Chromo-Electric Field Energy in Quark Models

Abstract

We study the contribution of the chromo-electric field to the total energy of the hadrons. We analyze the case of quarks considered as extended sources of the field. Specific forms of the interaction potential of the quarks are obtained. Moreover, the color charge distribution of these sources allows to determine the zero-point energy that is commonly introduced, as a free (independent) parameter, in the total quark model Hamiltonian of the hadronic systems. The ground states of charmonium (qq) and nucleon (qqq) are studied in more detail: their mass is calculated within a relativized dynamical model and the expectation value of the chromo-electric field energy is consistently obtained.

Calculation of the One-loop Box Integral at Finite Temperature and Density

“…The vector interaction is constructed according to the model proposed in work [2]. In that model, the quarks are considered as extended sources of the chromo-electric field.…”

“…Considering the objective of the present work, the contents of Section 2 of [2] can be synthetically rewritten in the following way.…”

“…As shown in [2], the color charge distributions give rise to a positive zeropoint self-energy that will be denoted as Vv in the present work (while the same quantity was defined W self in [2]). It is given by the following relation:…”

“…To this aim, we assume a non-pointlike distribution of their chromo-electric charge. This model has been studied in detail in work [2].…”

“…To avoid repetition, the reader will be directed to the specific parts of works [1] and [2], when necessary. In those works, the reader can also find the references on which the whole study is based.…”