The phenomenology of muons and neutrinos underground is important because of its relevance to studies of neutrino properties and searches for astrophysical neutrinos with deep detectors. Formulas for production and fluxes of atmospheric neutrinos were given in Chapter 6. A summary of measurements of the vertical muon flux at sea level is included in Figure 6.2. The classic discussion of highenergy muon fluxes and their measurement deep underground is the review of Barrett, Bollinger, Cocconi, Eisenberg and Greisen in 1952 [254], which is still a useful reference.

There are two contributions to the flux of muons in deep detectors, penetrating atmospheric muons from above and neutrino-induced muons from all directions, as shown in Figure 8.1. The lines in the figure show the angular distribution of muons at various depths underground assuming a flat overburden of uniform density. The calculation for atmospheric muons is made by evaluating the integral flux of muons in each direction from the integral form of Eq. 6.36 evaluated at the energy required to reach the given depth. Equation 8.5 is used to relate slant depth in m.w.e. to energy, as discussed in Section 8.1. The calculation of the neutrinoinduced muons is discussed in Section 8.3.3. The intersections of the muon flux lines with the νμ-induced flux line indicate the zenith angles at which the two contributions are equal for each depth. The data are from the SNO detector, which has a flat overburden under 5.89 km.w.e.

Essential to the phenomenology of both muons and muon neutrinos is energy loss of high-energy muons during propagation. We therefore begin this chapter with a discussion of muon energy loss. We then apply the results both to atmospheric muons that penetrate to deep detectors and to muons produced by charged current interaction of νμ in or near underground detectors. We also describe the signatures of all three neutrino flavors in underground detectors.

Passage of muons through matter

The energy loss equation for muons has the same form as for electrons (Eq. 5.10). The ionization loss rate is nearly constant for relativistic muons, with a broad minimum below 1 GeV of ∼ 1.8 MeV/(g/cm2) in rock and a logarithmic rise at higher energy.