Two-, Three-, and Four-Particle Spatial Correlations Among Tertiary Cosmic Ray Muons

Abstract Showers of muons which result from interactions of primary cosmic rays high in the atmosphere appear deep underground as bundles of nearly parallel muons. For threshold energies of 1 TeV and arrival zenith angles of 45 degrees, those events having a small mean number of muons are described by a power law distribution in shower size having an exponent of ≅−3.7 and a radial density distribution that decreases with distance R from the shower axis a little less rapidly than exp(− R /5.4 m). Comparison of new data on four muon spatial correlations in terms of the same phenomenology with data on two and three muon spatial correlations from previous experiments suggests that the shower size distribution steepens and the shower radial density distribution broadens with increasing shower size (i.e., with increasing mean energy of the primary cosmic ray at a given threshold energy of the muons observed). These results might be explained by a basically geometrical effect due either to a total inelastic cross section which rises with energy or by an enhanced contribution from the interactions of secondaries. If the effect does not have a geometrical origin, then it may be necessary to reformulate the input to shower development calculations which have assumed that interaction products are described by factored, uncorrelated single particle statistical distributions. The relationships between the inclusive distributions predicted by theory and those of the empirical phenomenology are explored in some detail.