[Paper Review] Applying Extensive Air Shower Universality to Ground Detector Data

Fabian Schmidt, M. Ave+2 more|ArXiv.org|Jun 13, 2007

Astrophysics and Cosmic Phenomena3 citations

TL;DR

This paper proposes a model-independent method to determine cosmic ray energy and muon content in extensive air showers using ground detector data by leveraging air shower universality. By exploiting the isotropy of cosmic ray arrival directions and fitting zenith-angle-dependent signals to a parametrization involving primary energy and muon normalization, the method achieves <10% systematic uncertainty in muon content measurement, enabling robust constraints on hadronic interaction models.

ABSTRACT

Air shower universality states that the electromagnetic part of hadron-induced extensive air showers (EAS) can be completely described in terms of the primary energy and shower age. In addition, simulations show that the muon part is well characterized by an overall normalization which depends on the primary particle and hadronic interaction model. We investigate the consequences of EAS universality for ground arrays, which sample EAS at large core distances, and show how universality can be used to experimentally determine the muon content as well as the primary energy of cosmic ray air showers in a model-independent way.

Motivation & Objective

• To develop a model-independent calibration of ground detector energy measurements in extensive air shower experiments.
• To determine the muon content of air showers without relying on hadronic interaction models.
• To exploit the isotropy of cosmic ray arrival directions to constrain the muon normalization parameter.
• To reduce systematic uncertainties in energy and composition measurements from hadronic model dependencies.
• To provide a method applicable across different energy ranges and detector configurations.

Proposed method

• The method uses air shower universality, where electromagnetic and muon signals at large core distances depend only on primary energy, shower age (via $X_{\rm max}$), and muon normalization $N_{\mu}$.
• A signal parametrization is constructed: $ S(E,\theta) = S_{\rm em}(E,\theta,\langle X_{\rm max}\rangle) + N_{\mu}(E) \cdot S_{\mu}(\theta,\langle X_{\rm max}\rangle) $, with $S_{\mu}$ as a reference muon signal.
• The muon normalization $N_{\mu}(E_{\rm ref})$ is determined by matching the number of events in equal $\sin^2\theta$ bins to a flat distribution, minimizing $\chi^2$/dof.
• Monte Carlo simulations with 1,000 realizations of ground array data (2,000 events >10^19 eV) are used to validate the method and quantify biases.
• Systematic bias in $N_{\mu}$ is estimated and subtracted, with total systematic uncertainty reduced to <10% when combined with $\langle X_{\rm max}\rangle$ constraints.
• The method enables a model-independent energy scale calibration and muon content measurement at any accessible energy.

Experimental results

Research questions

• RQ1 Can the muon content of extensive air showers be measured independently of hadronic interaction models?
• RQ2 How can the isotropy of cosmic ray arrival directions be used to constrain the muon normalization parameter $N_{\mu}$?
• RQ3 What is the achievable systematic uncertainty in $N_{\mu}$ when combining signal parametrization with $\langle X_{\rm max}\rangle$ constraints?
• RQ4 To what extent does the method reduce model dependence in ground detector energy calibration?
• RQ5 Can this approach be applied to real data from existing experiments like the Pierre Auger Observatory?

Key findings

• The method achieves a total systematic uncertainty in $N_{\mu}$ of less than 10%, primarily limited by statistical fluctuations and $\langle X_{\rm max}\rangle$ measurement errors.
• For pure proton composition, the method exhibits a ~14% bias in $N_{\mu}$ determination, which is significantly reduced for iron showers due to smaller fluctuations.
• The muon normalization $N_{\mu}$ is determined by fitting the zenith-angle distribution of events to a flat $\sin^2\theta$ distribution using a signal parametrization with adjustable $N_{\mu}$.
• The energy scale is calibrated model-independently once $N_{\mu}$ is determined, enabling reliable energy reconstruction without hadronic model assumptions.
• The method has been successfully applied to data from the Pierre Auger Observatory, yielding constraints on hadronic interaction models.
• The approach remains robust across different hadronic interaction models (QGSJetII, Sibyll, Fluka) and primary compositions (proton, iron, mixed).