Confinement and dynamical chiral symmetry breaking in a non-perturbative renormalizable quark model

Abstract

Inspired by the construction of the Gribov-Zwanziger action in the Landau gauge, we introduce a quark model exhibiting both confinement and chiral symmetry aspects. An important feature is the incorporation of spontaneous chiral symmetry breaking in a renormalizable fashion. The quark propagator in the condensed vacuum turns out to be of a confining type. Besides a real pole, it exhibits complex conjugate poles. The resulting spectral form is explicitly shown to violate positivity, indicative of its unphysical character. Moreover, the ensuing quark mass function fits well to existing lattice data. To further validate the physical nature of the model, we identify a massless pseudoscalar (i.e. a pion) in the chiral limit and present estimates for the ρ meson mass and decay constant. * david.dudal@kuleuven-kulak.be † msguimaraes@uerj.br ‡ l.palhares@thphys.uni-heidelberg.de § sorella@uerj.br 1 arXiv:1303.7134v4 [hep-ph] 6 Jan 2016 1. We refer to Section 2 for some more details, next to the existing literature [45].

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

“…As far as the refined Gribov-Zwanziger framewrok is concerned, a possible mechanism to take into account matter confinement was proposed in [2,[24][25][26] in the Landau gauge. More precisely, as will be reviewed in Sect.…”

“…The proposal made in [2,[24][25][26] consists in generalizing the introduction of the non-local horizon function to the matter sector, in complete analogy with the gluon sector. Moreover, as in the gluon sector, the non-local matter coupling term can be cast in local form, giving rise to a fully local and renormalizable action.…”

“…Moreover, as in the gluon sector, the non-local matter coupling term can be cast in local form, giving rise to a fully local and renormalizable action. In [2,[24][25][26], this prescription was implemented for scalar fields in the adjoint representation of the gauge group and for spinor fields in the fundamental representation. The whole procedure was carried out in the Landau gauge, for which the refined Gribov-Zwanziger setup was well established, see also [54] and the references therein for the maximal Abelian gauge.…”

Extracting topological information from momentum space propagators

“…For the obtained values of parameters coming from a lattice fit [12,13,15], (M 3 , m 2 , µ), Away from this critical surface, the N 3 jumps. To set the mind, working in unspecified mass units, for (−1, 1, 1) we have N 3 = 0; for (−1.01, 1, 1), N 3 = −1 and for (−0.99, 1, 1),…”

“…Inspired by the power of MST in the classification of the vacuum of quantum field theories, we propose a new topologically invariant object that is not only sensitive to the full analytic structure of fermionic propagators, but that can also be applied to bosonic field propagators. Particularly, we will consider here the case of certain classes of fits to lattice fermion propagators [12][13][14][15] and gluon propagators [16][17][18][19], although the proposed tool can be applied to any relativistic fermionic or bosonic propagator. Hence, the present results give rise to a considerable enhancement of the power, as well as applicability, of MST.…”