Studying the mass sensitivity of air-shower observables using simulated cosmic rays

Using simulations, we investigate the mass sensitivity of cosmic-ray air-shower observables for sites at the South Pole and Malargüe, Argentina, the respective locations of the IceCube Neutrino Observatory and the Pierre Auger Observatory. Exact knowledge of observables from air-shower simulations was used to study the event-by-event mass separation between proton, helium, oxygen, and iron primary cosmic rays with a Fisher linear discriminant analysis. Dependencies on the observation site as well as the energy and zenith angle of the primary particle were studied in the ranges from <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mn>10</a:mn><a:mn>16.0</a:mn></a:msup><a:mi>–</a:mi><a:msup><a:mn>10</a:mn><a:mn>18.5</a:mn></a:msup><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>eV</a:mi></a:math> and 0° to 60°; they are mostly weak and do not change the qualitative results. Promising proton-iron mass separation is achieved using combined knowledge of all studied observables, also when typical reconstruction uncertainties are accounted for. However, even with exact measurements, event-by-event separation of intermediate-mass nuclei is challenging and better methods than the Fisher discriminant and/or the inclusion of additional observables will be needed. As an individual observable, high-energy muons (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mo>></c:mo><c:mn>500</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>GeV</c:mi></c:math>) provide the best event-by-event mass discrimination, but the combination of muons of any energy and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>X</e:mi><e:mi>max</e:mi></e:msub></e:math> provides already a high event-by-event separation between proton-iron primaries at both sites. We also confirm that the asymmetry and width parameters of the air-shower longitudinal profile, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>R</g:mi></g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>L</i:mi></i:math>, are mass sensitive. Only <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>R</k:mi></k:math> seems to be suitable for event-by-event mass separation, but <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>L</m:mi></m:math> can potentially be used to statistically determine the proton-helium ratio. Overall, our results motivate the coincident measurement of several air-shower observables, including at least <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>X</o:mi><o:mi>max</o:mi></o:msub></o:math> and the sizes of the muonic and electromagnetic shower components, for the next generation of air-shower experiments.