📝 Abstract

In the near future the energy region above few hundreds of TeV may really be accessible for measurements of the atmospheric muon spectrum by the IceCube array. Therefore one expects that muon flux uncertainties above 50 TeV, related to a poor knowledge of charm production cross sections and insufficiently examined primary spectra and composition, will be diminished. We give predictions for the very high-energy muon spectrum at sea level, obtained with the three hadronic interaction models, taking into account also the muon contribution due to decays of the charmed hadrons.

💡 Analysis

In the near future the energy region above few hundreds of TeV may really be accessible for measurements of the atmospheric muon spectrum by the IceCube array. Therefore one expects that muon flux uncertainties above 50 TeV, related to a poor knowledge of charm production cross sections and insufficiently examined primary spectra and composition, will be diminished. We give predictions for the very high-energy muon spectrum at sea level, obtained with the three hadronic interaction models, taking into account also the muon contribution due to decays of the charmed hadrons.

📄 Content

arXiv:0906.3791v2 [astro-ph.HE] 3 Sep 2010 June 1, 2018 2:3 WSPC/INSTRUCTION FILE AM˙PeV˙v2 ATMOSPHERIC MUON FLUX AT PEV ENERGIES S. I. SINEGOVSKY, A. A. KOCHANOV, T. S. SINEGOVSKAYA, Irkutsk State University, Gagarin Blvd 20, Irkutsk, RU-664003 Russia sinegovsky@api.isu.ru A. MISAKI, Research Institute for Science and Technology, Waseda U., Tokyo, 169-8555, Japan Innovative Research Organization, Saitama U., Saitama, Japan N. TAKAHASHI Graduate School of Science and Technology, Hirosaki U., Hirosaki 036-8561, Japan In the near future the energy region above few hundreds of TeV may really be accessible for measurements of the atmospheric muon spectrum with IceCube array. Therefore one expects that muon flux uncertainties above 50 TeV, related to a poor knowledge of charm production cross sections and insufficiently examined primary spectra and composition, will be diminished. We give predictions for the very high-energy muon spectrum at sea level, obtained with the three hadronic interaction models, taking into account also the muon contribution due to decays of the charmed hadrons. Keywords: cosmic ray muons, high-energy hadronic interactions PACS numbers: 95.85.Ry, 13.85.Tp

1. Introduction The atmospheric muon flux as well as muon neutrino flux at high energies are in- evitably dominated by the prompt component due to decays of the charmed hadrons (D±, D0, D0, D± s Λ+ c , . . .), hence the prompt neutrino flux becomes the major source of the background in the search for a diffuse astrophysical neutrino flux1–4. Insufficiently explored processes of the charm production give rise to most uncer- tainty in the muon and neutrino fluxes. IceCube, the first to begin operating as the km3 neutrino telescope, has the real capability5,6 to measure the atmospheric muon spectrum at energies up to 1 PeV and to shed light on the feasible range of the cross sections for the charmed particle production. Besides, an ambiguity in high-energy behaviour of pion and kaon production cross sections affects essentially the atmospheric muon (neutrino) flux. Recent calculations7 reveal differences (up to factor 1.8 at 10 PeV) in the neutrino flux because of uncertain description of the hadronic proceses involving light quarks at high energies. 1 June 1, 2018 2:3 WSPC/INSTRUCTION FILE AM˙PeV˙v2 2 In this work we extend to higher energies the conventional muon flux calculations basing on the known hadronic interaction models with usage reliable data of the primary cosmic ray measurements. We present results of the conventional muon flux calculations in the energy range 105–108 GeV using hadronic models QGSJET- II8,9, SIBYLL 2.110,11, EPOS12,13 as well as the model by Kimel and Mokhov14 (KM), that were tested also in recent atmospheric muon flux calculations15,16. In order to compare the uncetainity of the conventional muon flux and prompt one we plot the prompt muon contrubition originating from decays of the charmed hadrons produced in collisions of cosmic rays with nuclei of air (for review see e.g. Refs. 17– 22).
2. The method The high-energy muon fluxes are calculated using the approach23 to solve the at- mospheric hadron cascade equations taking into account non-scaling behavior of in- clusive particle production cross-sections, rise of total inelastic hadron-nuclei cross- sections, and the non-power law primary spectrum (see also Ref. 16). To obtain the differential energy spectra of protons p(E, h) and neutrons n(E, h) at the atmosphere depth h one needs to solve the set of equations: ∂N ±(E, h) ∂h = −N ±(E, h) λN(E)

1 λN(E) Z 1 0 Φ± NN(E, x)N ±(E/x, h)dx x2 , (1) where N ±(E, h) = p(E, h) ± n(E, h), Φ± NN(E, x) = E σin pA(E) dσpp(E0, E) dE ± dσpn(E0, E) dE  E0=E/x , λN(E) = 1/  N0σin pA(E)  is the nucleon interaction length in the atmosphere, x = E/E0 is the fraction of the primary nucleon energy E0 carried away by the secondary nucleon, dσab/dE is the cross sections for inclusive reaction a + A →b + X. The boundary conditions for Eq. (1) are N ±(E, 0) = p0(E) ± n0(E). Suppose that the solution of the system is N ±(E, h) = N ±(E, 0) exp  −h(1 −Z± NN(E, h)) λN(E)  , (2) where Z± NN(E, h) are unknown functions. Substituting Eq. (2) into Eq. (1) we find the equation for these functions Z± NN (Z-factors): ∂(hZ± NN) ∂h

Z 1 0 Φ± NN(E, x)η± NN(E, x) exp  −hD± NN(E, x, h)  dx, (3) where η± NN(E, x) = x−2N ±(E/x, 0)/N ±(E, 0), D± NN(x, E, h) = 1 −Z± NN(E/x, h) λN(E/x) −1 −Z± NN(E, h) λN(E) . (4) June 1, 2018 2:3 WSPC/INSTRUCTION FILE AM˙PeV˙v2 3 By integrating Eq. (3) we obtain the nonlinear integral equation Z± NN(E, h) = 1 h Z h 0 dt Z 1 0 dxΦ± NN(E, x)η± NN(E, x) exp  −tD± NN(E, x, t)  , (5) which can be solved by iterations. The simple choice of zero-order approximation is Z±(0) NN (E, h) = 0, that is D±(0) NN (E, x, h) = 1/λN(E/x) −1/λN(E). For the n-th step we find Z±(n) NN (E, h) = 1 h Z h 0 dt Z 1 0 dxΦ± NN(E, x)η± NN(E, x) exp h −tD±(n−1) NN (E, x, t) i , (6) where D±(n−1) NN (E, x, h) = 1 −Z±(n−1) NN (E/x, h) λN(E/x) −1 −Z±(n−1) NN

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