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Urko Reinosa

Publications and source records attributed to Urko Reinosa.

At least 19 recordsLinked to original sources
arXiv2026

Deconfinement transition within the Curci-Ferrari model -- Renormalization scale and scheme dependences

We analyze the confinement/deconfinement transition of pure Yang-Mills theories within the framework of the center-symmetric Landau gauge supplemented by a Curci-Ferrari mass term that models the effect of the associated Gribov copies in the infrared. In addition to providing details for earlier one-loop calculations in that framework, we explore how the results depend on the renormalization scale and/or on the renormalization scheme. We find that the predicted values for the transition temperatures of SU($2$) and SU($3$) Yang-Mills theories are similar in both schemes and are little sensitive to the renormalization scale $μ$ over a wide range of values including the standard range $\smash{μ\in[πT,4πT]}$. These values are also close both to those obtained from a minimal sensitivity principle and to those of lattice simulations, especially in the SU($3$) case. These results further confirm the good behavior of perturbative calculations within the Curci-Ferrari model and support the adequacy of the latter as an effective description of Yang-Mills theories in the infrared. We perform a similar analysis for the spinodal temperatures in the SU($3$) case and for the Polyakov loop, the order parameter associated to the breaking of center symmetry.

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arXiv2026

Mesons, baryons and the confinement/deconfinement transition

We identify an observable that could operate as a probe of the quark versus hadron content of a bath of quarks and gluons at finite temperature and chemical potential. To this purpose, we relate the Polyakov and anti-Polyakov loops, which determine how energetically costly it is to bring an external static quark or antiquark probe into the thermal bath, to the ability of that medium to provide favorable conditions for the formation of meson-like or baryon-like configurations that would screen the probes.

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arXiv2026

Interplay between the chiral and deconfinement transitions from a Curci-Ferrari-based Polyakov loop potential

We couple the two-flavor Nambu--Jona-Lasinio model to a gluonic background corresponding to the gauge-field expectation value in the center-symmetric Landau gauge. Low-energy features in this gauge are captured by a center-symmetric extension of the Curci-Ferrari model and provide a good grasp on key aspects of the confinement/deconfinement transition. Within this framework, we can investigate the interplay between the chiral and deconfinement transitions. Compared to other approaches based on multi-parameter Ansätze of the Polyakov loop potential fixed from comparison to finite-temperature lattice data, the modeling of the glue sector in the present set-up depends on only one phenomenological parameter that can be fixed by comparison to lattice data in the vacuum. We detail the structure of the phase diagram, with special emphasis on the finite density axis, and compute thermodynamical observables relevant for applications. We also highlight the properties of the recently introduced net quark number response of the medium as a sensible probe of the phases of QCD, in particular as a tool to disambiguate the nature of certain regions of the phase diagram where the use of the Polyakov loops could lead to misinterpretations. Finally, we critically assess the sensitivity of our results to the various parameters, both in the glue sector and in the chiral sector.

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arXiv2025

SU($N_c$) confinement and color $N_c$-ality

In a recent work, we have argued that the net quark number gained by a bath of quarks and gluons upon bringing an external static quark probe, while being equal to $1$ in the high temperature, deconfined phase, is equal to $0$ or $3$ in the low temperature, confined phase, depending on the value of the quark chemical potential. This establishes a clear-cut connection between the confinement of a medium as probed by order parameters such as the Polyakov loop, and the ability of that same medium to screen the quark probe into states with the same net quark content as mesons or baryons. In this work, we extend these findings to the SU($N_c$) color group, consider color probes in various (fundamental and non-fundamental) representations, and conjecture a rationale of how these results could be recovered from a purely thermodynamic argument that shortcuts the use of the Euclidean functional framework, while emphasizing the role of color $N_c$-ality as a proxy for center symmetry within the Minkowskian framework.

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arXiv2025

Scenario for quark confinement from infrared safe Yang-Mills dynamics

We revisit the non-Abelian dipole problem in the context of a simple semiclassical approach that incorporates some essential features of the infrared sector of Yang-Mills theories in the Landau gauge, in particular, the fact that both the running coupling and the gluon propagator remain finite at infrared scales and that the latter shows positivity violations that reflects the presence of massless modes. We obtain a simple flux tube solution in a controlled approximation scheme, which we compare to the results of lattice simulations.

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arXiv2025

Using net quark number gain to probe the phases of QCD

We discuss an observable that probes the content of a QCD medium at finite temperature and chemical potential, the net quark number gain. It is the response of the thermal bath to a static quark or antiquark probe. While insignificant at high temperatures, it reveals the bath's tendency to form meson-like or baryon-like configurations (depending on the probe and chemical potential) at low temperatures, which would screen the probe's color charge. The net quark number gain also helps explain how a single quark/antiquark can be added to a supposedly confining medium in the first place: the latter provides the missing quarks/antiquarks to form hadron-like states. We sketch the derivation of this general result for temperatures much smaller than the constituent quark masses and discuss possible further applications to study the various features of the QCD phase diagram.

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arXiv2025

Heavy-quark corner of the Columbia plot from the center-symmetric Curci-Ferrari model

We investigate the heavy-quark corner of the Columbia plot using the gluon potential derived from the Curci-Ferrari extension of the Faddeev-Popov gauge fixing in the center-symmetric Landau gauge, as a proxy for the Polyakov loop potential. In line with the observation that Landau gauge couplings are not that large in the case of heavy-quark QCD, we consider a one-loop approximation and test its consistency by using various renormalization schemes while investigating the dependence of our results on the renormalization scale. We find that the main qualitative features of the phase structure in the heavy-quark regime are reproduced. Our results agree quantitatively with those of simulations to $10\%$ accuracy, which is the expected precision of the one-loop calculations in applications of the Curci-Ferrari model to Yang-Mills or heavy-quark QCD theories.

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arXiv2025

The infrared-safe Minkowskian Curci-Ferrari model

We discuss the existence of Landau-pole-free renormalization group trajectories in the Minkowskian version of the Curci-Ferrari model as a function of a running parameter $q^2$ associated to the four-vector $q$ at which renormalization conditions are imposed, and which can take both space-like ($\smash{q^2<0}$) and time-like ($\smash{q^2>0}$) values. We discuss two possible extensions of the infrared-safe scheme defined in Ref. [Phys. Rev. D, 84, 045018, 2011] for the Euclidean version of the model, which coincide with the latter in the space-like region upon identifying $\smash{Q^2\equiv-q^2}$ with the square of the renormalization scale in that reference. The first extension uses real-valued renormalization factors and leads to a flow in the time-like region with a similar structure as the flow in the space-like region (or in the Euclidean model), including a non-trivial fixed point and a family of trajectories bounded at all scales by the value of the coupling at this fixed point. Interestingly, the fixed point in the time-like region has a much smaller value of $λ\equiv g^2N/16π^2$ than the corresponding one in the space-like region, a value closer to the perturbative boundary $\smash{λ=1}$. However, in this real-valued infrared-safe scheme, the flow cannot connect the time-like and space-like regions. Thus, it is not possible to deduce the relevant time-like flow trajectory from the sole knowledge of a space-like flow trajectory. To try to cure this problem, we investigate a second extension of the Euclidean IR-safe scheme, which allows for complex-valued renormalization factors. We discuss under which conditions these schemes can make sense and study their ability to connect space- and time-like flow trajectories. In particular, we investigate to which types of time-like trajectories the perturbative space-like trajectories are mapped onto.

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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

Aspects of confinement within non-Abelian gauge theories

These lectures cover two aspects: first, irrespectively of the particular approach followed to tackle the QCD phase diagram, we introduce some tools that help discussing the confinement/deconfinement transition in the continuum; second, within one particular continuum approach, based on the Curci-Ferrari model, we illustrate the use of these various notions in order the describe to the confinement/deconfinement transition.

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arXiv2024

Three lectures on the Curci-Ferrari model

In these lectures, we review the status of the Curci-Ferrari model as a phenomenological approach to Landau gauge-fixed YM theories in the infrared. More precisely, after discussing some of the general properties of the model, we explain in full detail the evaluation of the one-loop two-point correlators that allowed for a successful comparison to the corresponding Landau-gauge lattice data. We also review the renormalization group flow of the model which controls its fate at high and low momentum scales.

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arXiv2024

Gauge fixing and physical symmetries

We analyze how gauge fixing, which is required by any practical continuum approach to gauge systems, can interfere with the physical symmetries of such systems. In principle, the gauge fixing procedure, which deals with the (unphysical) gauge symmetry, should not interfere with the other (physical) symmetries. In practice, however, there can be an interference which takes two different forms. First, depending on the considered gauge, it might not always be simple or possible to devise approximation schemes that preserve the physical symmetry constraints on (gauge-independent) observables. Second, even at an exact level of discussion, the (gauge-dependent) effective action for the gauge field, and thus the related vertex functions, may not reflect the physical symmetries of the problem. We illustrate these difficulties using a very general class of gauge fixings that contains the usual gauge fixings as particular cases. Using background field techniques, we then propose specific gauge choices that allow one to keep the physical symmetries explicit, both at the level of the observables and at the level of the effective action for the gauge field. Our analysis is based on the notion of invariance modulo gauge transformations. This is not only a convenient framework to discuss symmetries in the presence of unphysical degrees of freedom, but it also allows one to reinterpret certain well known phenomena in gauge theories without the need to invoke the conceptually annoying ``breaking of a gauge symmetry''.

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arXiv2023

Center-symmetric Landau gauge: Further signatures of confinement

In a recent article [1], we have identified new signatures for the Yang-Mills deconfinement transition, based on the finite-temperature longitudinal or (chromo-)electric gluon propagator as computed in the center-symmetric Landau gauge. Here, we generalize these considerations into a systematic study of the center symmetry identities obeyed by the correlation functions in this gauge. Any violation of these constraints signals the breaking of center symmetry and can thus serve as a probe for the deconfinement transition.

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arXiv2022

Small parameters in infrared QCD: The pion decay constant

We continue our investigation of the QCD dynamics in terms of the Curci-Ferrari effective Lagrangian, a deformation of the Faddeev-Popov one in the Landau gauge with a tree-level gluon mass term. In a previous work we have studied the dynamics of chiral symmetry breaking at the level of the quark propagator and, in particular, the dynamical generation of a constituent quark mass. In the present article, we study the associated Goldstone mode, the pion, and we compute the pion decay constant in the chiral limit. Our approach exploits the fact that the coupling (defined in the Taylor scheme) in the pure gauge sector is perturbative, as observed in lattice simulations which, together with a $1/N_c$-expansion, allows for a systematic, controllable approximation scheme in the low energy regime of QCD. At leading order, this leads to the well-known rainbow-ladder resummation. We study the region of parameter space of the model that gives physical values of the pion decay constant. This allows one to constrain the gluon mass parameter as a function of the coupling using a physically measured quantity.

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arXiv2022

Two-loop three-gluon vertex from the Curci-Ferrari model and its leading infrared behavior to all loop orders

We evaluate the three-gluon vertex with one vanishing external momentum within the Curci-Ferrari (CF) model at two-loop order and compare our results to Landau-gauge lattice simulations of the same vertex function for the SU(2) and SU(3) gauge groups in four dimensions. The parameters of the model being adjusted by fitting the two-point functions to lattice data, our evaluation of the three-gluon vertex arises as a pure prediction. We find that two-loop corrections systematically improve the agreement between the model and the lattice data as compared to earlier one-loop calculations, with a better agreement in the SU(3) case, as already seen in previous studies [1,2]. We also analyze the renormalization scheme dependence of our calculation. In all cases, this dependence diminishes when two-loop corrections are included, which is consistent with the perturbative CF paradigm. In addition, we study the low momentum regime of the three-gluon vertex in relation with the possibility of zero-crossing. Within the CF model, we show that the leading infrared behavior of the exact vertex is given by the same linear logarithm that arises at one-loop order, multiplied by the all orders cubic ghost dressing function at zero-momentum (we provide similar exact results for other vertex functions). We argue that this property remains true within the FP framework under the assumption that the resummed gluon propagator features a decoupling behavior. This shows that the zero-crossing is a property of the exact three-gluon vertex function. Within the CF model, we find however that the scale of the zero-crossing is considerably reduced when going from one- to two-loop order. This seems consistent with some recent lattice simulations [3]. Our analysis also allows us to support recent claims about the dominance of the tree-level tensor component [4].

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arXiv2022

Signatures of the Yang-Mills deconfinement transition from the gluon two-point correlator

We evaluate the longitudinal or (chromo-)electric Yang-Mills gluon propagator in the recently proposed center-symmetric Landau gauge at finite temperature [1]. To model the effect of the Gribov copies in the infrared, we use the Curci-Ferrari model which, in turn, allows us to rely on perturbative calculations. At one-loop order in the SU(2) case, the so-obtained longitudinal gluon propagator provides a clear signature for Z2 center-symmetry breaking with a singular behavior, characteristic of a continuous phase transition. This is in sharp contrast with what is found within the standard Landau gauge. We also identify various signatures for Z3 center-symmetry breaking in the SU(3) case in the form of genuine order parameters. Among those, we find that the gluon propagator, although degenerate along the diagonal color directions in the confining phase, becomes non-degenerate in the deconfined phase. Our results open new ways of identifying the transition from correlation functions both within continuum approaches and on the lattice.

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arXiv2021

Two loop calculation of Yang-Mills propagators in the Curci-Ferrari model

The Landau-gauge gluon and ghost correlation functions obtained in lattice simulations can be reproduced qualitatively and, to a certain extent, quantitatively if a gluon mass is added to the standard Faddeev-Popov action. This has been tested extensively at one loop, for the two and three point correlation functions of the gluons, ghosts and quarks. In this article, we push the comparison to two loops for the gluon and ghost propagators. The agreement between lattice results and the perturbative calculation considerably improves. This validates the Curci-Ferrari action as a good phenomenological model for describing the correlation functions of Yang-Mills theory in the Landau gauge. It also indicates that the perturbation theory converges fairly well, in the infrared regime.

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