Lepton Fluxes from Atmospheric Charm

TL;DR

This paper reassesses atmospheric lepton fluxes from charm using perturbative QCD with next-to-leading order corrections, emphasizing uncertainties from extrapolations of gluon distributions at small x. It develops a cascade framework based on Z-moments to connect charm production and decay to observable lepton fluxes, and systematically analyzes the total cross section, charm energy distribution, hadronization fractions, and decay moments. The main finding is that charm-induced prompt leptons become dominant over conventional fluxes around $E\sim 10^5$ GeV, with predictions highly sensitive to PDFs and scale choices due to small-x gluon behavior. The study concludes that perturbative charm alone cannot explain TeV-range muon excesses, suggesting a potential role for nonperturbative models and highlighting the need for high-energy data to constrain small-x QCD dynamics.

Abstract

We reexamine the charm contribution to atmospheric lepton fluxes in the context of perturbative QCD. We include next-to-leading order corrections and discuss theoretical uncertainties due to the extrapolations of the gluon distributions at small-x. We show that the charm contribution to the atmospheric muon flux becomes dominant over the conventional contribution from pion and kaon decays at energies of about 10^5 GeV. We compare our fluxes with previous calculations.

Figures (10)

• Figure 1: The NLO $c\bar{c}$ production cross section in $pN$ collisions versus beam energy for $m_c=1.3$ and 1.5 GeV. The CTEQ3 parton distribution functions are used with $M=\mu=m_c$. The data are taken from the summary in Ref. [28].
• Figure 2: A plot of NLO $\sigma _{pN}^{c\bar{c}}$ versus beam energy for $m_c=1.3$ GeV using the CTEQ3 (solid) and D- (dashed) parton distribution functions with $M=2m_c$ and $\mu=m_c$. Also show is the CTEQ3 NLO prediction with $M=\mu=m_c$ (dot-dashed). The data are the same that appear in Fig. 1.
• Figure 3: The function $K(E,x_E)$ defined in Eq. (3.3) versus $x_E$ for $E=10^3$ GeV and $10^6$ GeV. The points come from the evaluation of $K$ using the results of Ref. [41,42] with error bars indicating numerical errors in the integration, and the curves are our fit to the ratio parameterized in Eq. (3.4).
• Figure 4: For $E=10^3$ (solid), 10$^6$ (dashed) and 10$^9$ GeV (dot-dashed), $d\sigma/dx_E$, including the factor of $K(E,x_E)$. The scales used are $\mu=m_c$ and $M=2m_c$, for $m_c$=1.3 GeV.
• Figure 5: For energies $E=10^4$ GeV, $10^6$ GeV and $10^8$ GeV, $dZ_{pc}(E)/dx_E$ versus $x_E$ for CTEQ3 (solid) and D- (dashed) parton distribution functions, where $\mu=m_c$ and $M=2m_c$.