BRST-driven cancellations and gauge invariant Green's functions

We study a fundamental, all order cancellation operating between graphs of distinct kinematic nature, which allows for the construction of gauge-independent effective self-energies, vertices, and boxes at arbitrary order.Comment: 4 pages, 3 figures. Contributed to QCD 03: High-Energy Physics International Conference in Quantum Chromodynamics, Montpellier, France, 2-9 July 200

The neutrino charge radius in the presence of fermion masses

We show how the crucial gauge cancellations leading to a physical definition of the neutrino charge radius persist in the presence of non-vanishing fermion masses. An explicit one-loop calculation demonstrates that, as happens in the massless case, the pinch technique rearrangement of the Feynman amplitudes, together with the judicious exploitation of a fundamental current relation leads to a completely gauge independent definition of the effective neutrino charge radius. Using the formalism of the Nielsen identities it is further proved that the same cancellation mechanism operates unaltered to all orders in perturbation theory.Comment: 26 pages, 8 figure

Nonperturbative gluon and ghost propagators for d=3 Yang-Mills

We study a manifestly gauge invariant set of Schwinger-Dyson equations to determine the nonperturbative dynamics of the gluon and ghost propagators in $d=3$ Yang-Mills. The use of the well-known Schwinger mechanism, in the Landau gauge, leads to the dynamical generation of a mass for the gauge boson (gluon in $d=3$), which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained from the numerical solution of these nonperturbative equations are in very good agreement with the results of $SU(2)$ lattice simulations.Comment: 25 pages, 8 figure

QCD effective charges from lattice data

We use recent lattice data on the gluon and ghost propagators, as well as the Kugo-Ojima function, in order to extract the non-perturbative behavior of two particular definitions of the QCD effective charge, one based on the pinch technique construction, and one obtained from the standard ghost-gluon vertex. The construction relies crucially on the definition of two dimensionful quantities, which are invariant under the renormalization group, and are built out of very particular combinations of the aforementioned Green's functions. The main non-perturbative feature of both effective charges, encoded in the infrared finiteness of the gluon propagator and ghost dressing function used in their definition, is the freezing at a common finite (non-vanishing) value, in agreement with a plethora of theoretical and phenomenological expectations. We discuss the sizable discrepancy between the freezing values obtained from the present lattice analysis and the corresponding estimates derived from several phenomenological studies, and attribute its origin to the difference in the gauges employed. A particular toy calculation suggests that the modifications induced to the non-perturbative gluon propagator by the gauge choice may indeed account for the observed deviation of the freezing values.Comment: 23 pages, 7 figure

Infrared finite effective charge of QCD

We show that the gauge invariant treatment of the Schwinger-Dyson equations of QCD leads to an infrared finite gluon propagator, signaling the dynamical generation of an effective gluon mass, and a non-enhanced ghost propagator, in qualitative agreement with recent lattice data. The truncation scheme employed is based on the synergy between the pinch technique and the background field method. One of its most powerful features is that the transversality of the gluon self-energy is manifestly preserved, exactly as dictated by the BRST symmetry of the theory. We then explain, for the first time in the literature, how to construct non-perturbatively a renormalization group invariant quantity out of the conventional gluon propagator. This newly constructed quantity serves as the natural starting point for defining a non-perturbative effective charge for QCD, which constitutes, in all respects, the generalization in a non-Abelian context of the universal QED effective charge. This strong effective charge displays asymptotic freedom in the ultraviolet, while in the low-energy regime it freezes at a finite value, giving rise to an infrared fixed point for QCD. Some possible pitfalls related to the extraction of such an effective charge from infrared finite gluon propagators, such as those found on the lattice, are briefly discussed.Comment: Invited talk given at LIGHT CONE 2008 Relativistic Nuclear and Particle Physics, July 7-11 2008 Mulhouse, Franc

The gluon mass generation mechanism: a concise primer

We present a pedagogical overview of the nonperturbative mechanism that endows gluons with a dynamical mass. This analysis is performed based on pure Yang-Mills theories in the Landau gauge, within the theoretical framework that emerges from the combination of the pinch technique with the background field method. In particular, we concentrate on the Schwinger-Dyson equation satisfied by the gluon propagator and examine the necessary conditions for obtaining finite solutions within the infrared region. The role of seagull diagrams receives particular attention, as do the identities that enforce the cancellation of all potential quadratic divergences. We stress the necessity of introducing nonperturbative massless poles in the fully dressed vertices of the theory in order to trigger the Schwinger mechanism, and explain in detail the instrumental role of these poles in maintaining the Becchi-Rouet-Stora-Tyutin symmetry at every step of the mass-generating procedure. The dynamical equation governing the evolution of the gluon mass is derived, and its solutions are determined numerically following implementation of a set of simplifying assumptions. The obtained mass function is positive definite, and exhibits a power law running that is consistent with general arguments based on the operator product expansion in the ultraviolet region. A possible connection between confinement and the presence of an inflection point in the gluon propagator is briefly discussed.Comment: 37 pages, 11 figures. Based on the talk given at the Workshop Dyson-Schwinger equations in modern mathematics and physics, ECT* (Trento) 22-26 September 2014. Review article contribution to the special issue of Frontiers of Physics (Eds. M. Pitschmann and C. D. Roberts

Schwinger mechanism in linear covariant gauges

In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully-dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modelled by means of certain physically motivated Ans\"atze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ans\"atze are compatible with the existence of nontrivial solutions. When such Ans\"atze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic "zero crossing", while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed.Comment: 27 pages, 9 figures; v2: typos corrected, version matching the published on

The QCD Effective Charge to All Orders

Using the pinch technique, we show how to construct the QCD effective charge to all orders.Comment: 4 pages, no figures. Contributed to QCD 02: High-Energy Physics International Conference in Quantum Chromodynamics, Montpellier, France, 2-9 July 200

The effective neutrino charge radius

It is shown that at one-loop order a neutrino charge radius (NCR) may be defined, which is ultraviolet finite, does not depend on the gauge-fixing parameter, nor on properties of the target other than its electric charge. This is accomplished through the systematic decomposition of physical amplitudes into effective self-energies, vertices, and boxes, which separately respect electroweak gauge invariance. In this way the NCR stems solely from an effective proper photon-neutrino one-loop vertex, which satisfies a naive, QED-like Ward identity. The NCR so defined may be extracted from experiment, at least in principle, by expressing a set of experimental electron-neutrino cross-sections in terms of the finite NCR and two additional gauge- and renormalization-group-invariant quantities, corresponding to the electroweak effective charge and mixing angle.Comment: Talk given at EPS2003 - Aachen, Germany, July 2003; 3 pages, no figure

The Pinch Technique to All Orders

The generalization of the pinch technique to all orders in perturbation theory is presented. The effective Green's functions constructed with this procedure are singled out in a unique way through the full exploitation of the underlying Becchi-Rouet-Stora-Tyutin symmetry. A simple all-order correspondence between the pinch technique and the background field method in the Feynman gauge is established.Comment: 10 pages, 4 figures; one reference added, typos corrected; final version to match the pubblished on