Gribov-Zwanziger horizon condition, ghost and gluon propagators and Kugo-Ojima confinement criterion - High Energy Physics - TheoryReport as inadecuate




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Abstract: We reexamine the conventional arguments concerned with the scaling anddecoupling solutions for the ghost and gluon propagators in the Landau gaugeYang-Mills theory. We point out a few issues to be clarified, which seems to beoverlooked in the previous investigations in this field, in the fullynon-perturbative treatment. We propose a trick which enables one to incorporatethe Gribov horizon directly into the self-consistent Schwinger-Dyson equationin the gauge-fixed Yang-Mills theory, using the Gribov-Zwanziger framework withthe horizon term. We obtain the following results, irrespective of the choiceof the horizon term. i We find that there exists a family of solutionsparameterized by one-parameter $w R0$ which was assumed to be zeroimplicitly. The family includes both the scaling and decoupling solutions, andspecification of the parameter discriminates between them. ii We observe thatthe inclusion of the horizon term cancels the ultraviolet divergence in theSchwinger-Dyson equation for the ghost propagator and the resultingnon-perturbative self-consistent solution becomes ultraviolet finite. Inother words, the horizon condition interpolates between the infrared behaviorand the ultraviolet one. This leads to the incompatibility of the conventionalmultiplicative renormalization scheme with the Gribov



Author: Kei-Ichi Kondo U. Tokyo-Chiba U.

Source: https://arxiv.org/



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