Chiral symmetry breaking revisited: the gap equation with lattice ingredients

We study chiral symmetry breaking in QCD, using as ingredients in the quark gap equation recent lattice results for the gluon and ghost propagators. The Ansatz employed for the quark-gluon vertex is purely non-Abelian, introducing a crucial dependence on the ghost dressing function and the quark-ghost scattering amplitude. The numerical impact of these quantities is considerable: the need to invoke confinement explicitly is avoided, and the dynamical quark masses generated are of the order of 300 MeV. In addition, the pion decay constant and the quark condensate are computed, and are found to be in good agreement with phenomenology.Comment: 3 pages, 5 figures. Talk presented at the Quark Confinement and the Hadron Spectrum - Madrid 2010, August 30th - September 3rd 2010, Madrid, Spai

New insights on non-perturbative Yang-Mills

In this talk we review some recent results on the infrared properties of the gluon and ghost propagators in pure Yang-Mills theories. These results are obtained from the corresponding Schwinger-Dyson equation formulated in a special truncation scheme, which preserves gauge invariance. The presence of massless poles in the three gluon vertex triggers the generation of a dynamical gluon mass (Schwinger mechanism in d=4), which gives rise to an infrared finite gluon propagator and ghost dressing function. As a byproduct of this analysis we calculate the Kugo-Ojima function, required for the definition of the non-perturbative QCD effective charge within the pinch technique framework. We show that the numerical solutions of these non-perturbative equations are in very good agreement with the results of SU(3) lattice simulations.Comment: Invited talk at XI Hadron Physics, Maresias, S\~ao Paulo, Brazil, 21-26 March, 201

Non-perturbative Green's functions and the QCD effective charge

Using as ingredients the non-perturbative solutions of various QCD Green's function obtained from Schwinger-Dyson equations (SDEs), we study two versions of the QCD effective charge. The first one obtained from the pinch technique gluon self-energy, and the second from the ghost-gluon vertex. Despite the distinct nature of their buildings blocks, the two effectives charges are almost identical in the entire range of momenta, due to a fundamental identity relating the ghost dressing function with the two form factors of Green's function, which is of central importance in the PT-BFM formalism. In this talk, we outline how to derive this crucial identity from the SDEs of the aforementioned Green's functions. The renormalization procedure that preserves the validity of this identity is discussed in detail. Most importantly, we show that due to the infrared finiteness of the gluon propagator, the QCD charge obtained with either definition freezes in the deep infrared, in agreement with theoretical and phenomenological expectations.Comment: 12 pages, 8 figures. Talk presented at the International Workshop on QCD Green's Functions, Confinement, and Phenomenology - QCD-TNT09, September 07 - 11 2009, ECT* Trento, Ital

On dynamical gluon mass generation

The effective gluon propagator constructed with the pinch technique is governed by a Schwinger-Dyson equation with special structure and gauge properties, that can be deduced from the correspondence with the background field method. Most importantly the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions, a property which allows for a meanigfull truncation. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles. The resulting integral equation, subject to a properly regularized constraint, is solved numerically, and the main features of the solutions are briefly discussed.Comment: Special Article - QNP2006: 4th International Conference on Quarks and Nuclear Physics, Madrid, Spain, 5-10 June 200