Dynamically Induced Scalar Quark Confinement

Abstract

We employ a functional approach to investigate the confinement problem in quenched Landau gauge QCD. We demonstrate analytically that a linear rising potential between massive quarks is generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities is driven by the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken. We have thus uncovered a novel mechanism that directly links chiral symmetry breaking with confinement.PACS numbers: 12.38. Aw, 12.38.Lg, 14.70.Dj, 11.30.Rd More than thirty years after the identification of nonAbelian gauge theory as the appropriate framework to describe the strong interactions we still lack a satisfactory understanding of the confinement phenomenon. Isolated particles with nonvanishing colour charges have not been observed in nature. This fact is supposed to be encoded in the infrared structure of QCD. In the quenched theory a gauge invariant signature of confinement is the area law of the Wilson loop at large distances. This behaviour corresponds to a linear rising potential between static colour charges in the fundamental representation of the gauge group. This signature has been unambiguously verified in lattice gauge QCD, see e.g. ref.[1]. However, the dynamical mechanism that generates the Wilson potential is still elusive. Since the underlying long range interaction is provided by gauge dependent objects, this mechanism may have a different appearance in different gauges. In this letter we present such a mechanism for covariant Landau gauge QCD.The idea of 'infrared slavery', i.e. the notion that infrared singularities generate confinement, dates back to the early seventies [2]. Speculations about the infrared behaviour of the running coupling at that time distinguish two cases: (A) the coupling develops an infrared fixed point and (B) the coupling diverges at small or zero momenta. The last possibility has been considered as the driving mechanism for the generation of infrared singularities and quark confinement. Today there is ample evidence from functional approaches that the first possibility is realised in the Yang-Mills sector of Landau gauge QCD: the running coupling freezes out at small momenta [3,4,5,6]. However, this does not imply that the Green's functions of Yang-Mills theory are finite in the infrared: Instead, depending on the number of ghost and gluon legs, many of the one-particle irreducible Green's functions are indeed singular in the limit that all external momenta vanish [6]. In this letter we demonstrate that these singularities also induce a corresponding singularity in the dressed quark-gluon vertex. As a consequence the running coupling defined from this vertex diverges at vanishing renormalization scale, and a linear potential between massive quarks is generated thereby realizing infrared slavery via an infrared singular quark-gluon vertex.Besides confinement the other fundamental property of infrared Q...

Unified description of seagull cancellations and infrared finiteness of gluon propagators

“…Some of the most representative works in this direction include: (i) Focusing only on the form factors of the tensors appearing in the tree-level vertex [first equation in (A2)], and using a power-counting scheme, the authors of [100] found that the infrared limit of the "symmetric configuration" (q 2 = r 2 = p 2 ) shows a divergent power-law behavior of the type (p 2 ) −3κ , where κ = 0.59 is the typical parameter of the so-called "scaling solutions".…”

Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory

“…This structure is certainly useful beyond the present investigation, for example if devising truncation schemes. Implicitly this was already used for enhancing the respective reliability: the coinciding results for the infrared asymptotics from DSE [8,9,10,12] and FRG [11,23,25] are non-trivial as the functional equations are sufficiently different.…”

“…In [12] the self-consistency of (64) for the whole tower of vertex DSEs has been shown. The dominance of ghost loops in the tower of DSEs is equivalent to the dominance of the Faddeev-Popov determinant over the Yang-Mills action, as proposed in [22].…”

“…Although both frameworks constitute an infinite hierarchy of coupled equations, they allow for the extraction of scaling laws for Green functions in the deep infrared [8,9,10,11,12].…”

Consequences of fully dressing quark–gluon vertex function with two-point gluon lines

“…The investigation of the infrared behavior of the ghost and gluon n-point functions of Refs. [17,18] The solutions of the gap equation (7) for the quark propagator amplitudes A(s) and B(s)…”