The Infrared Behaviour of the Pure Yang–Mills Green Functions

Abstract

We study the infrared behaviour of the pure Yang-Mills correlators using relations that are well defined in the non-perturbative domain. These are the Slavnov-Taylor identity for three-gluon vertex and the Schwinger-Dyson equation for ghost propagator in the Landau gauge. We also use several inputs from lattice simulations. We show that lattice data are in serious conflict with a widely spread analytical relation between the gluon and ghost infrared critical exponeessencnts. We conjecture that this is explained by a singular behaviour of the ghost-ghost-gluon vertex function in the infrared. We show that, anyhow, this discrepancy is not due to some lattice artefact since lattice Green functions satisfy the ghost propagator Schwinger-Dyson equation. We also report on a puzzle concerning the infrared gluon propagator: lattice data seem to favor a constant non vanishing zero momentum gluon propagator, while the Slavnov-Taylor identity (complemented with some regularity hypothesis of scalar functions) implies that it should diverge.

Exciting flavored bound states

“…Our motivation is to verify whether a fully consistent, simultaneous numerical solution of the heavy-quark DSE and heavy-light pseudoscalar meson BSE can be obtained with a modern approach to the rainbow-ladder (RL) truncation based on the interaction proposed by Qin et al [41]. This Ansatz produces an infrared behavior of the interaction, commonly described by a "dressing function" G(k 2 ) [32], congruent with the decoupling solution found in DSE and lattice studies of the gluon propagator [7][8][9][10][11][12][13][14][15][16][17]21]. Indeed, the gluon propagator is found to be a bounded and regular function of spacelike momenta with a maximum value at k 2 = 0.…”

Gauge bosons at zero and finite temperature

“…The idea that this quantity could be of interest is supported by the fact that in almost all cases a differing value of (23) also leads to a differing value of the ghost propagator at zero momentum 16 [66,84,106,[114][115][116]. However, without knowledge of all Gribov copies, this cannot be made an exact statement at the current time.…”

Critical end point in the presence of a chiral chemical potential

“…The forces responsible for confinement appear to generate more than 98% of the mass of visible matter [1,2]. This is DCSB, a quantum field theoretical effect that is expressed and explained via, inter alia, the appearance of momentum-dependent massfunctions for quarks [3][4][5][6] and gluons [7][8][9][10][11][12], and helicityflipping terms in quark-gauge-boson vertices [13][14][15][16][17][18], all in the absence of any Higgs-like mechanism.Owing to the complexity of strong interaction theory, attempts are often made to develop insights concerning confinement, DCSB, and the associated phase diagram in …”

“…(12), by observing that QCD is asymptotically free, so highmomentum modes should not materially influence nonperturbative strong interaction phenomena. Indeed, the contact interaction itself can broadly be reconciled with QCD by imagining that the necessary regularization function is a coarse but useful representation of the transition between nonperturbative infrared dynamics, such as gluon mass-generation [7][8][9][10][11][12], and the domain of asymptotic freedom. Adopting this perspective, it seems that internal consistency requires one to use a definition of Ω F which employs the same (or similar) cutoff used in connection with Ω V .…”