Presentación de resultados

Figure 36: dN/dxlab for positive pions produced by fluka in p-air collisions

at different kinetic energies of the proton projectile.

In the final state of a high energy interaction one finds the fragments of the target nucleus, a leading nucleon that carries the baryon number of the projectile, a number of mesons, mostly pions, with a non-negligible contribution of kaons. In addition one has to consider the production of nucleon-antinucleon pairs and of heavy flavors. In order to characterize the features of nucleon-air collisions that are relevant in this discussion, I recall few fundamental quantities introduced in Section 1.2: the nucleon-air cross- sections, the distribution of the energy fraction carried away by produced particles and the “spectrum weighted moments” Zij, all as a function of

projectile energy.

In fluka, total, elastic and inelastic cross-sections for hadron-nucleus collisions are derived in the framework of the Glauber formalism, using as input the tabulated data (when they exist) of the Particle Data Group for hadron-hadron collisions.

Figure 37: dN/dxlab for negative pions produced by fluka in p-air collisions

at different kinetic energies of the proton projectile.

For our purposes, particle production can be conveniently studied in terms of a longitudinal non-dimensional variable like xlab = Ej/Ei, which is the ratio

of the total energies of the secondary particle j over the primary particle i (xlab

is approximately equal to xF in the forward region). We can then construct the

dNij/dxlabdistributions. These are the differential multiplicity distributions of

secondary j as produced by primary i in collisions with air nuclei as a function of xlab. Examples of the xlab distribution in p-air collisions predicted by fluka

are shown in Figs. 36-39, respectively, for produced π+_{, π}−

, K+ _{and K}−

, at different kinetic energy of the projectile. Here xlab is defined as the ratio of

secondary total energy with respect to the primary total energy. The spectrum weighted moments are defined as

Zij = Z 1 0 xlab
γ−1dNij dxlab dxlab (46)

where γ = 2.7 is the approximate spectral index of the differential cosmic ray spectrum. Their use in the literature is justified by the fact that the inclusive yield of secondary cosmic ray particles at a given energy is almost proportional

Figure 38: dN/dxlab for positive kaons produced by fluka in p-air collisions

at different kinetic energies of the proton projectile.

to Z, when the primary spectrum is a power law with a constant spectral index in the whole useful energy spectrum. This is a good approximation for nucleon energies exceeding the TeV scale, but it is not the case in the range of energies considered in this work, since a single power law does not fit the primary spectrum. However, they remain a useful and commonly accepted tool to characterize and compare different interaction models. The resulting spectrum weighted moments for the energies shown in Figs. 36-39 are tabulated in Table 4.

Figure 39: dN/dxlab for negative kaons produced by fluka in p-air collisions

at different kinetic energies of the proton projectile.

E_kp (GeV) p nucl π+ _π− K+ _K− 5 0.499436 0.735440 0.0313886 0.0169552 0.00066900 1.43247e-05 10 0.271731 0.424942 0.0403301 0.0240934 0.00315013 5.02071e-04 30 0.199909 0.291563 0.0422783 0.0283846 0.00481658 1.72275e-03 50 0.185910 0.268332 0.0428086 0.0291373 0.00528883 2.09420e-03 100 0.179621 0.254491 0.0430343 0.0297099 0.00560599 2.43725e-03 Table 4: Spectrum weighted moments (for a spectral index of the differential

primary spectrum γ = 2.7) for secondary particles produced in p-air collisions as a function of the projectile kinetic energy.

Figure 40: Primary proton energy distributions for different muon (left) and neutrino (right) energies.

Figure 41: Muon (left) and neutrino (right) over-all ratios related to π and K contributions.

In Figs. 40-45 we show fluka calculations of particles in the atmosphere and at ground level. In Fig. 40 are shown distributions of primary proton

Figure 42: Muon (left) and neutrino (right) spectra with contributions from π and K decay.

Figure 43: Production altitude for muons (left) and neutrinos (right) that reach the ground level. Green line: from µ decay. Red line: from π decay. Blue line: from K decay.

energy related to protons that produce µ and ν at ground level with energies into fixed windows (“response curves” [1]). Note that muons are produced in average by a primary proton of E0 ∼ 10Eµ. In Fig. 41 are shown the muon

and neutrino over-all ratios related to π and K contributions. Above 100 GeV kinematic effects make K more efficient than π in ν production. Fig. 42 shows muon and neutrino spectra with contributions from π and K decay. In Fig. 43

Figure 44: Atmospheric π − µ energy correlation at ground level.

Figure 45: µ − ν energy correlation at ground level for muons from π and K decay.

are shown the production altitude for muons and neutrinos that reach the ground level. Fig. 44 represents the atmospheric π − µ energy correlation at ground level. For example, a muon of 10 GeV comes from a pion of ∼17 GeV. Fig. 45 represents the µ − ν energy correlation at ground level for muons from π and K decay.