Gluon Sector Research Articles

Pseudoscalar mesons from a PNJL model at zero temperature

We study pseudoscalar π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi $$\\end{document}, K and η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} meson properties, such as masses and couplings, in dense matter at zero temperature. We use a recently proposed phenomenological quark model, known as the PNJL0, which takes into account the confinement/deconfinement phase transition by means of the traced Polyakov loop (Φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varPhi $$\\end{document}) which serves as an order parameter at zero temperature. We consider two different scenarios, namely, symmetric quark matter with equal chemical potentials for all the flavors, and the beta equilibrated matter. In the latter case the hadron-quark phase transition is implemented by a two model approach. For the hadron side we use a relativistic mean-field model with density dependent couplings. We show that Φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varPhi $$\\end{document} induces abrupt changes in the mesons properties with gap sizes regulated by the phenomenological gluonic sector of the model.

Reduction of pseudocritical temperatures of chiral restoration and deconfinement phase transitions in a magnetized PNJL model

We investigate the chiral restoration and deconfinement phase transitions under an external magnetic field in the frame of a Pauli-Villars regularized Polyakov loop extended Nambu-Jona-Lasinio model. A running Polyakov loop scale parameter T0(eB) is introduced to mimic the reaction of the gluon sector to the presence of magnetic fields. It is found that a decreasing T0(eB) with magnetic fields can realize the inverse magnetic catalysis phenomena of chiral condensates of u and d quarks, increase of Polyakov loop, and the reduction of pseudocritical temperatures of chiral restoration and deconfinement phase transitions. Published by the American Physical Society 2024

Effective locality in the pure gluon sector

About 12 years ago, the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of QCD. This non-perturbative phenomenon is dubbed Effective Locality. In a much simpler way than in QCD, the most remarkable and intriguing aspects of Effective Locality are presented here, in the Yang–Mills theory on Minkowski spacetime.

Equation of State of Cold Quark Matter to O(α_{s}^{3}lnα_{s}).

Accurately understanding the equation of state (EOS) of high-density, zero-temperature quark matter plays an essential role in constraining the behavior of dense strongly interacting matter inside the cores of neutron stars. In this Letter, we study the weak-coupling expansion of the EOS of cold quark matter and derive the complete, gauge-invariant contributions from the long-wavelength, dynamically screened gluonic sector at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant α_{s}. This elevates the EOS result to the O(α_{s}^{3}lnα_{s}) level, leaving only one unknown constant from the unscreened sector at N3LO, and places it on par with its high-temperature counterpart from 2003.

Planck formula for the gluon parton distribution in the proton

In this paper, we describe the gluon parton distribution function (PDF) in the proton, deduced by data from the ATLAS and HERA experiments, in the framework of the parton statistical model. The best fit parameters involved in the Planck formula that describes the gluon distribution are consistent with the results obtained from analysis of LHC deep inelastic proton–proton scattering processes. Remarkably, the agreement between the statistical model and the experimental gluon distributions is obtained with the same value of the “temperature” parameter [Formula: see text] found by fitting the valence parton distributions from deep inelastic scattering. This result corroborates the validity of the statistical approach in the gluon sector.

Nambu-Jona-Lasinio model correlation functions from QCD

We treat quantum chromodynamics (QCD) using a set of Dyson-Schwinger equations derived, in differential form, with the Bender-Milton-Savage technique. In this way, we are able to derive the low energy limit that assumes the form of a non-local Nambu-Jona-Lasinio model with all the parameters properly fixed by the QCD Lagrangian and the determination of the mass gap of the gluon sector.

Parametrization of quark and gluon generalized parton distributions in a dynamical framework

We present a parametrization of the chiral even generalized parton distributions, $H$, $E$, $\stackrel{\texttildelow{}}{H}$, $\stackrel{\texttildelow{}}{E}$, for the quark, antiquark, and gluon, in the perturbative QCD (pQCD)-parton framework. Parametric analytic forms are given as a function of two equivalent sets of variables $x$, $\ensuremath{\xi}$, $t$ (symmetric frame) and $X$, $\ensuremath{\zeta}$, $t$ (asymmetric frame), at an initial scale, ${Q}_{o}^{2}$. In the $X>\ensuremath{\zeta}$ region, a convenient and flexible form is obtained as the product of a Regge term $\ensuremath{\propto}{X}^{\ensuremath{-}\ensuremath{\alpha}+{\ensuremath{\alpha}}^{\ensuremath{'}}t}$, describing the low $X$ behavior, times a spectator model-based functional form depending on various mass parameters; the behavior at $X<\ensuremath{\zeta}$ is determined using the generalized parton distributions symmetry and polynomiality properties. The parameters are constrained using data on the flavor separated nucleon electromagnetic elastic form factors, the axial and pseudoscalar nucleon form factors, and the parton distribution functions from both the deep inelastic unpolarized and polarized nucleon structure functions. For the gluon distributions we use, in particular, constraints provided by recent lattice QCD moments calculations. The parametrization's kinematical range of validity is $0.0001\ensuremath{\le}X\ensuremath{\le}\phantom{\rule{0ex}{0ex}}0.85$, $0.01\ensuremath{\le}\ensuremath{\zeta}\ensuremath{\le}0.85$, $0\ensuremath{\le}\ensuremath{-}t\ensuremath{\le}1\text{ }\text{ }{\mathrm{GeV}}^{2}$, $2\ensuremath{\le}{Q}^{2}\ensuremath{\le}100\text{ }\text{ }{\mathrm{GeV}}^{2}$. With the simultaneous description of the quark, antiquark, and gluon sectors, this parametrization represents a first tool enabling a global QCD analysis of deeply virtual exclusive experiments.

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.

Two-loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes

We consider two-loop renormalization of high-dimensional Lorentz scalar operators in the gluonic sector of QCD. These operators appear also in the Higgs effective theory obtained by integrating out the top quark loop in the gluon fusion process. We first discuss the classification of operators and how to construct a good set of basis using both off-shell field theory method and on-shell form factor formalism. To study loop corrections, we apply efficient unitarity-IBP strategy and compute the two-loop minimal form factors of length-3 operators up to dimension sixteen. From the UV divergences of form factor results, we extract the renormalization matrices and analyze the operator mixing behavior in detail. The form factors we compute are also equivalent to Higgs plus three-gluon amplitudes that capture high-order top mass corrections in Higgs EFT. We obtain the analytic finite remainder functions which exhibit several universal transcendentality structures.

Thermodynamical phases in a PNJL model at zero temperature

The confinement/deconfinement transition described the Polyakov–Nambu–Jona–Lasinio (PNJL) model is extended to be operative at zero temperature regime. In this study, the scalar and vector channel interaction strengths of the original PNJL model are modified by introducing a dependence on the traced Polyakov loop. In such a way the effective interactions depend on the quark phase and in turn provides a backreaction of the quarks to the gluonic sector, also at zero temperature. On general grounds from quantum chromodynamics this is an expected feature. The thermodynamics of the extended model (PNJL0) is studied in detail. It presents along with a suitable choice of the Polyakov potential, a first order confined/deconfined quark phase transition even at T=0. We also show that the vector channel plays an important role in order to allow varPhi ne 0 solutions for the PNJL0 model. Furthermore, the sensitivity of the combined quarkyonic and deconfinement phases to the vector interaction strength and the proposed parametrization of the Polyakov-loop potential at T=0 allowed to set a window for the bulk values of the relevant parameters.

What Can We Learn About QCD and Collider Physics from N=4 Super Yang–Mills?

Tremendous ongoing theory efforts are dedicated to developing new methods for quantum chromodynamics (QCD) calculations. Qualitative rather than incremental advances are needed to fully exploit data that are still to be collected at the LHC. The maximally supersymmetric Yang–Mills theory, [Formula: see text] super Yang–Mills (sYM), shares with QCD the gluon sector, which contains the most complicated Feynman graphs but also has many special properties and is believed to be solvable exactly. It is natural to ask what we can learn from advances in [Formula: see text] sYM for addressing difficult problems in QCD. With this in mind, I review several remarkable developments and highlights of recent results in [Formula: see text] sYM. This includes all-order results for certain scattering amplitudes, novel symmetries, surprising geometrical structures of loop integrands, novel tools for the calculation of Feynman integrals, and bootstrap methods. While several insights and tools have already been carried over to QCD and have contributed to state-of-the-art calculations for LHC physics, I argue that there is a host of further fascinating ideas waiting to be explored.

The Electroweak Phase Transition in a Spontaneously Magnetized Plasma

We investigate the electroweak phase transition (EWPT) in the Minimal (One Higgs doublet) Standard Model (SM) with account for the spontaneous generation of magnetic and chromo-magnetic fields. As it is known, in the SM for the mass of a Higgs boson greater than 75 GeV, this phase transition is of the second order. But, according to Sakharov’s conditions for the formation of the baryon asymmetry in the early Universe, it has to be strongly of the first order. In the Two Higgs doublets SM, there is a parametric space, where the first-order phase transition is realized for the realistic Higgs boson mass mH = 125 GeV. On the other hand, in the hot Universe, the spontaneous magnetization of a plasma had happened. The spontaneously generated (chromo) magnetic fields are temperature-dependent. They influence the EWРT. The color chromomagnetic fields B3 and B8 are created spontaneously in the gluon sector of QCD at a temperature T > Td higher the deconfinement temperature Td. The usual magnetic field H has also to be spontaneously generated. For T close to the TEWPT , these magnetic fields could change the kind of the phase transition.

Low-Momentum Pion Enhancement from Schematic Hadronization of a Gluon-Saturated Initial State

We study the particle production in the early stage of the ultrarelativistic heavy-ion collisions. To this end the Boltzmann kinetic equations for gluons and pions with elastic rescattering are considered together with a simple model for the parton-hadron conversion process (hadronisation). It is shown that the overpopulation of the gluon phase space in the initial state leads to an intermediate stage of Bose enhancement in the low-momentum gluon sector which due to the gluon-pion conversion process is then reflected in the final distribution function of pions. This pattern is very similar to the experimental finding of a low-momentum pion enhancement in the ALICE experiment at the CERN Large Hadron Collider (LHC). Relations to the thermal statistical model of hadron production and the phenomenon of thermal and chemical freeze-out are discussed in this context.

Gauge-invariant decomposition of meson energy in two-dimensional QCD

This work is driven by our curiosity towards some basic questions in QCD: how is the energy of a moving hadron partitioned among different gauge-invariant sectors in QCD Hamiltonian? How is the energy of an massless pion separated between quark and gluon sectors, particularly in the soft pion limit? Is it possible to decompose the celebrated Gell-Mann-Oakes-Renner (GOR) relation? To what extent can we justify the quark potential model from the field-theoretical mass decomposition for heavy quarkonium? Due to limitation of contemporary nonperturbative tools, we do not yet know answers to these questions in realistic QCD. In this work, we take the 't Hooft model (two-dimensional QCD in large-$N$ limit) as a prototype model that mimics some essential aspects of the true QCD. We investigate the gauge-invariant energy decomposition of a flavor-neutral meson that can carry an arbitrary momentum (including stationary case), with meson species ranging from massless pion to bottomonium. All the aforementioned questions can be addressed satisfactorily within this model, in particular some unexpected patterns related to pion are discovered for the first time in two-dimensional QCD. We hope that our study can offer some useful clues and stimulation for future investigations on hadron energy decomposition in realistic QCD.

Coupled kinetic equations for fermions and bosons in the relaxation-time approximation

Kinetic equations for quarks and gluons are solved numerically in the relaxation time approximation for the case of one-dimensional boost-invariant geometry. Quarks are massive and described by the Fermi-Dirac statistics, while gluons are massless and obey Bose-Einstein statistics. The conservation laws for the baryon number, energy, and momentum lead to two Landau matching conditions which specify the coupling between the quark and gluon sectors and determine the proper-time dependence of the effective temperature and baryon chemical potential of the system. The numerical results illustrate how a non-equlibrium mixture of quarks and gluons approaches hydrodynamic regime described by the Navier-Stokes equations with appropriate forms of the kinetic coefficients. The shear viscosity of a mixture is the sum of the shear viscosities of quark and gluon components, while the bulk viscosity is given by the formula known for a gas of quarks, however, with the thermodynamic variables characterising the mixture. Thus, we find that massless gluons contribute in a non-trivial way to the bulk viscosity of a mixture, provided quarks are massive. We further observe the hydrodynamization effect which takes place earlier in the shear sector than in the bulk one. The numerical studies of the ratio of the longitudinal and transverse pressures show, to a good approximation, that it depends on the ratio of the relaxation and proper times only. This behaviour is connected with the existence of an attractor solution for conformal systems.

A non-perturbative study of matter field propagators in Euclidean Yang\u2013Mills theory in linear covariant, Curci\u2013Ferrari and maximal Abelian gauges

In this work, we study the propagators of matter fields within the framework of the refined Gribov–Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang–Mills theory. In full analogy with the pure gluon sector of the refined Gribov–Zwanziger action, a non-local long-range term in the inverse of the Faddeev–Popov operator is added in the matter sector. Making use of the recent BRST-invariant formulation of the Gribov–Zwanziger framework achieved in Capri et al. (Phys Rev D 92(4):045039, 2015), (Phys Rev D 94(2):025035, 2016), (Phys Rev D 93(6):065019, 2016), (arXiv:1611.10077 [hep-th]), Pereira et al. (arXiv:1605.09747 [hep-th]),the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci–Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement.

Renormalization functions for Nf=2 and Nf=4 twisted mass fermions

We present results on the renormalization functions of the quark field and fermion bilinears with up to one covariant derivative. For the fermion part of the action we employ the twisted mass formulation with $N_f{=}2$ and $N_f{=}4$ degenerate dynamical quarks, while in the gluon sector we use the Iwasaki improved action. The simulations for $N_f{=}4$ have been performed for pion masses in the range of 390MeV - 760MeV and at three values of the lattice spacing, $a$, corresponding to $\beta{=}1.90,\,1.95,\,2.10$. The $N_f{=}2$ action includes a clover term with $c_{\rm sw}{=}1.57551$ at $\beta{=}2.10$, and three ensembles at different values of $m_\pi$. The evaluation of the renormalization functions is carried out in the RI$'$ scheme using a momentum source. The non-perturbartive evaluation is complemented with a perturbative computation, which is carried out at one-loop level and to all orders in the lattice spacing, $a$. For each renormalization function computed non-perturbatively we subtract the corresponding lattice artifacts to all orders in $a$, so that a large part of the cut-off effects is eliminated. The renormalization functions are converted to the ${\overline{\rm MS}}$ scheme at a reference energy scale of $\mu{=}2$ GeV after taking the chiral limit.

From gluon topology to chiral anomaly: Emergent phenomena in quark-gluon plasma

Heavy-ion collision experiments at RHIC and the LHC have found a new emergent phase of QCD, a strongly coupled quark-gluon plasma (sQGP) that is distinctively different from either the low temperature hadron phase or the very high temperature weakly coupled plasma phase. Highly nontrivial emergent phenomena occur in such sQGP and two examples will be discussed in this contribution: the magnetic component of sQGP that stems from topologically nontrivial configurations in the gluon sector; and the anomalous chiral transport that arises as macroscopic manifestation of microscopic chiral anomaly in the quark sector. For both examples, their important roles in explaining pertinent heavy-ion data will be emphasized.

A Study on the Form Factors of Hadrons

The form factors of the heavy mesons like Bc+ , ηb, B0s, F+, B0 , D, ψ, ϕ, proton and also deuteron are investigated in the framework of the statistical model for low momentum transfer Q in the range 0.01 ≤ Q2 ≤ 0.1 GeV2.It has been observedthat the heavy-light flavour mesonic form factors show a scaling behavior in the aforesaid low Q2 range. The proton form factor also shows almost scaling in the aforesaid range whereas the deuteron form factor shows a clear violation indicating large contribution from sea quarks and gluon sector.

Early quark production and approach to chemical equilibrium

We perform real-time lattice simulations of out-of-equilibrium quark production in non-Abelian gauge theory in 3+1-dimensions. Our simulations include the backreaction of quarks onto the dynamical gluon sector, which is particularly relevant for strongly correlated quarks. We observe fast isotropization and universal behavior of quarks and gluons at weak coupling and establish a quantitative connection to previous pure glue results. In order to understand the strongly correlated regime, we perform simulations for a large number of flavors and compare them to those obtained with two light quark flavors. By doing this we are able to provide estimates of the chemical equilibration time.