Proc. Neutrino Astrophysics - MPP Theory Group

112
Atmospheric Muons and Neutrinos Above 1 TeV
P. Gondolo
Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)
Föhringer Ring 6, 80805 München, Germany
The ultimate background to high energy neutrino astronomy are the neutrinos produced in
the interaction of cosmic rays with the Earth atmosphere. A cosmic ray nucleus penetrates on
average ≈ 60 g/cm 2 of atmosphere before colliding with an air nucleus. The secondary mesons
produced in the collision can propagate an additional ≈ 100 g/cm 2 , but if their lifetime is
short enough they may decay before interacting with air. Their semileptonic decays then
produce an atmospheric neutrino flux.
The competition between interaction with air and decay is at the basis of the energy
and angular dependence of the atmospheric neutrino fluxes. Let us compare the mean free
path of mesons in air to the distance they travel in a mean lifetime. In a cascade developing
vertically downwards, the primary interaction occurs at a height of ≈ 20 km, and the mean
free path is ≈ 10 km; in a cascade developing horizontally, the primary interaction is ≈ 500 km
from the observer, and the mean free path is ≈ 100 km. The distance travelled in a mean
lifetime increases linearly with the meson momentum: d = pτ/m, where p, τ, and m are the
meson momentum, lifetime and mass. For p = 1 TeV, pions and kaons can travel kilometers
(d π + = 55.9 km, d K 0 L = 31.2 km, d K + = 7.52 km), but charmed mesons only centimeters
(d D 0 = 6.65 cm, d D + = 1.70 cm, d D + s = 7.1 cm, d Λ + c = 2.7 cm).
As a consequence: (1) vertical pions and kaons do not have time to decay before interacting
with air, while horizontal pions and kaons decay readily: the subsequent “conventiona”
neutrino flux is stronger in the horizontal than in the vertical direction; (2) charmed mesons
decay promptly whether vertical or horizontal: the subsequent “prompt” neutrino flux is the
same in the horizontal and in the vertical direction; (3) as the energy increases, the mesons
live longer, and fewer and fewer pions and kaons have time to decay within the available mean
free path, while all charmed mesons have time to decay: 1 the energy spectrum of conventional
neutrinos is steeper than that of prompt neutrinos by one power of energy.
The different energy dependence means that beyond a certain energy, the atmospheric
neutrino flux is dominated by decays of charmed mesons. The energy at which this happens
depends on the relative strength of charmed and non-charmed meson production in
the primary nucleus-nucleus collision. Unfortunately, laboratory data do not extend up to
the relevant energies. One could either look for help from measurements of the atmospheric
muons produced in association with the neutrinos or extrapolate laboratory data with the
help of a theoretical model for charm production.
In a search for muons, prompt and conventional components could be separated by their
different angular dependence. Several attempts have been made with underground experiments
and with air shower detectors. In underground experiments, high energy muons,
prompt muons in particular, come only from directions close to the horizon, where unfortunately
there is an intense muon background generated by low-energy atmospheric neutrinos
in the rock surrounding the detector. Subtraction of this neutrino-induced background is
a source of big systematic errors [1] which spoil the search for prompt muons. Air shower
1 At high enough energy (≈ EeV), also charm decays are fewer and fewer for an analogous reason.