Event-by-Event Study of Space-Time Dynamics in Flux-Tube Fragmentation

In the semi-classical description of the flux-tube fragmentation process for hadron production and hadronization in high-energy $e^+e^-$ annihilations and $pp$ collisions, the rapidity-space-time ordering and the local conservation laws of charge, flavor, and momentum provide a set of powerful tools that may allow the reconstruction of the space-time dynamics of quarks and mesons in exclusive measurements of produced hadrons, on an event-by-event basis. We propose procedures to reconstruct the space-time dynamics from event-by-event exclusive hadron data to exhibit explicitly the ordered chain of hadrons produced in a flux tube fragmentation. As a supplementary tool, we infer the average space-time coordinates of the $q$-$\bar q$ pair production vertices from the $\pi^-$ rapidity distribution data obtained by the NA61/SHINE Collaboration in $pp$ collisions at $\sqrt{s}$ = 6.3 to 17.3 GeV.