Abstract
We present a detailed study of the subtle interplay transpiring at the level of two integral equations that are instrumental for the dynamical generation of a gluon mass in pure Yang-Mills theories. The main novelty is the joint treatment of the Schwinger-Dyson equation governing the infrared behavior of the gluon propagator and of the integral equation that controls the formation of massless bound-state excitations, whose inclusion is instrumental for obtaining massive solutions from the former equation. The self-consistency of the entire approach imposes the requirement of using a single value for the gauge coupling entering in the two key equations; its fulfilment depends crucially on the details of the three-gluon vertex, which contributes to both of them, but with different weight. In particular, the characteristic suppression of this vertex at intermediate and low energies enables the convergence of the iteration procedure to a single gauge coupling, whose value is reasonably close to that extracted from related lattice simulations.
Highlights
The nonperturbative aspects of the gluon propagator, ΔaμνbðqÞ, are considered to be especially relevant for the qualitative and quantitative understanding of a wide range of important physical phenomena, such as confinement, chiral symmetry breaking, and bound-state formation
We present a detailed study of the subtle interplay transpiring at the level of two integral equations that are instrumental for the dynamical generation of a gluon mass in pure Yang-Mills theories
We have carried out an extensive analysis of the interlocked dynamics between the Schwinger-Dyson equations (SDEs) of the gluon propagator Δðq2Þ and a Bethe-Salpeter equations (BSEs) that generates massless bound state poles
Summary
The nonperturbative aspects of the gluon propagator, ΔaμνbðqÞ, are considered to be especially relevant for the qualitative and quantitative understanding of a wide range of important physical phenomena, such as confinement, chiral symmetry breaking, and bound-state formation. An indispensable ingredient is the presence of massless poles of the type 1=q2 in the vertices with one B leg, which enter into the QB gluon self-energy This particular non-analytic terms must contribute nontrivially to the realization of the STIs satisfied by the corresponding fully-dressed vertices. This discrepancy appears to be more than acceptable given the approximations implemented when deriving both the SDE and the BSE, and, in particular, the simplifications applied in the renormalization of the former, and the truncations imposed when constructing the kernel of the latter
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