P o S(Confinement8)174 Infrared Behavior of Three-Point Functions in Landau Gauge Yang-Mills Theory

The three-gluon and ghost-gluon vertices of Landau gauge Yang-Mills theory are investigated in the low momentum regime. Due to ghost dominance in the infrared we can use the known power law behavior for the propagators to determine analytically the complete momentum dependence of the dressing functions. Besides a uniform, i. e. all momenta going to zero, divergence, we find additional singularities, if one momentum alone goes to zero, while the other two remain constant. At these asymmetric points we can extract additional infrared exponents, which cor-roborate previous results and expand the known fixed point solution of Landau gauge Yang-Mills theory, where the uniform infrared exponents for all vertex functions are known. Calculations in two and three dimensions yield qualitatively similar results. We find several dressing functions diverging like (p2)1−2κ, if only the gluon momentum p goes to zero. Of these many are longitudinal and do not contribute to Dyson-Schwinger equations. The divergent transversal parts are additionally suppressed by the corresponding tensor. The longitu-dinal dressing function of the ghost-gluon vertex behaves similarly, when the gluon momentum becomes small compared to the ghost momentum, whereas all its other dressing functions van-ish at the asymmetric points. The uniform momentum dependence of the three-gluon vertex is determined as (p2)−3κ, while the ghost-gluon vertex stays finite in this limit