Charm production and high energy atmospheric muon and neutrino fluxes

Abstract

Production of muons and neutrinos in cosmic ray interactions with the atmosphere has been investigated with Monte Carlo models for hadronic interactions. The resulting conventional muon and neutrino fluxes (from π and K decays) agree well with earlier calculations, whereas our prompt fluxes from charm decays are significantly lower than earlier estimates. Charm production is mainly considered as a well defined perturbative QCD process, but we also investigate a hypothetical nonperturbative intrinsic charm component in the proton. The lower charm rate implies better prospects for detecting very high energy neutrinos from cosmic sources. IntroductionThe flux of muons and neutrinos at the earth has an important contribution from decays of particles produced through the interaction of cosmic rays in the atmosphere (for a recent introduction see [1]). This has an interest in its own right, since it reflects primary interactions at energies that can by far exceed the highest available accelerator energies. It is also a background in studies of neutrinos from cosmic sources as attempted in large neutrino telescopes, such as Amanda [2], Baikal [3], Dumand [4] and Nestor [5].Here we present a detailed study of muon and neutrino production in cosmic ray interactions with nuclei in the atmosphere using Monte Carlo simulations [6].At GeV energies the atmospheric muon and neutrino fluxes are dominated by 'conventional' sources, i.e. decays of relatively long-lived particles such as π and K mesons. This is well understood from earlier studies [7,8,9], with which our investigations agree. With increasing energy, the probability increases that such particles interact in the atmosphere before decaying. This implies that even a small fraction of short-lived particles can give the dominant contribution to high energy muon and neutrino fluxes. These 'prompt' muons and neutrinos arise through semi-leptonic decays of hadrons containing heavy quarks, most notably charm.Available data in the multi-TeV energy range, obtained with surface and underground detectors (see e.g. refs. [10][11][12][13]), are still too discrepant to draw definitive conclusions on the flux of 1 thunman@tsl.uu.se 2 ingelman@tsl.uu.se, also at DESY, Hamburg.

Rigidity dependent knee and cosmic ray induced high energy neutrino fluxes

“…Concerning the meson cascade equations, they are usually solved by considering separately the low energy solution φ L M (which neglects the interaction and regeneration terms, since λ M ≫ λ d M at low energies) and the high energy solution φ H M (which neglects instead the decay term, since λ M ≪ λ d M at very high energies) [2,3,4]. The high energy solution is given by…”

“…The CR particles reaching the top of the atmosphere produce secondary fluxes of hadrons and leptons that are usually described by means of coupled cascade equations [2,3,4,5], which can be solved analytically under appropriate symplifying assumptions. In this work we will compute the fluxes of muon neutrinos and antineutrinos, which are the ones more readily detectable at underground detectors.…”

“…The decay moments used in this work were calculated by fitting the β− dependence of the relevant moments tabulated in [4] for 2.7 ≤ β ≤ 4, which were determined with Lund Monte Carlo simulation programs. Then, the asymptotic low and high energy neutrino fluxes can now be determined from the equations (13) and (16), which involve the meson decay moments and the corresponding high and low energy meson fluxes derived in equations (11) and (12).…”

“…The associated steepening in the induced neutrino fluxes has been obtained in the literature [4,7], but these works usually assume for simplicity that the dominant CR component consists of protons, and only some crude attempts have been done trying to generalise these predictions to heavier compositions [6].…”

“…Several groups have studied the charm particle production by CRs [4,5,6], which actually requires to take into account next to leading order (NLO) processes, which increase the charm production by more than a factor of two, and the cross sections are sensitive to the values of the partonic distribution functions at very small values of the scaling variable x, what introduces further uncertainties in the results, due to the need to extrapolate beyond the measured range. Even if the charmed mesons (D ± , D 0 , D s , Λ c , ...) are produced at a rate ∼ 10 −4 with respect to the non-charmed ones, their very short decay time, with L D ≃ 2 km(E D /10 PeV), implies that the prompt neutrino spectral slope just follows the CR slope, and hence the prompt neutrinos eventually dominate the atmospheric neutrino fluxes above a PeV in the vertical direction, and somewhat above that energy at large zenith angles 1 .…”