Astroparticle Physics

7.2 Cosmic Rays at Sea Level 149muons. If one assumes that primary protons interact withprotons and neutrons of atomic nuclei in the atmospherewhere the multiplicity of produced pions is usually quitelarge, the charge ratio of muons, N(µ + )/N(µ − ), can beestimated by considering the possible charge exchange reactions:p + N → p ′ + N ′ + kπ + + kπ − + rπ 0 ,p + N → n + N ′ + (k + 1)π + + kπ − + rπ 0 (7.3).In this equation k and r are the multiplicities of the producedparticle species and N represents a target nucleon. If oneassumes that for the reactions in (7.3) the cross sections arethe same, the charge ratio of pions is obtained to beR = N(π+ )N(π − ) = 2k + 1 = 1 + 12k 2k . (7.4)For low energies k = 2 and thereby R = 1.25. Since thisratio is transferred to muons by the pion decay, one wouldexpect a similar value for muons. Experimentally one observesthat the charge ratio of muons at sea level is constantover a wide momentum range and takes on a value ofN(µ + )/N(µ − ) ≈ 1.27 . (7.5)In addition to ‘classical’ production mechanisms ofmuons by pion and kaon decays, they can also be producedin semileptonic decays of charmed mesons (for example,D 0 → K − µ + ν µ and D + → ¯K 0 µ + ν µ , D − →K 0 µ − ¯ν µ ). Since these charmed mesons are very short-lived(τ D 0 ≈ 0.4ps, τ D ± ≈ 1.1 ps), they decay practically immediatelyafter production without undergoing interactionsthemselves. Therefore, they are a source of high-energymuons. Since the production cross section of charmedmesons in proton–nucleon interactions is rather small, Ddecays contribute significantly only at very high energies.Figure 7.12 already showed that apart from muons alsosome nucleons can be observed at sea level. These nucleonsare either remnants of primary cosmic rays, which, however,are reduced in their intensity and energy by multipleinteractions, or they are produced in atmospheric hadroncascades. About one third of the nucleons at sea level areneutrons. The proton/muon ratio varies with the momentumof the particles. At low momenta (≈ 500 MeV/c) ap/µ ratio N(p)/N(µ) of about 10% is observed decreasingtolargermomenta(N(p)/N(µ)≈ 2% at 1 GeV/c,N(p)/N(µ) ≈ 0.5% at 10 GeV/c).charge exchange reactionsmuonsfrom semileptonic decaysnucleon component