Gribov horizon andi-particles: About a toy model and the construction of physical operators

Abstract

Restricting the functional integral to the Gribov region Ω leads to a deep modification of the behavior of Euclidean Yang-Mills theories in the infrared region. For example, a gluon propagator of the Gribov type, k 2 k 4 +γ 4 , can be viewed as a propagating pair of unphysical modes, called here i-particles, with complex masses ±iγ 2 . From this viewpoint, gluons are unphysical and one can see them as being confined. We introduce a simple toy model describing how a suitable set of composite operators can be constructed out of i-particles whose correlation functions exhibit only real branch cuts, with associated positive spectral density. These composite operators can thus be called physical and are the toy analogy of glueballs in the Gribov-Zwanziger theory.

Analytic structure of QCD propagators in Minkowski space

“…Out of the real axis, in the complex plane, the propagator has two conjugated poles at (Re p 2 , Im p 2 ) ≈ (0.16, ±0.60) GeV 2 , close to the imaginary axis, as predicted by the i-particle scenario [36] emerging from the refined version [42][43][44] of the Gribov-Zwanziger model [45]. It is remarkable that, by a fit of the data, in Ref.…”

“…Important insights also come from physically motivated phenomenological models, providing simplified analytical descriptions that can be easily continued to Minkowski space [35][36][37][38][39][40][41][42]. For instance, the existence of complex poles was predicted by the refined version [42][43][44] of the Gribov-Zwanziger model [45].…”

On the Analytic Structure of Scalar Glueball Operators

“…The algorithm we use here is described in detail in [21], where as an example the analytical results from [12] were reproduced. Let us consider the case of the RGZ propagator fit of [19],…”

“…In the following we will use two different fits for the gluon propagator and calculate the glueball correlator numerically. In simple cases this is also possible analytically, see, e. g. [11,12]. For future applications a numeric procedure is certainly advantageous as it allows, for instance, to use also numerical data as became available only recently [13].…”

Analytical solution for the correlator with Gribov propagators

“…That confinement can be naturally encoded in analytical properties of QCD Green's functions is an old-fashioned conjecture [1][2][3][4][5][6][7][8][9]. Quark and gluon propagators with complex conjugated singularities are long-standing outcomes of many Bethe-Salpeter and Schwinger-Dyson equation (SDEs) studies [10][11][12][13][14][15][16], noting here that considered propagators, either calculated or phenomenologically used, usually exhibit not one but several complex conjugated poles (infinite number of poles with zero measure i.e.…”