Dynamical chiral symmetry breaking and confinement with an infrared-vanishing gluon propagator?

Abstract

We study a model Dyson-Schwinger equation for the quark propagator closed using an Ansatz for the gluon propagator of the form D(q) -q2/[(q2)' + b4] and two Ansatze for the quark-gluon vertex: the minimal Ball-Chiu form and the modified form suggested by Curtis and Pennington. Using the quark condensate as an order parameter, we find that there is a critical value of b = b, such that the model does not support dynamical chiral symmetry breaking for b > b,. We discuss and apply a confinement test which suggests that, for all values of b, the quark propagator in the model is not confining. Together these results suggest that this Ansatz for the gluon propagator is inadequate as a model since it does not yield the expected behavior of QCD.

Phase diagram and thermal properties of strong-interaction matter

“…We consider confinement as a violation of reflection positivity by coloured Schwinger functions. This associates it with dynamically-driven changes in the analytic structure of QCD's propagators and vertices [50][51][52][53][54][55] that occur because both gluons and quarks acquire running mass distributions, which are large at infrared momenta. This leads to the emergence of a length-scale ς ≈ 0.5 fm, whose existence and size is evident in all continuum and lQCD studies of dressed-gluons and -quarks: ς characterises the material change in their analytic structure [6,35,56,57].…”

Scale-setting, flavor dependence, and chiral symmetry restoration

“…These advances enabled us to introduce a parametrisation of the running interaction [Eq. (14), Fig. 4], which respects its modelindependent infrared and ultraviolet behaviours, and simultaneously expresses its dependence on the number n f = 2 + N f , N f = 1, .…”

“…∆(k 2 0) = 1/m 2 g , m g 0.5 GeV [1][2][3][4][5][6], which entails that the long-range propagation characteristics of gluons are dramatically affected by their self-interactions. A similar feature is expressed in the dressed-quark propagator [7][8][9]; and, hence, it is now known that the Schwinger functions of both these elementary coloured excitations violate reflection positivity, a sufficient condition for confinement [10][11][12][13][14][15][16][17][18][19][20][21]. A consistent picture is thus beginning to emerge: strong dynamics generates IR cutoffs in QCD so that long-wavelength (λ 2/m g ∼ 1 fm) coloured-modes decouple and their role in hadron physics is superseded by interactions between light-hadrons [22][23][24][25].…”

Hadron properties and Dyson–Schwinger equations

“…i.e., the Schwinger function is positive definite and the mass of the asymptotic, propagating state is given by 3 − lim…”

“…It is plain that no function S(p 2 ) which falls-off faster than 1/p 2 at large spacelike momenta can be expressed in this way. An appreciation of the importance of the axiom associated with reflection positivity has led to the formulation of a confinement test [3]. With a momentum-space Schwinger function, S(p), in hand, the first step is to calculate…”