Spectrum of cosmic-ray nucleons and the atmospheric muon charge ratio

Abstract: Interpretation of measurements of the muon charge ratio in the TeV range depends on the spectra of protons and neutrons in the primary cosmic radiation and on the inclusive cross sections for production of $\pi^\pm$ and $K^\pm$ in the atmosphere. Recent measurements of the spectra of cosmic-ray nuclei are used here to estimate separately the energy spectra of protons and neutrons and hence to calculate the charge separated hadronic cascade in the atmosphere. From the corresponding production spectra of $\mu^+$ and $\mu^-$ the $\mu^+/\mu^-$ ratio is calculated and compared to recent measurements. The comparison leads to a determination of the relative contribution of kaons and pions. Implications for the spectra of $\nu_\mu$ and $\bar{\nu}_\mu$ are discussed.

• The paper refines cosmic-ray nucleon spectra and muon charge ratio using a detailed analysis of hadronic cascade processes and decay channels.
• It employs spectrum-weighted moments for pion and kaon production, highlighting the unique impact of K⁺ in shaping high-energy interactions.
• The study correlates updated cosmic-ray composition data with muon charge predictions, aligning theoretical models with experimental observations.

Overview of Cosmic Ray Nucleons and Atmospheric Muon Charge Ratio

The paper authored by Thomas K. Gaisser explores critical aspects of high-energy cosmic ray interactions in the atmosphere, focusing specifically on the spectra of cosmic-ray nucleons and their influence on the atmospheric muon charge ratio. This study brings new estimations on the spectra of cosmic-ray protons and neutrons, which are foundational for understanding the charge-separated hadronic cascades that occur upon interaction with atmospheric particles. The resulting calculations provide insights into the production spectra of $\mu^+$ and $\mu^-$, leading to predictions of the $\mu^+/\mu^-$ ratio and its comparison with recent experimental measurements.

Analysis Framework

Contrary to the simpler analytic approximations used in previous studies, this paper utilizes a more detailed derivation of the muon charge ratio, integrating spectrum-weighted moments for $\pi^\pm$ and $K^\pm$ production processes. This approach is rooted in the groundwork laid by Lipari and builds on recent primary cosmic-ray composition data from experiments like ATIC and CREAM. The paper also discusses how energy-dependent changes, particularly in helium and heavier nuclei spectra, impact these calculations.

Production Channels and Their Implications

A significant portion of the analysis explores different decay channels, primarily focusing on the charged pion and kaon channels. The research underscores the importance of associated production processes, particularly for the $K^+$ kaon channel, which lacks a comparable $K^-$ counterpart in forward beam interactions, significantly impacting the muon charge ratio at high energies.

Gaisser elaborates on the atmospheric cascade equations and kinematics, addressing the low- and high-energy limits of muon and neutrino production, providing a comprehensive view on how these decay processes contribute to the muon charge ratio. Moreover, the paper raises attention to the significance of kaon decays in high-energy neutrino contexts, illustrating that kaons become more crucial for neutrino production at higher energy levels.

Primary Cosmic Ray Spectrum and Composition

Through a rigid analysis of primary spectra, the paper accommodates recent direct measurements and extrapolations to higher energies by employing a three-component model influenced by Hillas's suggestions. This method assumes separate galactic and extragalactic contributions to cosmic-ray populations, which correlates with features observed in the cosmic ray spectrum, such as the knee.

In redefining nucleon spectra, Gaisser's model nicely aligns with cosmic ray data, validating assumptions about cosmic-ray composition over a broad energy range. The energy-dependent parameter $\delta_0$, reflecting the proton-neutron composition asymmetry, is particularly critical for accurately predicting the muon charge ratio from experimental data.

Results and Data Interpretation

Gaisser's calculations pertaining to the muon charge ratio demonstrate a reasonable consistency with observational data from experiments like MINOS and OPERA. The subtle differences attributed to the primary cosmic-ray density and composition are thoroughly analyzed, reaffirming existing models while also fine-tuning them in light of measured muon charge ratios.

The comparisons elucidate that small changes in parameters, specifically those affecting associated kaon production, can significantly modify the fit between theoretical predictions and empirical measurements. Gaisser’s analysis suggests revised values for spectrum-weighted moments of associated production, cementing kaon's critical role in understanding atmospheric neutrinos.

Practical and Theoretical Implications

This paper lays substantial groundwork for subsequent studies aimed at refining particle interaction models in the Earth’s atmosphere. With cosmic-ray composition at its core, the research extends implications for the production rates of high-energy neutrinos, which are pivotal in the burgeoning field of astrophysical neutrino observations. Additionally, understanding the primary cosmic-ray nucleon spectrum is a stepping-stone towards unraveling the origins and propagation of cosmic rays through interstellar mediums and their potential sources, offering an enriched perspective for theoretical cosmic-ray models.

Moving forward, we can anticipate more precise measurements and simulations to emerge, advancing the comprehension of cosmic-ray interactions and their broader implications for particle physics and cosmological models. Insights from this study not only augment the theoretical understanding but also propel observational strategies for atmospheric and astrophysical phenomena in the high-energy spectrum.