutrinos coming straight up through the diameter of the Earth, and at higher energy for larger angles. Hoshina (2008) discusses the angular resolution of IceCube for neutrino-induced muons from muon neutrinos in this energy band, where more than 50% of events can be reconstructed within one degree of their true direction. The charged current neutrino cross sections in this energy range are known to within ±2% (Cooper-Sarkar and Sarkar, 2008). In this paper, I focus on the angular distributions of muon neutrinos produced in the atmosphere and their uncertainties.
the energy spectrum and composition of the primary cosmic radiation,
production of pions, kaons and charmed hadrons in collisions of nucleons and other hadrons with nuclei of the atmosphere,
kinematics of hadron decays to neutrinos, and
the density profile of the atmosphere.
Critical energies in GeV.
∼ 5 × 107
At low energy, the neutrino spectrum follows the same power law as the parent hadrons. At high energy, the probability of decay of a charged pion or kaon is suppressed relative to hadronic interaction by a factor proportional to the energy of the meson. This suppression is represented by the denominator of each term in Eq. (5). Asymptotically at high energy the neutrino spectrum has an extra factor of 1/E relative to the spectrum at low energy, which is proportional to the primary cosmic-ray spectrum. This steepening of the neutrino spectrum occurs at higher energy for larger zenith angles as a consequence of the sec(θ) factor, which occurs because particle production occurs higher in less dense atmosphere for large angles. The factors B iv in the denominators are ratios of spectrum-weighted kinematic factors for meson decay to neutrinos to account for the fact that the decay occurs from a steeper spectrum at higher energy. Close to the horizontal (θ > 70°) the curvature of the Earth is significant and the secant is to be evaluated at the local zenith angle where the particle production occurs, which is less than the zenith angle of the trajectory at the detector (Lipari, 1993).
Parameterizations of the form of Eq. (5) represent detailed numerical and Monte Carlo calculations rather well. The corresponding parametric equations for muons can be compared directly to the many measurements of atmospheric muons. Such a comparison is made in figure 24.4 Gaisser and Stanev (2008), for example. (See also figure 4 of Gaisser (2005).)
Uncertainties in the angular dependence arise primarily from uncertainties in the level of kaon production for E v ∼ 10 TeV and at higher energy from the more uncertain level of charm production. Ideally one would simply measure the downward atmospheric neutrino flux and compare it with the upward neutrino flux from the opposite direction and use the ratio Earth-in to Earth-out to measure the density profile in a way that is independent of the intrinsic angular dependence of the atmospheric neutrino beam. In reality this unfortunately cannot be done because the relatively high intensity of downward atmospheric muons hides the downward atmospheric neutrinos. Because of the close genetic relation between v μ and μ of Eq. (1) and the corresponding equation for pions, a measurement of downward atmospheric muons provides some control of the angular dependence. This constraint, while valid and worth pursuing, is of limited practical use in this context because of the fact that most muons come from decay of charged pions while, in the high energy range of interest here, most neutrinos come from decay of kaons.
Uncertainties in the calculated intensity of atmospheric neutrinos at high energy due to uncertain knowledge of hadronic interactions were estimated by Agrawal et al. (1996). The single largest source of uncertainty in the TeV range and above is from the uncertainty in kaon production, in particular in the factor ZpK+. This uncertainty was estimated as ±13% in the 10–100 TeV range.
Although the charm channel for atmospheric neutrinos is formally the same as for pions and kaons, there are two large quantitative differences. One is that production of charm in hadronic interactions is very much smaller than production of pions and kaons. The other is that the critical energy is so high (because of the short charm lifetime) that muons and neutrinos from decay of charmed hadrons will continue in the low-energy regime of Eq. (5) with the same, relatively hard, spectrum as the primary cosmic-ray nucleons and with an isotropic angular distribution.
In the model of Bugaev et al. atmospheric neutrinos from charm decay become equal in intensity to neutrinos from decay of kaons and pions at approximately 100 TeV. A more recent calculation (Enberg et al., 2008) predicts a level of charm production an order of magnitude lower than the model of Bugaev et al. In this case, the crossover occurs about a factor of two higher in energy.
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