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The composition of ultra-high energy cosmic rays is an important issue inastroparticle physics research, and additional experimental results arerequired for further progress. Here we investigate what can be learned from thestatistical correlation factor r between the depth of shower maximum and themuon shower size, when these observables are measured simultaneously for a setof air showers. The correlation factor r contains the lowest-order moment of atwo-dimensional distribution taking both observables into account, and it isindependent of systematic uncertainties of the absolute scales of the twoobservables. We find that, assuming realistic measurement uncertainties, thevalue of r can provide a measure of the spread of masses in the primary beam.Particularly, one can differentiate between a well-mixed composition (i.e., abeam that contains large fractions of both light and heavy primaries) and arelatively pure composition (i.e., a beam that contains species all of asimilar mass). The number of events required for a statistically significantdifferentiation is ~ 200. This differentiation, though diluted, is maintainedto a significant extent in the presence of uncertainties in the phenomenologyof high energy hadronic interactions. Testing whether the beam is pure orwell-mixed is well motivated by recent measurements of the depth of showermaximum.

Sensitivity of the correlation between the depth of shower maximum and the muon shower size to the cosmic ray composition