Two- and three-body color flux tubes in the Chromo Dielectric Model

Abstract

Using the framework of the Chromo Dielectric Model we perform an analysis of color electric flux tubes in meson-like $q\bar{q}$ and baryon-like $qqq$ quark configurations. We discuss the Abelian color structure of the model and point out a symmetry in color space as a remnant of the SU(3) symmetry of QCD. The generic features of the model are discussed by varying the model parameters. We fix these parameters by reproducing the string tension $\tau =980$MeV/fm and the transverse width $\rho =0.35$fm of the $q\bar{q}$ flux tube obtained in lattice calculations. We use a bag constant $B^{1/4}=(240-260)$MeV, a glueball mass $m_g=(1000-1700)$MeV and a strong coupling constant $C_F{\alpha }_s=0.2-0.3$. We show that the asymptotic string profile of an infinitely long flux tube is already reached for $q\bar{q}$ separations $R\ge 1.0$fm. A connection to the Dual Color Superconductor is made by extracting a magnetic current from the model equations and a qualitative agreement between the two descriptions of confinement is shown. In the study of the $qqq$ system we observe a $\mathsf{\Delta }$-like geometry for the color electric fields and a \textsf{Y}-like geometry in the scalar fields both in the energy density distribution and in the corresponding potentials. The resulting total $qqq$ potential is described neither by the $\mathsf{\Delta }$-picture nor by the \textsf{Y}-picture alone.

Comments: 32 pages, 35 eps-figures, revised version, some references + 1 eps-file added, to be published in Phys.Rev.D