Calculation of conventional and prompt lepton fluxes at very high energy

TL;DR

Addresses calculating atmospheric lepton fluxes (conventional and prompt) with implications for astrophysical neutrino searches. Introduces a matrix-form numerical solution of coupled cascade equations that accommodates diverse hadronic interaction models, primary cosmic-ray spectra, and realistic atmospheric profiles, including heavy-flavor contributions. Demonstrates applications to prompt flux calculations and to tracing intermediate-particle contributions across zenith angles and energies. The method is efficient on standard hardware and the code is publicly available, enabling broader use and cross-checks.

Abstract

An efficient method for calculating inclusive conventional and prompt atmospheric leptons fluxes is presented. The coupled cascade equations are solved numerically by formulating them as matrix equation. The presented approach is very flexible and allows the use of different hadronic interaction models, realistic parametrizations of the primary cosmic-ray flux and the Earth's atmosphere, and a detailed treatment of particle interactions and decays. The power of the developed method is illustrated by calculating lepton flux predictions for a number of different scenarios.

Figures (10)

• Figure 1: Decay lengths $\lambda_{dec}$ for a subset of hadrons, evaluated at $h_{atm}=8$ km. Superimposed is the interaction length $\lambda_{int}$ of $K^\pm$.
• Figure 2: Models of the cosmic ray nucleon spectrum and the neutron fraction. Gaisser-Stanev-Tilav (GST) Gaisser:2013tu and Hillas-Gaisser (H3a) Gaisser:2012em are recent 3 generation/5 mass component models. The proton-only broken power law model by Thunman et al. (TIG) thunman_1996 has been often used for calculation of the prompt flux in the past. The poly-gonato model Horandel:2003go focuses on the flux below and at the knee and it is not applicable at very high energies.
• Figure 3: Primary model dependence of the atmospheric conventional + prompt neutrino flux. The model abbreviations are described in the caption of Fig. \ref{['fig:primary_spectrum']}.
• Figure 4: Atmospheric density dependence on $X$, calculated using parameterizations for the US Standard Atmosphere us_std_atmosphere and the South Pole as implemented in CORSIKA Heck:ut, and the NRLMSISE-00 model. Solid lines represent a trajectory for $\theta = 0^\circ$ and dashed for $\theta = 70^\circ$.
• Figure 5: Ratio of the flux calculated with different atmospheric models to the flux with US Standard atmosphere (USStd). The parameters and names are described in the caption of Fig. \ref{['fig:atm_comparison']}. The primary model is H3a and the interaction model SIBYLL-2.3 RC1. A vertical trajectory ($\theta = 0^\circ$) is represented by solid and a horizontal ($\theta = 90^\circ$) by dashed lines.