Abstract
Due to the nonperturbative masslessness of the ghost field, ghost loops that contribute to gluon Green's functions in the Landau gauge display infrared divergences, akin to those one would encounter in a conventional perturbative treatment. This is in sharp contrast with gluon loops, in which the perturbative divergences are tamed by the dynamical generation of a gluon mass acting as an effective infrared cutoff. In this paper, after reviewing the full nonperturbative origin of this divergence in the two-gluon sector, we discuss its implications for the three- and four-gluon sector, showing in particular that some of the form factors characterizing the corresponding Green's functions are bound to diverge in the infrared.
Highlights
In the past few years, the infrared (IR) behavior of Yang-Mills Green’s functions in the Landau gauge has been the subject of numerous studies both in the continuum and on the lattice
It has been firmly established that the gluon propagator saturates at small momenta in a way consistent with the presence of a dynamically generated gluon mass [6, 7, 8, 9]; the ghost propagator is instead essentially free in the same momentum region: in this case it is the ghost dressing function that saturates to a finite non-vanishing value [10, 11]
It turns out that n-point functions exhibiting an ‘ancestor’ ghost-loop, will develop a logarithmic IR singularity: the contribution of such diagram will correspond to a pure logarithm, log q2/μ2, which is unprotected, in the sense that there is no mass term in its argument that could tame the corresponding divergence in the low momenta region
Summary
In the past few years, the infrared (IR) behavior of Yang-Mills Green’s functions in the Landau gauge has been the subject of numerous studies both in the continuum and on the lattice. It has been firmly established that the gluon propagator saturates at small momenta in a way consistent with the presence of a dynamically generated gluon mass [6, 7, 8, 9]; the ghost propagator is instead essentially free in the same momentum region: in this case it is the ghost dressing function (defined as q2 times the propagator, see below) that saturates to a finite non-vanishing value [10, 11]. The advantage of employing the BQI (2), and considering the BQ self-energy diagrams rather than the QQ ones, resides in the fact that owing to the background Ward identity, all subsets of graphs enclosed within each box of Fig. 1 give rise to a transverse contribution [14, 15, 16] Their individual treatment, or, the total omission of entire subsets from one’s analysis, does not tamper with the transversality of the gluon selfenergy. Where on the right-hand side we assume that one is evaluating only the terms that vanishes as q2 goes to zero (the non vanishing terms contributing instead to the mass equation, see [7, 8])
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