arXiv subjects

Joannis Papavassiliou

Publications and source records attributed to Joannis Papavassiliou.

At least 37 records · Page 2Linked to original sources

arXiv2016

Symmetry preserving truncations of the gap and Bethe-Salpeter equations

Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one- and two-body problems, which must be preserved in any veracious treatment of mesons as bound-states. In this connection, one may view the dressed gluon-quark vertex, $Γ_μ^a$, as fundamental. We use a novel representation of $Γ_μ^a$, in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel, $K$, that is symmetry-consistent with a given quark gap equation. A strength of the scheme is its ability to expose and capitalise on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of $H$-diagrams in $K$, which are two-particle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of $Γ_μ^a$ in a Bethe-Salpeter kernel nor expressed as a member of the class of crossed-box diagrams. Thus, there are no general circumstances under which the WGT identities essential for a valid description of mesons can be preserved by a Bethe-Salpeter kernel obtained simply by dressing both gluon-quark vertices in a ladder-like truncation; and, moreover, adding any number of similarly-dressed crossed-box diagrams cannot improve the situation.

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arXiv2014

Bridging a gap between continuum-QCD and ab initio predictions of hadron observables

Within contemporary hadron physics there are two common methods for determining the momentum-dependence of the interaction between quarks: the top-down approach, which works toward an ab initio computation of the interaction via direct analysis of the gauge-sector gap equations; and the bottom-up scheme, which aims to infer the interaction by fitting data within a well-defined truncation of those equations in the matter sector that are relevant to bound-state properties. We unite these two approaches by demonstrating that the renormalisation-group-invariant running-interaction predicted by contemporary analyses of QCD's gauge sector coincides with that required in order to describe ground-state hadron observables using a nonperturbative truncation of QCD's Dyson-Schwinger equations in the matter sector. This bridges a gap that had lain between nonperturbative continuum-QCD and the ab initio prediction of bound-state properties.

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arXiv2014

Gluon propagator with dynamical quarks

We review recent work on the effects of quark loops on the gluon propagator in the Landau gauge, relying mainly on the Schwinger-Dyson equations that describe the two-point sector of QCD. Particularly important in this context is the detailed study of how the standard gluon mass generation mechanism, which is responsible for the infrared finiteness of the quenched gluon propagator, is affected by the inclusions of dynamical quarks. This issue is especially relevant and timely, given the qualitative picture that emerges from recent unquenched lattice simulations. Our results demonstrate clearly that the gluon mass generation persists, and that the corresponding saturation points of the unquenched gluon propagators are progressively suppressed, as the number of quark flavors increases.

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arXiv2013

The effective gluon mass and its dynamical equation

We present the general derivation of the full nonperturbative equation that governs the momentum evolution of the dynamically generated gluon mass, in the Landau gauge. The gluon mass originates from the inclusion of longitudinally coupled vertices containing massless poles of non-perturbative origin, which preserve the form of the fundamental Slavnov-Taylor identities of the theory. The equation is obtained within the PT-BFM formalism, where the corresponding Schwinger-Dyson equation involves a reduced number of fully dressed diagrams. The resulting homogeneous integral equation is solved numerically for the entire range of physical momenta, yielding positive-definite and monotonically decreasing gluon masses, in agreement with a variety of less formal considerations.

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arXiv2011

Infrared properties of the gluon mass equation

The gauge-invariant generation of a dynamical, momentum-dependent gluon mass is intimately connected with the presence of non-perturbative massless poles in the vertices of the theory, which trigger the well-known Schwinger mechanism. In the deep infrared the integral equation that governs this effective gluon mass assumes a particularly simple form, which may be derived following two seemingly different, but ultimately equivalent procedures. In particular, it may be obtained either as a deviation from a special identity that enforces the masslessness of the gluon in the absence of massless poles, or as a direct consequence of the appearance of a non-vanishing bound-state wave function, associated with the details of the actual formation of these massless poles. In this presentation we demonstrate that, due to profound relations between the various ingredients, the two versions of the gluon mass equation are in fact absolutely identical.

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arXiv2011

Schwinger mechanism in QCD

The generation of a momentum-dependent gluon mass proceeds through a sophisticated implementation, at the level of the Schwinger-Dyson equation for the gluon propagator, of the Schwinger mechanism, whose central dynamical ingredient is the nonperturbative formation of longitudinally coupled massless bound-state excitations. In addition to triggering the aforementioned mechanism, these excitations introduce poles in the various off-shell Green's functions of the theory, in such a way as to maintain the Slavnov-Taylor identities intact in the presence of massive gluon propagators, acting effectively as composite Nambu-Goldstone bosons. In this work we focus on the dynamics leading to the actual formation of such bound states. Specifically, we derive and solve numerically an approximate version of the homogeneous Bethe-Salpeter equation governing the wave function of this special bound state. It is found that this integral equation admits physically meaningful non-trivial solutions, indicating that the QCD dynamics produce one of the crucial ingredients required for the gauge-invariant generation of a gluon mass.

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arXiv2011

Gauge invariant Ansatz for a special three-gluon vertex

We construct a general Ansatz for the three-particle vertex describing the interaction of one background and two quantum gluons, by simultaneously solving the Ward and Slavnov-Taylor identities it satisfies. This vertex is known to be essential for the gauge-invariant truncation of the Schwinger-Dyson equations of QCD, based on the pinch technique and the background field method. A key step in this construction is the formal derivation of a set of crucial constraints (shown to be valid to all orders), relating the various form factors of the ghost Green's functions appearing in the aforementioned Slavnov-Taylor identity. When inserted into the Schwinger-Dyson equation for the gluon propagator, this vertex gives rise to a number of highly non-trivial cancellations, which are absolutely indispensable for the self-consistency of the entire approach.

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arXiv2011

A gauge-technique Ansatz for the three gluon vertex of the background field method

The vertex connecting one background gluon with two quantum ones constitutes a central ingredient in the gauge-invariant Schwinger-Dyson equation that determines the non-perturbative dynamics of the gluon propagator. This vertex satisfies a Ward identity with respect to the background gluon, and a Slavnov-Taylor identity with respect to the two quantum gluons. We present a complete Ansatz for this vertex, which satisfies both aforementioned identities. This entire construction depends crucially on a set of constraints relating the various form-factors of the ghost Green's functions appearing in the Slavnov-Taylor identity satisfied by the vertex. The validity of these constraints is demonstrated to all orders.

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arXiv2010

Nonperturbative gluon and ghost propagators in d=3

We study the nonperturbative gluon and ghost propagators in d=3 Yang-Mills, using the Schwinger-Dyson equations of the pinch technique. The use of the Schwinger mechanism leads to the dynamical generation of a gluon mass, which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained are in very good agreement with the results of SU(2) lattice simulations.

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arXiv2009

Gluon masses without seagull divergences

The study of dynamical gluon mass generation at the level of Schwinger-Dyson equation involves a delicate interplay between various field-theoretic mechanisms The underlying local gauge invariance remains intact by resorting to the well-known Schwinger mechanism, which is assumed to be realized by longitudinally coupled bound state poles, produced by the non-perturbative dynamics of the theory. These poles are subsequently included into the Schwinger-Dyson equation of the gluon propagator through the three-gluon vertex, generating a non-vanishing gluon mass, which, however, is expressed in terms of divergent seagull integrals. In this talk we explain how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. The ability to trigger this identity depends, in turn, on the details of the three-gluon vertex employed, and in particular, on the exact way the bound state poles are incorporated. A concrete example of a vertex that triggers the aforementioned identity is constructed, the ensuing cancellation of all seagull divergences is explicitly demonstrated, and a finite gluon mass is obtained. Due to the multitude of conditions that must be simultaneously satisfied, this construction appears to be exclusively realized within the PT-BFM framework. The resulting system of integral equations gives rise to a gluon mass that displays power-law running and an effective charge which, due to the presence of the gluon mass, freezes in the infrared at a finite (non-vanishing) value.

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arXiv2009

Gluon mass generation without seagull divergences

Dynamical gluon mass generation has been traditionally plagued with seagull divergences, and all regularization procedures proposed over the years yield finite but scheme-dependent gluon masses. In this work we show how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. The ability to trigger the aforementioned identity hinges crucially on the particular Ansatz employed for the three-gluon vertex entering into the Schwinger-Dyson equation governing the gluon propagator. The use of the appropriate three-gluon vertex brings about an additional advantage: one obtains two separate (but coupled) integral equations, one for the effective charge and one for the gluon mass. This system of integral equations has a unique solution, which unambiguously determines these two quantities. Most notably, the effective charge freezes in the infrared, and the gluon mass displays power-law running in the ultraviolet, in agreement with earlier considerations.

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arXiv2009

Scrutinizing the Green's functions of QCD: Lattice meets Schwinger-Dyson

The Green's functions of QCD encode important information about the infrared dynamics of the theory. The main non-perturbative tools used to study them are their own equations of motion, known as Schwinger-Dyson equations, and large-volume lattice simulations. We have now reached a point where the interplay between these two methods can be most fruitful. Indeed, the quality of the lattice data is steadily improving, while a recently introduced truncation scheme for the Schwinger-Dyson equations makes their predictions far more reliable. In this talk several of the above points will be reviewed, with particular emphasis on how to enforce the crucial requirement of gauge invariance at the level of the Schwinger-Dyson equations, the detailed mechanism of dynamical gluon mass generation and its implications for the ghost sector, the non-perturbative effective charge of QCD, and the indirect extraction of the Kugo-Ojima function from existing lattice data.

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arXiv2009

Non-perturbative QCD effective charges

Using gluon and ghost propagators obtained from Schwinger-Dyson equations (SDEs), we construct the non-perturbative effective charge of QCD. We employ two different definitions, which, despite their distinct field-theoretic origin, give rise to qualitative comparable results, by virtue of a crucial non-perturbative identity. Most importantly, the QCD charge obtained with either definition freezes in the deep infrared, in agreement with theoretical and phenomenological expectations. The various theoretical ingredients necessary for this construction are reviewed in detail, and some conceptual subtleties are briefly discussed.

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arXiv2007

Gauge-invariant truncation scheme for the Schwinger-Dyson equations of QCD

We present a new truncation scheme for the Schwinger-Dyson equations of QCD that respects gauge invariance at any level of the dressed loop expansion. When applied to the gluon self-energy, it allows for its non-perturbative treatment without compromising the transversality of the solution, even when entire sets of diagrams (most notably the ghost loops) are omitted, or treated perturbatively.

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arXiv2007

Effective gluon mass and infrared fixed point in QCD

We report on a special type of solutions for the gluon propagator of pure QCD, obtained from the corresponding non-linear Schwinger-Dyson equation formulated in the Feynman gauge of the background field method. These solutions reach a finite value in the deep infrared and may be fitted using a massive propagator, with the crucial characteristic that the effective ``mass'' employed depends on the momentum transfer. Specifically, the gluon mass falls off as the inverse square of the momentum, as expected from the operator-product expansion. In addition, one may define a dimensionless quantity, which constitutes the generalization in a non-Abelian context of the universal QED effective charge. This strong effective charge displays asymptotic freedom in the ultraviolet whereas in the low-energy regime it freezes at a finite value, giving rise to an infrared fixed point for QCD.

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arXiv2007

Power-law running of the effective gluon mass

The dynamically generated effective gluon mass is known to depend non-trivially on the momentum, decreasing sufficiently fast in the deep ultraviolet, in order for the renormalizability of QCD to be preserved. General arguments based on the analogy with the constituent quark masses, as well as explicit calculations using the operator-product expansion, suggest that the gluon mass falls off as the inverse square of the momentum, relating it to the gauge-invariant gluon condensate of dimension four. In this article we demonstrate that the power-law running of the effective gluon mass is indeed dynamically realized at the level of the non-perturbative Schwinger-Dyson equation. We study a gauge-invariant non-linear integral equation involving the gluon self-energy, and establish the conditions necessary for the existence of infrared finite solutions, described in terms of a momentum-dependent gluon mass. Assuming a simplified form for the gluon propagator, we derive a secondary integral equation that controls the running of the mass in the deep ultraviolet. Depending on the values chosen for certain parameters entering into the Ansatz for the fully-dressed three-gluon vertex, this latter equation yields either logarithmic solutions, familiar from previous linear studies, or a new type of solutions, displaying power-law running. In addition, it furnishes a non-trivial integral constraint, which restricts significantly (but does not determine fully) the running of the mass in the intermediate and infrared regimes. The numerical analysis presented is in complete agreement with the analytic results obtained, showing clearly the appearance of the two types of momentum-dependence, well-separated in the relevant space of parameters. Open issues and future directions are briefly discussed.

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arXiv2007

Pinch Technique for Schwinger-Dyson equations

In the context of scalar QED we derive the pinch technique self-energies and vertices directly from the Schwinger-Dyson equations. After reviewing the perturbative construction, we discuss in detail the general methodology and the basic field-theoretic ingredients necessary for the completion of this task. The construction requires the simultaneous treatment of the equations governing the scalar self-energy and the fundamental interaction vertices. The resulting non-trivial rearrangement of terms generates dynamically the Schwinger-Dyson equations for the corresponding Green's functions of the background field method. The proof relies on the extensive use of the all-order Ward-identities satisfied by the full vertices of the theory and by the one-particle-irreducible kernels appearing in the usual skeleton expansion. The Ward identities for these latter quantities are derived formally, and several subtleties related to the structure of the multiparticle kernels are addressed. The general strategy for the generalization of the method in a non-Abelian context is briefly outlined, and some of the technical difficulties are discussed.

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arXiv2006

Analyzing dynamical gluon mass generation

We study the necessary conditions for obtaining infrared finite solutions from the Schwinger-Dyson equation governing the dynamics of the gluon propagator. The equation in question is set up in the Feynman gauge of the background field method, thus capturing a number of desirable features. Most notably, and in contradistinction to the standard formulation, the gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. Various subtle field-theoretic issues, such as renormalization group invariance and regularization of quadratic divergences, are briefly addressed. The infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is presented.

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