arXiv subjects

Giorgio Comitini

Publications and source records attributed to Giorgio Comitini.

17 recordsLinked to original sources

arXiv2026

The analytic structure of the QCD propagators, confinement, and deconfinement

We present the first complete calculation of the analytic structure of the zero-spatial-momentum finite-temperature Landau-gauge gluon propagator carried out at one loop by a massive deformation of QCD perturbation theory -- the screened massive expansion -- at temperatures ranging from $T=0$ to $T\approx 3T_{c}$. We find no signatures of deconfinement in the form of meaningful changes in said structure. We argue that, beyond Euclidean space, massive perturbative methods -- including the Curci-Ferrari model -- might be missing crucial dynamical information as a consequence of the perturbative violation of QCD's Ward identities.

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arXiv2026

Nonperturbative Higgs-Schwinger mechanism at the origin of the gluon mass and color confinement

Evidence from lattice and continuum studies supports the existence of a fully nonperturbative Higgs mechanism generating mass for gluons in linear covariant gauges. The broken charge is the Kugo-Ojima charge. The corresponding unphysical Goldstone boson is a bound-state superposition of two gluons, three gluons, a ghost-antighost, and a quark-antiquark pair. Mass generation occurs via the Schwinger mechanism, triggered by the formation of the Goldstone boson. Once corrected for symmetry breaking, the color charge operator is unbroken and confining.

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arXiv2025

One-loop analytic structure of the deep-infrared Landau-gauge gluon propagator at finite temperature

With the aim of looking for signatures of deconfinement, the poles and the spectral function of the Landau-gauge gluon propagator are investigated at one loop, vanishing spatial momentum and finite temperature within the framework of the screened massive expansion of pure Yang-Mills theory and of full QCD. When computed using both temperature-independent parameters optimized by principles of gauge invariance and temperature-dependent parameters obtained by fitting lattice data at zero Matsubara frequency, the propagator is found to have a pair of complex-conjugate poles in its squared complexified frequency variable throughout the considered temperature interval, ranging from $T=0$ to temperatures $T>T_{c}$ of interest to quark-gluon plasma phenomenology. The spectral function is found to violate positivity and not to develop sharp peaks over said temperature interval. In full QCD, a simple model is used for mass generation in the infrared quark sector; the dependence of our results on the quark masses is discussed.

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arXiv2025

Topological Susceptibility in the Superconductive Phases of Quantum Chromodynamics: a Dyson-Schwinger Perspective

We test non-perturbative gluon propagators recently studied in the literature, by computing the topological susceptibility, $\chi$, of the superconductive phases of Quantum Chromodynamics at high density. We formulate the problem within the High-Density Effective Theory, and use the 2-particle irreducible formalism to compute the effective potential of the dense phases. We focus on superconductive phases with two and three massless flavors. Within this formalism, we write a Dyson-Schwinger equation in the rainbow approximation for the anomalous part of the quark propagator in the superconductive phases, in which the non-perturbative gluon propagator plays its role. We complete the model by adding a $U(1)_A$-breaking term whose coupling is fixed perturbatively at large quark chemical potential. We then use the effective potential to compute $\chi$ in the superconductive phases. We finally discuss implications of the results for the axion mass in superdense phases of Quantum Chromodynamics.

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arXiv2024

QCD phase diagram from the gluon propagator at finite temperature and density

The screened massive expansion of full QCD is used in conjunction with a model for infrared quark masses to compute the Landau-gauge gluon propagator at finite temperature and baryonic density. Analytic expressions up to a one-dimensional momentum integral are provided for the propagator, and its behavior is studied at zero Matsubara frequency with respect to temperature, chemical potential, and the parameters of the expansion. The phase diagram of QCD is explored under the assumption that the deconfinement temperature can be identified as the position of the maximum of the longitudinal gluon propagator at zero Matsubara frequency and fixed spatial momentum.

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arXiv2023

Dynamically massive linear covariant gauges: setup and first results

We discuss the possibility to obtain a massive Landau gauge, based on the local composite operator (LCO) effective action framework combined with the Zimmerman reduction of couplings prescription. As a way to deal with the gauge ambiguity, we check that the ghost propagator remains positive, a necessary condition for gluon field configurations beyond the Gribov region to be negligible. We pay attention to the BRST invariance of the construction, allowing for a future generalization to a class of massive linear covariant gauges. As a litmus test, we compare our predictions to the lattice data for the two-point functions in Landau gauge introducing the "Dynamically Infrared-Safe" renormalization scheme, including the renormalization group optimization of both the gap equation and the two-point functions. We also discuss the relation to and differences with the Curci-Ferrari model, the usefulness of which in providing an effective perturbative description of non-perturbative Yang-Mills theories became clear during recent years.

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arXiv2023

Perturbative methods in non-perturbative Quantum Chromodynamics

The objective of this thesis is to present two new perturbative frameworks for the study of low-energy Quantum Chromodynamics (QCD), termed the Screened Massive Expansion and the Dynamical Model. Both the frameworks paint a picture of the infrared regime of QCD which is consistent with the current knowledge provided by the lattice calculations and by other non-perturbative methods, displaying dynamical mass generation in the gluon sector and a massless ghost propagator. The Screened Massive Expansion achieves this by operating a shift of the QCD perturbative series, performed by adding a mass term for the transverse gluons in the kinetic part of the Faddeev-Popov Lagrangian and subtracting it back from its interaction part so that the total action remains unchanged. The Dynamical Model, on the other hand, interprets the generation of a dynamical mass for the gluons as being triggered by a non-vanishing condensate of the form $\langle (A^{h})^{2}\rangle$, where $A^{h}$ is a gauge- and BRST-invariant non-local version of the gluon field, and explores the consequences of the inclusion of the former in the partition function of the theory. Since the main focus of this thesis is on the gauge sector of QCD, most of our calculations will be carried out in the context of pure Yang-Mills theory. There we will show that the gluon and the ghost propagator derived by making use of the two frameworks are in good agreement with the Euclidean Landau-gauge lattice data, within the limits of a one-loop approximation. During the course of the thesis we will address topics such as the first-principles status of the two methods, the absence of Landau poles from the strong running coupling constant and the extension of the Screened Massive Expansion to finite temperatures and to full QCD. Future research prospects are discussed in the Conclusions.

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arXiv2023

Lifetime and confinement of a quasi-gluon

The existence of genuine complex conjugated poles in the gluon propagator is discussed and related to confinement, string tension and condensates. The existence of the anomalous poles leads to an untrivial analytic continuation from Euclidean to Minkowski space, where the pole part of the propagator is related to the spectrum of excited quasigluons.

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arXiv2022

Analytic continuation and physical content of the gluon propagator

The analytic continuation of the gluon propagator is revised in the light of recent findings on the possible existence of complex conjugated poles. The contribution of the anomalous pole must be added when Wick rotating, leading to an effective Minkowskian propagator which is not given by the trivial analytic continuation of the Euclidean function. The effective propagator has an integral representation in terms of a spectral function which is naturally related to a set of elementary (complex) eigenvalues of the Hamiltonian, thus generalizing the usual K\"allen-Lehmann description. A simple toy model shows how the elementary eigenvalues might be related to actual physical quasiparticles of the non-perturbative vacuum.

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arXiv2022

The Nielsen identities in screened theories

One-loop explicit expressions are derived for the gluon Nielsen identity in the formalism of the screened massive expansion for Yang-Mills theory. The gauge-parameter-independence of the poles and residues is discussed in a strict perturbative context and, more generally, in extended resummation schemes. No exact formal proof was reached by the approximate resummation schemes, but some evidence is gathered in favor of an exact invariance of the phase, consistently with previous numerical studies.

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arXiv2021

Screened massive expansion of the quark propagator in the Landau gauge

The infrared behavior of the quark propagator is studied at one loop and in the Landau gauge ($\xi=0$) using the screened massive expansion of full QCD and three different resummation schemes for the quark self-energy. The shift of the expansion point of perturbation theory, which defines the screened expansion, together with a non-standard renormalization of the bare parameters, proves sufficient to describe the dynamical generation of an infrared quark mass also in the chiral limit. Analytically, the scale for such a mass is set by a mass parameter $M$, whose value is fixed by a fit to the lattice data for quenched QCD. The quark mass function $\mathcal{M}(p^{2})$ is shown to be in very good agreement with the lattice results. The quark $Z$-function, on the other hand, shows the wrong qualitative behavior in all but one of the studied resummation schemes, where its behavior is qualitatively correct, but only at sufficiently high energies.

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arXiv2021

Thermal extension of the screened massive expansion in the Landau gauge

The massive screened expansion for pure SU(3) Yang-Mills theory is extended to finite temperature in the Landau gauge. All thermal integrals are evaluated analytically up to an external one-dimensional integration, yielding explicit integral representations of analytic functions which can be continued to the whole complex plane. The gluon propagator is first explored in the Euclidean space by making use of parameters obtained from first principles, which were already found to accurately reproduce the lattice data at zero temperature. Within such a scheme, the agreement with the lattice at $T\neq 0$ turns out to be only qualitative. The description improves provided that the parameters are tuned in a temperature-dependent way by a fit to the data, carried out separately for each component of the propagator; in particular, the transverse component closely follows the lattice data, while the agreement of the longitudinal component with the data is poor at small momenta and moderately high temperatures. The dispersion relations of the quasi-gluon are then extracted from the pole trajectory in the complex plane using the fitted parameters. A crossover is found for the mass, suppressed by temperature like an order parameter in the confined phase, while increasing like an ordinary thermal mass in the deconfined phase.

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arXiv2020

One-loop RG improvement of the screened massive expansion in the Landau gauge

The RG improvement of the screened massive expansion is studied at one loop in two renormalization schemes, the momentum subtraction (MOM) scheme and the screened momentum subtraction (SMOM) scheme. The respective Taylor-scheme running couplings are shown not to develop a Landau pole, provided that the initial value of the coupling is sufficiently small. The improved ghost and gluon propagators are found to behave as expected, displaying dynamical mass generation for the gluons and the standard UV limit of ordinary perturbation theory. In the MOM scheme, when optimized by a matching with the fixed-coupling framework, the approach proves to be a powerful method for obtaining propagators which are in excellent agreement with the lattice data already at one loop. After optimization, the gluon mass parameter is left as the only free parameter of the theory and is shown to play the same role of the ordinary perturbative QCD scale $Λ_{\text{QCD}}$.

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arXiv2019

Perturbation theory of non-perturbative Yang-Mills theory: a massive expansion from first principles

The main objective of this thesis is to present a new analytical framework for low-energy QCD that goes under the name of massive, or "screened", perturbative expansion. The massive perturbative expansion is motivated by the phenomenon of dynamical mass generation, by which the gluons acquire a mass of the order of the QCD scale $Λ_{\text{QCD}}$ in the limit of vanishing momentum. It is a simple extension of ordinary perturbation theory that consists in a shift of the expansion point of the Yang-Mills perturbative series with the aim of treating the transverse gluons as massive already at tree-level, while leaving the total action of the theory unchanged. The new framework will be formulated in the context of pure Yang-Mills theory, where the lattice data is readily available for comparison and the perturbative results have been perfected by enforcing the gauge invariance of the analytical structure of the gluon propagator.

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arXiv2019

The gluon propagator in linear covariant $R_ξ$ gauges

Explicit analytical expressions are derived for the gluon propagator in a generic linear covariant $R_ξ$ gauge, by a screened massive expansion for the exact Faddeev-Popov Lagrangian of pure Yang-Mills theory. At one-loop, if the gauge invariance of the pole structure is enforced, the gluon dressing function is entirely and uniquely determined, without any free parameter or external input. The gluon propagator is found finite in the IR for any $ξ$, with a slight decrease of its limit value when going from the Landau gauge ($ξ=0$) towards the Feynman gauge ($ξ=1$). An excellent agreement is found with the lattice in the range $0<ξ<0.5$ where the data are available.

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arXiv2018

Mass generation and deconfinement in pure Yang-Mills theory: a variational study

A simple variational argument based on the Gaussian Effective Potential (GEP) is put forward to give evidence for mass generation and deconfinement in pure Yang-Mills SU(N) theory. The GEP analysis shows that the massless gaussian vacuum of Yang-Mills theory is perturbatively unstable towards a massive gaussian vacuum, indicating that a massive expansion is the natural choice for computations in YMT. At finite temperature, the GEP provides an optimal temperature-dependent mass parameter for the expansion and signals the occurrence of a weakly first-order phase transition at $T_{c}\approx$ 255 MeV for $N=3$. The equation of state is found to be in good agreement with the lattice data. This work is complemented with review material on the standard and massive expansions of Yang-Mills theory and on the formalism of quantum field theory at finite temperature. Comparisons are made with lattice results and numerical tables are provided to support our findings.

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arXiv2018

Variational study of mass generation and deconfinement in Yang-Mills theory

A very simple variational approach to pure SU($N$) Yang-Mills theory is proposed, based on the Gaussian effective potential in a linear covariant gauge. The method provides an analytical variational argument for mass generation. The method can be improved order by order by a perturbative massive expansion around the optimal trial vacuum. At finite temperature, a weak first-order transition is found (at $T_c\approx 250$ MeV for $N=3$) where the mass scale drops discontinuously. Above the transition the optimal mass increases linearly as expected for deconfined bosons. The equation of state is found in good agreement with the lattice data.

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