Gluon Propagator Research Articles

Nonlocal quark scalar condensate from the Dyson–Schwinger equation and the gluon vacuum polarization based on the OPE approach

Operator-product expansion (OPE) can be employed to obtain the lowest-order, nonlocal quark scalar condensate component of gluon vacuum polarization. In particular, the nonlocal quark scalar condensate can be calculated by solving the Dyson–Schwinger equation (DSE) of QCD. Then, field-theoretical aspects of the gluon vacuum polarization and nonperturbative gluon propagator are considered in the Landau gauge. The gluon propagator we obtained is finite in the infrared domain, where the single gluon mass [Formula: see text] can be determined. Our results for the [Formula: see text] ratio range of that from 1.32 to 1.36, which agrees with previous determinations for this ratio. Then, the analytic structure of the gluon propagators from the OPE results is explored. The analysis of the gluon Schwinger function finds clear evidence of the positivity violations in the gluon propagator. In addition, the results of replacing the OPE simplified quark loop with the full quark one-loop are calculated in vacuum to investigate how good the OPE approximation approach is. The results demonstrate that the OPE approach provides a good approximate method to calculate the full light [Formula: see text] quark loop in vacuum. In particular, the OPE approach can well approximate the approach with full quark one-loop in a specific model. Finally, a new method for obtaining the chemical potential dependence of the gluon vacuum polarization and the dressed gluon propagators is developed.

Constituent quark axial current couplings to light vector mesons in the vacuum and with a weak magnetic field

Unusual constituent quark axial current couplings to light vector mesons, $\rho$ and $\omega$, are derived in the vacuum and under weak magnetic field by considering a quark-antiquark interaction mediated by a non perturbative gluon exchange. Similarly, light axial mesons are found to couple anomalously with the constituent quark vector current. These interactions are of the type of the Wess-Zumino-Witten terms, being strongly anisotropic and dependent on the vector (or axial) meson polarization. They also provide axial (vector) form factors for the vector (axial) mesons and are quite small, suppressed nearly by $1/{M^*}^2$ with respect to the vector mesons minimal coupling to the quark vector current. Some three leg meson vertices are also presented: $\pi-\rho-A_1$ and $V_1V_2 A$ (where $V_1,V_2$ are vector mesons and $A$ an axial meson). A vector and axial-vector mesons mixing is identified at non zero magnetic field which however can contribute only in the presence of a third particle or in a medium. Numerical results are presented for different effective gluon propagators.

A novel background field approach to the confinement-deconfinement transition

We propose a novel approach to the confinement-deconfinement transition in Yang-Mills theories in the context of gauge-fixed calculations. The method is based on a background-field generalisation of the Landau gauge (to which it reduces at vanishing temperature) with a given, center-symmetric background. This is to be contrasted with most implementations of background field methods in gauge theories, where one uses a variable, self-consistent background. Our proposal is a bona fide gauge fixing that can easily be implemented on the lattice and in continuum approaches. The resulting gauge-fixed action explicitly exhibits the center symmetry of the nonzero temperature theory that controls the confinement-deconfinement transition. We show that, in that gauge, the electric susceptibility diverges at a second order transition [e.g., in the SU(2) theory], so that the gluon propagator is a clear probe of the transition. We implement our proposal in the perturbative Curci-Ferrari model, known for its successful description of various infrared aspects of Yang-Mills theories, including the confinement-deconfinement transition. Our one-loop calculation confirms our general expectation for the susceptibility while providing transition temperatures in excellent agreement with the SU(2) and SU(3) lattice values. Finally, the Polyakov loops above the transition show a more moderate rise, in contrast to previous implementations of the Curci-Ferrari model using a self-consistent background, and our SU(3) result agrees quite well with the lattice data in the range [0,2T_c][0,2Tc].

Exploiting the scheme dependence of the renormalization group improvement in infrared Yang–Mills theory

Within the refined Gribov–Zwanziger scenario for four-dimensional Yang–Mills theory in the Landau gauge, a gluon mass term is generated from the restriction of the gauge field configurations to the first Gribov region. Tissier and Wschebor have pointed out that adding a gluon mass term to the usual Faddeev–Popov action yields one-loop renormalization group improved gluon and ghost propagators which are in reasonable agreement with the lattice data even in the infrared regime. In this work, we extend their analysis to several alternative renormalization schemes and show how the renormalization scheme dependence can be used to achieve an almost perfect matching to the lattice data for the gluon and ghost propagators.

Position-space gluon propagator from quenched lattice QCD

We report novel lattice QCD results for the position-space gluon propagator in Landau gauge from quenched simulations. Using standard Wilson action, we computed gluon propagator in position space with a detailed treatment of hypercubic errors. Gluon propagator is scrutinized in position-space, discussing on the usefulness of the long-distance behavior of gluon propagator for constraining the gluon spectral function or the deep infrared running of the gluon propagator in momentum-space.

Massive gluons in Curci-Ferrari model for describing infrared QCD

At large energy quarks and gluons behave as free particles and therefore the standard perturbative analysis of QCD gives very good results. However, this is not the situation in the low energy regime of QCD which is generally treated with nonperturbative methods. In spite of this, lattice simulations observe that the expansion parameter is not large in the gluonic sector. In particular, the coupling constant do not reach a Landau pole in the infrared as it is expected by standard perturbation theory. On top of this, lattice simulations find that the gluon propagator behaves as a massive propagator in the infrared. Motivated by these observations we use a model that includes a mass for the gluon (Curci-Ferrari) that can reproduce the same kind of behaviour for the gluon propagator and also a similar expansion parameter as the one found by the lattice. In this proceeding we show some of the results of quenched correlation functions obtained by using that small parameter for computing one and two loops corrections. At the end, we compare them with lattice data obtaining very good results.

Heavy quark dynamics in a strongly magnetized medium

We present a calculation of the heavy quark momentum diffusion coefficients in a strongly magnetized medium, within the Lowest Landau Level (LLL) approximation. In particular, we use the Hard Thermal Loop (HTL) resummed effective gluon propagator, generalized for a hot and magnetized medium. Using this effective HTL gluon propagator along with the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Going beyond the static limit of the heavy quark, we also show numerical results for these coefficients in two special cases where the heavy quark is moving either parallel or perpendicular to the external magnetic field.

Dynamical fermions, centre vortices, and emergent phenomena

The non-trivial ground-state vacuum fields of QCD form the foundation of matter. Here we examine the centre vortices identified within the ground-state fields of lattice QCD. We aim to understand the manner in which dynamical fermions in the QCD vacuum alter the centre-vortex structure. Using modern visualisation techniques, the centre-vortex structure of pure-gauge and dynamical-fermion fields is quantified and compared. We then explore the impact this modified structure has on measures of confinement and dynamical mass generation. The string tension of the static quark potential, positivityviolation in the gluon propagator, and dynamical mass generation in the overlap quark propagator are of particular interest. The impact of dynamical fermions is significant and provides new insights into the role of centre vortices in underpinning both confinement and dynamical chiral symmetry breaking in QCD.

Improving the cold quark-matter pressure via soft interactions at N3LO

The propagation of long-wavelength gluons through a dense QCD medium at high baryon chemical potential μB is qualitatively modified by the effects of screening, arising from scatterings off the high-momentum quarks in the medium. This same screening phenomenon also impacts gluons occurring in loop corrections to the pressure of cold quark matter, leading to contributions from the parametric scale αs1/2μB, starting at next-to-next-to-leading order (N2LO) in the strong coupling constant αs. At next-to-next-to-next-to-leading order (N3LO), interactions between these long-wavelength gluonic modes contribute to the pressure. These interaction corrections have recently been computed in Ref [1, 2], and the inclusion of these interactions slightly improves the convergence of the equation of state of cold quark matter. In these proceedings, we present these results and provide details summarizing how this lengthy calculation was performed.

Deconfinement in pure gauge SU(3) Yang-Mills theory: the ghost propagator

The ghost propagator in Landau gauge is studied at finite temperature below and above Tc using lattice QCD simulations. For high temperatures, we find that the ghost propagator is enhanced, compared to the confined phase. The results suggest that the ghost propagator can be used to identify the phase transition, similarly to the gluon propagator case.

Mass generation in Landau-gauge Yang-Mills theory

A longstanding question in QCD is the origin of the mass gap in the Yang-Mills sector of QCD, i.e., QCD without quarks. In Landau gauge QCD this mass gap, and hence confinement, is encoded in a mass gap of the gluon propagator, which is found both in lattice simulations and with functional approaches. While functional methods are well suited to unravel the mechanism behind the generation of the mass gap, a fully satisfactory answer has not yet been found. In this work we solve the coupled Dyson-Schwinger equations for the ghost propagator, gluon propagator and three-gluon vertex. We corroborate the findings of earlier works, namely that the mass gap generation is tied to the longitudinal projection of the gluon self-energy, which acts as an effective mass term in the equations. Because an explicit mass term is in conflict with gauge invariance, this leaves two possible scenarios: If it is viewed as an artifact, only the scaling solution survives; if it is dynamical, gauge invariance can only be preserved if there are longitudinal massless poles in either of the vertices. We find that there is indeed a massless pole in the ghost-gluon vertex, however in our approximation with the assumption of complete infrared dominance of the ghost this pole is only present for the scaling solution. We also put forward a possible mechanism that may reconcile the scaling solution, with an infrared dominance of the ghost, with the decoupling solutions based on longitudinal poles in the three-gluon vertex as seen in the PT-BFM scheme.

The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking

We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in QCD. To this end, we consider transverse Slavnov-Taylor identities that constrain the transverse quark-gluon vertex and derive its eight associated scalar form factors. The complete vertex can be expressed in terms of the quark’s mass and wave-renormalization functions, the ghost-dressing function, the quark-ghost scattering amplitude and a set of eight form factors. The latter parametrize the hitherto unknown nonlocal tensor structure in the transverse Slavnov-Taylor identity which arises from the Fourier transform of a four-point function involving a Wilson line in coordinate space. We determine the functional form of these eight form factors with the constraints provided by the Bashir-Bermudez vertex and study the effects of this novel vertex on the quark in the Dyson-Schwinger equation using lattice QCD input for the gluon and ghost propagators. We observe significant dynamical chiral symmetry breaking and a mass gap that leads to a constituent mass of the order of 500 MeV for the light quarks. The flavor dependence of the mass and wave-renormalization functions as well as their analytic behavior on the complex momentum plane is studied and as an application we calculate the quark condensate and the pion’s weak decay constant in the chiral limit. Both are in very good agreement with their reference values.

Ghost and Gluon Propagators at Finite Temperatures within a Rainbow Truncation of Dyson–Schwinger Equations

Ghost and Gluon Propagators at Finite Temperatures within a Rainbow Truncation of Dyson–Schwinger Equations

Ghost spectral function from the spectral Dyson-Schwinger equation

We compute the ghost spectral function in Yang-Mills theory by solving the corresponding Dyson-Schwinger equation for a given input gluon spectral function. The results encompass both scaling and decoupling solutions for the gluon propagator input. The resulting ghost spectral function displays a particle peak at vanishing momentum and a negative scattering spectrum, whose infrared and ultraviolet tails are obtained analytically. The ghost dressing function is computed in the entire complex plane, and its salient features are identified and discussed.

Reconstructing propagators of confined particles in the presence of complex singularities

Propagators of confined particles, especially the Landau-gauge gluon propagator, may have complex singularities as suggested by recent numerical works as well as several theoretical models, e.g., motivated by the Gribov problem. In this paper, we study formal aspects of propagators with complex singularities in reconstructing Minkowski propagators starting from Euclidean propagators by the analytic continuation. We derive the following properties rigorously for propagators with arbitrary complex singularities satisfying some boundedness condition. The two-point Schwinger function with complex singularities violates the reflection positivity. In the presence of complex singularities, while the holomorphy in the usual tube is maintained, the reconstructed Wightman function on the Minkowski spacetime becomes a nontempered distribution and violates the positivity condition. On the other hand, the Lorentz symmetry and locality are kept intact under this reconstruction. Finally, we argue that complex singularities can be realized in a state space with an indefinite metric and correspond to confined states. We also discuss consequences of complex singularities in the Becchi-Rouet-Stora-Tyutin formalism. Our results could open up a new way of understanding a confinement mechanism, mainly in the Landau-gauge Yang-Mills theory.

⟨A2⟩ asymmetry and gluon propagators in lattice SU(3) gluodynamics at T≃Tc

We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two $A^2$ gluon condensate as well as the infrared behavior of the gluon propagators at $T\simeq T_c$ in the Landau-gauge $SU(3)$ lattice gauge theory. We find that a very significant correlation of the real part of the Polyakov loop with the asymmetry as well as with the longitudinal propagator makes it possible to determine the critical behavior of these quantities. We obtain the screening masses in different Polyakov-loop sectors and discuss the dependence of chromoelectric and chromomagnetic interactions of static color charges and currents on the choice of the Polyakov-loop sector in the deconfinement phase.

Pion superfluid phase transition at finite isospin chemical potential

The pion superfluidity phase transition at $T-\mu_I$ and $\mu_q-\mu_I$ planes are studied in the framework of Dyson-Schwinger equations. The rainbow truncation and Gaussian effective gluon propagator are employed to calculate pion condensate, $\langle\pi\rangle$, as a function of $\mu_I$ at finite $T$ and $\mu_q$. At $T=(0, 80, 113, 120)$~MeV, the $\langle\pi\rangle$ keeps zero when $\mu_I$ is less than a critical value $\mu_{Ic}(T)$. The $\langle\pi\rangle$ at $T=113$~MeV agrees with the lattice QCD result. At the $T-\mu_I$ plane, the pion superfluid phase appears at low temperature and high isospin chemical potential region. At finite $\mu_q$, $\langle\pi\rangle$ varying with $\mu_I$ almost coincide for $\mu_q<400$~MeV. At $\mu_q-\mu_I$ plane, the pion superfluid phase appears at $\mu_I\gtrsim m_\pi$ when $\mu_q<400$~MeV.

Ghost dynamics in the soft gluon limit

We present a detailed study of the dynamics associated with the ghost sector of quenched QCD in the Landau gauge, where the relevant dynamical equations are supplemented with key inputs originating from large-volume lattice simulations. In particular, we solve the coupled system of Schwinger-Dyson equations that governs the evolution of the ghost dressing function and the ghost-gluon vertex, using as input for the gluon propagator lattice data that have been cured from volume and discretization artifacts. In addition, we explore the soft gluon limit of the same system, employing recent lattice data for the three-gluon vertex that enters in one of the diagrams defining the Schwinger-Dyson equation of the ghost-gluon vertex. The results obtained from the numerical treatment of these equations are in excellent agreement with lattice data for the ghost dressing function, once the latter have undergone the appropriate scale-setting and artifact elimination refinements. Moreover, the coincidence observed between the ghost-gluon vertex in general kinematics and in the soft gluon limit reveals an outstanding consistency of physical concepts and computational schemes.

Locating the critical endpoint of QCD: Mesonic backcoupling effects

We study the effects of pion and sigma meson backcoupling on the chiral order parameters and the QCD phase diagram and determine their effect on the location of the chiral critical endpoint. To this end, we solve a coupled set of truncated Dyson-Schwinger equations for Landau gauge quark and gluon propagators with ${N}_{\mathrm{f}}=2+1$ dynamical quark flavors and explicitly backcoupled mesons. The corresponding meson bound-state properties and the quark-meson Bethe-Salpeter vertices are obtained from their homogeneous Bethe-Salpeter equation. We find chiral-restoration effects of the pion and/or sigma meson backcoupling and observe a (small) shift of the critical endpoint towards smaller chemical potentials. The curvature of the chiral crossover line decreases. Our results indicate that the location of the critical endpoint in the phase diagram is mainly determined by the microscopic degrees of freedom of QCD (in contrast to its critical properties).

Yang-Mills propagators in linear covariant gauges from Nielsen identities

We calculate gluon and ghost propagators in Yang-Mills theory in linear covariant gauges. To that end, we utilize Nielsen identities with Landau gauge propagators and vertices as the starting point. We present and discuss numerical results for the gluon and ghost propagators for values of the gauge parameter $0<\xi \le 5$. Extrapolating the propagators to $\xi \to \infty $ we find the expected qualitative behavior. We provide arguments that our results are quantitatively reliable at least for values $\xi\lesssim 1/2$ of the gauge fixing parameter. It is shown that the correlation functions, and in particular the ghost propagator, change significantly with increasing gauge parameter. In turn, the ghost-gluon running coupling as well as the position of the zero crossing of the Schwinger function of the gluon propagator remain within the uncertainties of our calculation unchanged.