Abstract
We present a detailed study of the dynamics associated with the ghost sector of quenched QCD in the Landau gauge, where the relevant dynamical equations are supplemented with key inputs originating from large-volume lattice simulations. In particular, we solve the coupled system of Schwinger-Dyson equations that governs the evolution of the ghost dressing function and the ghost-gluon vertex, using as input for the gluon propagator lattice data that have been cured from volume and discretization artifacts. In addition, we explore the soft gluon limit of the same system, employing recent lattice data for the three-gluon vertex that enters in one of the diagrams defining the Schwinger-Dyson equation of the ghost-gluon vertex. The results obtained from the numerical treatment of these equations are in excellent agreement with lattice data for the ghost dressing function, once the latter have undergone the appropriate scale-setting and artifact elimination refinements. Moreover, the coincidence observed between the ghost-gluon vertex in general kinematics and in the soft gluon limit reveals an outstanding consistency of physical concepts and computational schemes.
Highlights
INTRODUCTIONIn the ongoing quest for unraveling the nonperturbative structure of QCD, considerable effort has been dedicated to the study of Green’s (correlation) functions by means of both continuous methods [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] and large-volume lattice simulations [31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46]
We present a detailed study of the dynamics associated with the ghost sector of quenched QCD in the Landau gauge, where the relevant dynamical equations are supplemented with key inputs originating from large-volume lattice simulations
We solve the coupled system of Schwinger-Dyson equations that governs the evolution of the ghost dressing function and the ghost-gluon vertex, using as input for the gluon propagator lattice data that have been cured from volume and discretization artifacts
Summary
In the ongoing quest for unraveling the nonperturbative structure of QCD, considerable effort has been dedicated to the study of Green’s (correlation) functions by means of both continuous methods [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] and large-volume lattice simulations [31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46]. The step is to implement the soft gluon limit (q → 0) directly at the level of the SDE for B1ðr; p; qÞ, which is converted to a dynamical equation for B1ðr; −r; 0Þ By virtue of this operation, the three-gluon vertex nested in one of the defining Feynman diagrams is projected naturally to its soft gluon limit, allowing us to replace it precisely by the function Lsgðr2Þ obtained from the lattice analysis of [98], without having to resort to any Ansätze or simplifying assumptions. The resulting B1ðr; −r; 0Þ is compared with the corresponding “slice” obtained from the full kinematic analysis of B1ðr; p; qÞ mentioned above, revealing excellent coincidence This coincidence, in turn, is indicative of an underlying consonance between elements originating from inherently distinct computational frameworks, such as the lattice and the SDEs. The article is organized as follows. In the Appendix A we present useful relations between the Taylor and soft gluon renormalization schemes, while in Appendix B we discuss the treatment of finite cutoff effects and lattice scale setting
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