Abstract
It is a long-standing question whether the confinement of matter fields in QCD has an imprint in the (gauge-dependent) correlation functions, especially the propagators. As the analytic structure plays an important role in this question, high-precision data is necessary for lattice investigations. Also, it is interesting how this depends on the dimensionality of the theory. To make a study over a wide range of parameters possible this suggests to use scalar particles. This is done here: The propagator of a fundamental scalar is studied in two, three, and four dimensions in quenched SU(2) Yang–Mills theory in minimal Landau gauge, both in momentum space and position space. Particular emphasis is put on the effects of renormalization. The results suggest a quite intricate volume dependence and the presence of an intrinsic mass scale, but no obvious connection to confinement.
Highlights
The confinement of matter particles in QCD is a very longstanding problem [1]
The results suggest a quite intricate volume dependence and the presence of an intrinsic mass scale, but no obvious connection to confinement
To understand whether the mass scale, as well as the other properties of the effective mass, are something which could be interpreted as a feature of physics, it is necessary to understand the dependence on the necessary renormalization
Summary
The confinement of matter particles in QCD is a very longstanding problem [1]. In particular, the question is whether the properties of the propagator describing the elementary particles, both gluons and matter, show signs of confinement1 [2–8]. Whether their analytical structure changes may give a hint as to how geometrical and dynamical confinement differ This requires one to study the propagator in the quenched case, where the Wilson potential is indefinitely rising in higher dimensions. All of this suggests to study the propagator of scalar matter in the quenched case to obtain further insights on the analytical structure, including the dependence on dimensionality. Having obtained the renormalized propagator, usage of the Schwinger function [3,12] should provide information on the analytic structure Besides these fundamental issues, the quenched calculation provides an excellent testbed to study the lattice artifacts and renormalization properties of the scalar propagator beyond perturbation theory, which is helpful in studies of the dynamical case [18,19,24].
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