Abstract
The shower center of gravity is used for studying the interconnection between shower longitudinal profile and hadronic interaction characteristics. The equations for the shower originated by high energy proton in the atmosphere are written and, within certain simplifications, solved for the case of logarithmically decreasing interaction length of hadrons in the air. The obtained expression explicitely splits into center of gravity of the purely electromagnetic cascade at the primary proton energy and modification of that by hadronic cascading and provides transparent view of the way in which hadronic interaction characteristics determine the longitudinal shower development.
Highlights
The shower center of gravity is used for studying the interconnection between shower longitudinal profile and hadronic interaction characteristics
The shower center of gravity is calculated for five generators of hadronic interactions: Sibyll[5], QGSJETII03[6, 7], QGSJETII-04[8, 9], EPOS 1.99[10, 11] and EPOS LHC[12]
Cascade equations for the proton shower center of gravity were solved under the assumptions of Feinman scaling, cascading only two types of hadrons, baryons and pions, neglecting pion decay and logarithmically decreasing proton and pion interaction lengths
Summary
(arXiv:1202.4989): Since long ago, numerous attempts have been undertaken to explicitely connect the air shower longitudinal profile, in particular the shower maximum depth (Xmax ), with hadronic interaction characteristics. Very approximate approaches were tried, from toy models to extensions of the Heitler model for the electromagnetic shower [1] to the hadronic shower [2,3,4] and all these have proven to be of not big quantitative help. A direct way to establish the connection is the use of the cascade theory. A problem is that the shower maximum is an inconvenient quantity for cascade equations. The shift between Xmax and CG is energy and generator dependent, having been successfully solved equations for CG would allow to look in detail into the dynamics of shower longitudinal development, which governs both Xmax and CG, and to see explicitely how interaction characteristics enter that dynamics
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