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. In particular in the quenched case a fundamental difference could be expected between adjoint and fundamental matter. In a preceding investigation the propagator of a fundamental scalar has been studied, showing no obvious sign of confinement. Here, complementary, the adjoint scalar propagator is investigated over a wide range of parameters in the minimal Landau gauge using lattice gauge theory. This study is performed in two, three, and four dimensions in quenched SU(2) Yang-Mills theory, both in momentum space and position space. No conclusive difference between both cases is found.
Highlights
The confinement1 of matter in QCD is a very longstanding problem [1]
Because of the larger systematic uncertainties, especially with respect to discretization, the interpretation of these quantities is more involved than in the fundamental case. In the latter case [23], the effective masses approached at long times a, more or less, physical behavior, indicating a would-be pole mass of about 200–250 MeV, with indications of positivity violations remaining at short times
As a flat curve would correspond to a physical particle of this mass, the best interpretation of this observation is that at this value of mr the renormalization scheme becomes the closest approximation to a pole scheme
Summary
The confinement of matter in QCD is a very longstanding problem [1]. In particular, it is especially unclear how to read off the confinement of a particle from its elementary correlation functions. The results are compatible with a violation of positivity in fermion propagators This is true for quarks both in the adjoint and the fundamental representation. This did not lead to any qualitative impact [23], and scalar matter behaved in the same way in all dimensions. As in [23], the quenched calculation will help to understand lattice artifacts and renormalization properties of the scalar propagator beyond perturbation theory This is helpful in studies of the dynamical case, which will, e.g., be relevant for studies of many kinds of grand-unified theories on the lattice [14], for which a host of predictions await nonperturbative precision tests [35] after exploratory investigations in the past [36,37]. Some preliminary results have been presented in [20]
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