Renormalization group analysis of the gluon mass equation

Autor(es)

Aguilar, A. C. ^{[1, 2]} ; Binosi, D. ^[3] ; Papavassiliou, J. ^{[4, 5, 6]}

Afiliação do(s) autor(es)

^[1] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP - Brazil

^[2] European Ctr Theoret Studies Nucl Phys & Related, I-38123 Villazzano - Italy

^[3] Fdn Bruno Kessler, I-38123 Villazzano - Italy

^[4] Univ Valencia, Dept Theoret Phys, E-46100 Valencia - Spain

^[5] Univ Valencia, IFIC, E-46100 Valencia - Spain

^[6] CSIC, E-46100 Valencia - Spain

• Tipo de documento: Artigo Científico
• Fonte: Physical Review D; v. 89, n. 8 APR 18 2014.
• Citações Web of Science: 26

Resumo

We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang-Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansatze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called ``power-law{''} running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned. (AU)

• Processo FAPESP: 12/15643-1 - Equações de Schwinger Dyson: uma ferrramenta para a QCD não-perturbativa
• Beneficiário: Arlene Cristina Aguilar
• Modalidade de apoio: Auxílio à Pesquisa - Regular