Model of the response of surface detectors to extensive air showers based on shower universality

We present a full model of surface-detector responses to extensive air showers. The model is motivated by the principles of air-shower universality and can be applied to different types of surface detectors. Here we describe a parametrization for both water-Cerenkov detectors and scintillator surface detectors, as for instance employed by the upgraded detector array of the Pierre Auger Observatory. Using surface detector data, the model can be used to reconstruct with reasonable precision shower observables such as the depth of the shower maximum <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>X</a:mi></a:mrow><a:mrow><a:mi>max</a:mi></a:mrow></a:msub></a:mrow></a:math> and the number of muons <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>R</c:mi><c:mi>μ</c:mi></c:msub></c:math>.