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Paulo J. Silva

Publications and source records attributed to Paulo J. Silva.

At least 19 recordsLinked to original sources
arXiv2026

The soft-gluon limit of the Landau gauge ghost-gluon vertex: results for pure Yang-Mills SU(3) theory from lattice simulations

This work reports on the computation of the ghost-gluon vertex for the pure Yang-Mills SU(3) gauge group, using lattice simulations and the Landau gauge. The simulations access only one of the form factors that describes the vertex. The form factor is estimated using large statistical ensembles of gauge configurations, with two different lattice spacings and two different volumes to check for finite size effects. Moreover, the calculation shows the importance of using lattice perturbation theory, instead of its continuum version, to correct for the breaking of rotational symmetry. The measured bare lattice form factors are compatible, within errors, for all the ensembles. The form factor has a maximum at momentum $\sim 1$ GeV, is suppressed in the infrared and is compatible with a constant behaviour at high momenta, in good agreement with the corresponding lattice estimations for the SU(2) gauge group.

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arXiv2025

The four-gluon and ghost-gluon vertices in the Landau gauge from lattice simulations

The computation of the four-gluon and ghost-gluon vertices in the Landau gauge using high statistical lattice ensembles for $32^4$ and $48^4$ volumes is addressed. For the four-gluon vertex, our previous results for the collinear kinematics are updated allowing to get a better coverage of the IR region. Furthermore, the one-particle irreducible ghost-gluon Green function in the soft gluon limit is computed covering, with precision, a large momentum region.

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arXiv2025

The four-gluon vertex from lattice QCD

The four-gluon one-particle irreducible Green function contributes to various quantities with phenomenological relevance. An example where the four-gluon plays a role is the determination of the gluon propagator, a basic building block for QCD, using continuum methods. This four leg Green function is poorly known and we are only starting to grasp its non-perturbative structure. Here, we report on the computation of the one-particle irreducible four-gluon Green function, in the Landau gauge, with lattice simulations. Besides stating the problems associated with the computation, several form factors that characterise this Green function are measured.

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arXiv2024

The center-symmetric Landau gauge meets the lattice

A lattice implementation of the recently introduced center-symmetric Landau gauge is discussed and its predictions confronted with numerical Monte Carlo simulations. It is shown that the link average and the link correlators computed in that gauge are order parameters of the confinement-deconfinement transition at nonzero temperature. Strictly speaking, this requires a specific treatment of the Gribov copies that we discuss in detail. The numerical simulations comply with the theoretical predictions for the link average computed below and above the deconfinement temperature. Our results show that, within appropriately chosen gauges, one can construct local order parameters for center symmetry, as proxies for the non-local Polyakov loop.

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arXiv2024

High statistical computation of the Landau gauge ghost-gluon vertex

The lattice computation of the one-particle irreducible ghost-gluon Green function in the Landau gauge is revisited with a set of large gauge ensembles. The large statistical ensembles enable a precise determination of this Green function over a wide range of momenta, accessing its IR and UV properties with a control on the lattice effects.

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arXiv2024

Four Gluon Vertex from Lattice QCD

A lattice QCD calculation for the four gluon one-particle irreducible Green function in the Landau gauge is discussed. Results for some of the associated form factors are reported for kinematical configurations with a single momentum scale. Our results show that the computation of this Green function requires large statistical ensembles with 10K or larger number of gauge configurations. The simulations considered herein have a clear Monte Carlo signal for momenta up to $\sim 1$ GeV. The form factors show an hierarchy, with the form factor associated with the tree level Feynman rule being dominant and essentially constant for the range of momenta accessed. The remaining form factors seem to increase as the momentum decreases, suggesting that a possible $\log$ divergence may occur. The computed form factors are, at least, in qualitative agreement with the results obtained with continuum approaches to this vertex, when available.

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arXiv2023

Computation of the Kugo-Ojima function from lattice simulations

In addition to its connection with a standard confinement criterion, the Kugo-Ojima function constitutes an indispensable component in a multitude of applications in the gauge sector of QCD. In the present work we report on preliminary results of an ongoing large-volume lattice simulation of this special function. In particular, the volume-dependence of the data is studied in detail, and a comparison with results obtained from Schwinger-Dyson equations is carried out.

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arXiv2023

The four-gluon vertex in Landau gauge

The Landau gauge four-gluon vertex is studied using high statistical lattice simulations for several momentum configurations. Furthermore, the outcome of the lattice QCD simulations is compared with calculations performed with continuum Schwinger-Dyson equations.

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arXiv2023

Deconfinement, Center Symmetry and the Ghost Propagator in Landau Gauge Pure SU(3) Yang-Mills Theory

The temperature dependence of the Landau gauge ghost propagator is investigated in pure SU(3) Yang-Mills theory with lattice QCD simulations. Its behavior around the confined-deconfined phase transition temperature, $T_c \sim 270$ MeV, is investigated. The simulations show that in the deconfined phase, the ghost propagator is enhanced for small momenta, $\lesssim 1$ GeV. Furthermore, the analysis of the spontaneous breaking of center symmetry on the ghost propagator is studied. Similarly as observed for the gluon propagator, the simulations result in a decoupling of the sectors where the phase of the Polyakov loop is either 0 or $\pm 2π/3$ sectors, with the latter remaining indistinguishable. The results point to the possible use of the ghost propagator as an "order parameter" for the confined-deconfined phase transition.

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arXiv2022

Compact QED: the photon propagator, confinement and positivity violation for the pure gauge theory

The lattice Landau gauge photon propagator for the pure gauge theory is revisited using large lattices. For the confined case we show that it has an associated linearly growing potential, it has a mass gap, that is related to the presence of monopoles, and its spectral function violates positivity. In the deconfined phase, our simulations suggest that a free field theory is recovered in the thermodynamic limit.

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arXiv2022

The Schwinger function, confinement and positivity violation in pure gauge QED

The lattice regularized pure gauge compact U(1) theory is an ideal laboratory to explore how confinement is realized as its phase diagram has a confined and a deconfined phase that depends on the value of the coupling constant, i.e. on $β$. Herein, the connection between confinement and positivity violation through the Schwinger function associated with the Landau gauge photon propagator is investigated. The simulations reported show a very clear link between the realization of confinement and positivity violation of the photon Schwinger function and, therefore, of the photon Källén-Lehmann spectral density. Furthermore, a mass scale that characterizes the decay of the Schwinger function for small time separations is computed and used to distinguish the two phases of the theory.

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arXiv2021

Lattice artefacts on the Landau gauge gluon propagator from hypercubic tensor representations

Lattice tensor representations are used to investigate the lattice Landau gauge gluon propagator for the 4-dimensional pure SU(3) Yang-Mills gauge theory. Due to the different symmetry structure of hypercubic lattices compared to the continuum space-time, lattice correlation functions are described by different tensor structures. Therefore, form factors describing lattice correlation functions have, in principle, non-trivial relations with the continuum counterparts. The use of several tensor bases respecting lattice symmetries, and the analysis of its completeness allows to quantify the deviations of the lattice results from the continuum theory, and also estimate the theoretical uncertainty in the propagator. Furthermore, our analysis tests continuum based relations with the lattice data and shows that the lattice Landau gauge gluon propagator is suitably described by a unique form factor, as in the continuum formulation. Additionally, we identified classes of kinematic configurations where these deviations are minimal and the continuum description of lattice tensors is improved.

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arXiv2021

Lattice pure gauge compact QED in the Landau gauge: the photon propagator, the phase structure and the presence of Dirac strings

In this work we investigate the lattice Landau gauge photon propagator together with the average number of Dirac strings in the compact formulation of QED for the pure gauge version of the theory as a function of the coupling constant. Their $β$ dependence show that these two quantities can be used to identify the confinement-deconfinement transition and that the nature of this transition is first order. Our results show that in the confined phase the propagator is always finite, the theory has a mass gap and the number of Dirac strings present in the configuration is two orders of magnitude larger than in the deconfined phase. Furthermore, in the deconfined phase where $ β\ge 1.0125$ the theory becomes massless, there are essentially no Dirac strings and the photon propagator diverges when the limit $p \rightarrow 0^+$ is taken. Our results illustrate the importance of the topological structures in the dynamics of the two phases.

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arXiv2021

Another look at the Landau gauge three-gluon vertex

We revisit the computation of the three-gluon vertex in the Landau gauge using lattice QCD simulations with large physical volumes of $\sim$ (6.5 fm)$^ 4$ and $\sim$ (8 fm)$^ 4$ and large statistical ensembles. For the kinematical configuration analysed, that is described by a unique form factor, an evaluation of the lattice artefacts is also performed. Particular attention is given to the low energy behaviour of vertex and its connection with evidence (or lack of it) of infrared ghost dominance.

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arXiv2021

Confinement/Deconfinement in 4D compact QED on the lattice

It has long been known that there is a phase transition between confined and unconfined phases of compact pure gauge QED on the lattice. In this work we report three manifestations of this phase change as seen in the Landau gauge photon propagator, the static potential, and distribution of Dirac Strings in the gauge fixed configurations. Each of these was calculated with large lattices with volumes: $32^4$, $48^4$ and $96^4$. We show that the confined phase manifests with a Yukawa type propagator with a dynamically generated mass gap, a linearly increasing potential, and a significant concentration of Dirac strings while the unconfined phase appears consistent with the continuum results: a free propagator, a near constant long-distance potential, and a small concentration of Dirac strings trending towards zero. Furthermore, the photon propagator is investigated in detail near the transition between the two phases.

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arXiv2021

Another look at the three-gluon vertex in the minimal Landau gauge

The lattice three-gluon vertex in the Landau gauge is revisited using a large physical volume $\sim(8\textrm{fm})^4$ and a large statistical ensemble. The improved calculation explores the symmetries of the hypercubic lattice to reduce the statistical uncertainties and addresses the evaluation of the lattice artefacts. Special attention is given to the low energy behaviour of the vertex and its relation to ghost dominance.

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arXiv2021

Looking at the analytic structure of Landau gauge propagators

We report on a study of the analytical structure of the Landau gauge gluon, ghost and quark propagators taken from lattice simulations using large physical volumes, to better access the IR region, and large gauge ensembles to reduce the statistical uncertainties. The investigation uses Padé approximants to look at poles and branch cuts for each of the propagators. For the gluon propagator we identify complex conjugate poles and a branch point. For the ghost propagator the procedure identifies a pole at zero momentum and a branch point for Minkowski-like momenta. The quark propagator appears to have a pole for Minkowski-like momenta that is correlated with the pion mass as expected from PCAC.

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