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 ($q \bar q$) and nucleon ($ q q q$) 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. \end{abstract}
Highlights
It is necessary to recall that the spectroscopy of hadronic systems has been successfully studied by means of various forms of Quark Models (QMs), partially related to Quantum Chromo-Dynamics (QCD), that can be grouped in the following categories: Bag Models (BMs), see for example references [7,8,9,10,11]; Constituent Quark Models (CQMs), see for example, for charmonium and so-called higher quarkonia, referenes [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]; for baryons, see for example references [32,33,34,35,36,37,38,39,40,41,42,43,44,45,46]; Quark Diquark Models (QDMs), see for example references [47,48,49,50,51,52,53,54,55,56,57,58,59,60,61]
Considering that we work in the framework of the CQM, we disregard, as discussed before, the three gluon interaction that is given by QCD
In order to write the chromo-electric field produced by the color distributions introduced above, we note that the field is always radial; we introduce the charge contained in a sphere of radius x: x
Summary
According to Quantum Chromo-Dynamics (QCD) the chromo-electric and chromo-magnetic fields, brought by the eight gluons, transmit the interaction among the quarks and contribute to the total energy of the hadrons. We recall that those peaks have been interpreted as new resonances given by pentaquark configurations This interpretation has been developed in the framework of the so-called hadro-quarkonium model, defined in this case, as baryo-charmonium model; for an orientation about this model, see references [63,64,65,66,67,68,69,70,71]. The hadro-quarkonium model has been used in Ferretti [76], in another context, to study some hadronic resonances that cannot be described accurately by CQMs as standard ccexcitations In this case, a variety of different theoretical interpretations has been proposed, including (as in the pentaquark case discussed above) kinematical effects related to rescattering. Lattice techniques [2] have been used to determine the quarkonium chromoelectric polarizability matrix elements
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