Do Instantons Like a Colorful Background.pdfVIP

a r X i v : h e p - p h / 0 6 0 8 1 7 1 v 1 1 5 A u g 2 0 0 6 DESY 06-122 HD-THEP 06-17 Do Instantons Like a Colorful Background? Holger Gies1, Joerg Jaeckel2, Jan M. Pawlowski1 and Christof Wetterich1 1Institut fuer Theoretische Physik, Philosophenweg 16, D-69120 Heidelberg, Germany 2Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, D-22607 Hamburg, Germany H.Gies@thphys.uni-heidelberg.de, joerg.jaeckel@desy.de, J.Pawlowski@thphys.uni-heidelberg.de, C.Wetterich@thphys.uni-heidelberg.de Abstract We investigate chiral symmetry breaking and color symmetry breaking in QCD. The ef- fective potential of the corresponding scalar condensates is discussed in the presence of non-perturbative contributions from the semiclassical one-instanton sector. We concen- trate on a color singlet scalar background which can describe chiral condensation, as well as a color octet scalar background which can generate mass for the gluons. Whereas a non-vanishing singlet chiral field is favored by the instantons, we have found no indication for a preference of color octet backgrounds. 1 Introduction Instantons, being pseudo-particles associated with tunneling processes, generate genuine non-perturbative effects in QCD. In the seminal work of ’t Hooft [1] it was realized that they mediate an effective interaction between (light) quarks [1, 2, 3, 4, 5, 6, 7, 8]. This “instanton interaction” is attractive in the color singlet channel; hence, instantons pre- sumably play a role in the mechanism of chiral symmetry breaking [9, 10, 11]. In addition, they also provide for an interaction in color octet channels or in color triplet and sextet “diquark” channels. Mean-field computations based on a point-like instanton interaction have been employed as a central tool for investigations of color superconductivity at high baryon density [12, 13, 14, 15, 16], or for a description the baryon and meson spectrum and interactions in the vacuum in a Higgs picture with spontaneous color symmetry brea