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The precise and efficient identification of the nature of the primary cosmicrays on an event-by-event basis stands as a fundamental aspiration for anycosmic ray observatory. In particular, the detection and characterization ofgamma ray events are challenged by their occurrence within an overwhelminglygreater flux of charged cosmic rays spanning several orders of magnitude. Theintricacies of distinguishing between cosmic ray compositions and the inherentuncertainties associated with hadronic interactions present formidablechallenges, which, if not properly addressed, can introduce significant sourcesof systematic errors. This work introduces a novel composition discriminantvariable, $P_{tail}^{\alpha}$, which quantifies the number of Water CherenkovDetectors with a signal well above the mean signal observed in WCDs located atan equivalent distance from the shower core, in events with approximately thesame energy at the ground. This new event variable is then shown to be, in thereconstructed energy range $10\,{\rm TeV}$ to $1.6\,{\rm PeV}$, well correlatedwith the total number of muons that hit, in the same event, all the observatorystations located at a distance greater than $200\,{\rm m}$ from the showercore. The two variables should thus have similar efficiencies in the selectionof high-purity gamma event samples and in the determination of the nature ofcharged cosmic ray events.

$P_{tail}^{\alpha}$: a high resolution gamma/hadron and composition discriminant variable for Water-Cherenkov Detector cosmic-ray observatories