Color separate singlets in $e^+e^-$ annihilation

TL;DR

This paper investigates the formation and hadronization of color singlet gluonic subsystems in $e^+e^-$ annihilation using a simplified color effective Hamiltonian approach, providing a straightforward method to estimate color reconnection effects.

Contribution

It introduces a simplified orthogonalization procedure for color singlet states and assesses the likelihood of separate gluonic subsystem hadronization in $e^+e^-$ collisions.

Findings

Limited possible states when considering $1/N_c^2$ contributions

A simple orthogonalization method for these states

MC study suggests short string configurations are dynamically favored

Abstract

We use the method of color effective Hamiltonian to study the properties of states in which a gluonic subsystem forms a color singlet, and we will study the possibility that such a subsystem hadronizes as a separate unit. A parton system can normally be subdivided into singlet subsystems in many different ways, and one problem arises from the fact that the corresponding states are not orthogonal. We show that if only contributions of order $1/N_c^2$ are included, the problem is greatly simplified. Only a very limited number of states are possible, and we present an orthogonalization procedure for these states. The result is simple and intuitive and could give an estimate of the possibility to produce color separated gluonic subsystems, if no dynamical effects are important. We also study with a simple MC the possibility that configurations which correspond to "short strings" are dynamically favored. The advantage of our approach over more elaborate models is its simplicity, which makes it easier to estimate color reconnection effects in reactions which are more complicated than the relatively simple $e^+e^-$ annihilation.