Gluon Confinement Research Articles

Signatures of a High Temperature QCD Transition in the Early Universe.

Beyond-Standard-Model extensions of QCD could result in quark and gluon confinement occurring well above at temperature around the GeV scale. These models can also alter the order of the QCD phase transition. Therefore, the enhanced production of primordial black holes (PBHs) that can accompany the change in relativistic degrees of freedom at the QCD transition could favor the production of PBHs with mass scales smaller than the Standard Model QCD horizon scale. Consequently, and unlike PBHs associated with a standard GeV-scale QCD transition, such PBHs can account for all the dark matter abundance in the unconstrained asteroid-mass window. This links beyond-Standard-Model modifications of QCD physics over a broad range of unexplored temperature regimes (around 10-10^{3} TeV) with microlensing surveys searching for PBHs. Additionally, we discuss implications of these models for gravitational wave experiments. We show that a first-order QCD phase transition at around 7TeV is consistent with the Subaru Hyper-Suprime Cam candidate event, while a transition of around 70GeV is consistent with OGLE candidate events and could also account for the claimed NANOGrav gravitational wave signal.

Geometric Confinement in Gauge Theories

In 1978, Friedberg and Lee introduced the phenomenological soliton bag model of hadrons, generalizing the MIT bag model developed in 1974 shortly after the formulation of QCD. In this model, quarks and gluons are confined due to coupling with a real scalar field ρ, which tends to zero outside some compact region S⊂R3 determined dynamically from the equations of motion. The gauge coupling in the soliton bag model runs as the inverse power of ρ, already at the semiclassical level. We show that this model arises naturally as a consequence of introducing the warped product metric dsM2+ρ2dsG2 on the principal G-bundle P(M,G)≅M×G with a non-Abelian group G over Minkowski space M=R3,1. Confinement of quarks and gluons in a compact domain S⊂R3 is a consequence of the collapse of the bundle manifold M×G to M outside S due to shrinking of the group manifold G to a point. We describe the formation of such regions S as a dynamical process controlled by the order parameter field ρ.

Gluon jets evolution in the quest for new physics

In this paper, our task is to review the evolution of Gluon Jets in view of the quest for physics beyond the Standard Model (SM) – the so called New Physics (NP). One of the major goals of the Large Hadron Collider (LHC) is to understand a new mode of matter called the Quark Gluon Plasma (QGP). This seemingly new form of matter consists of a confinement of quarks and gluons observed at very high temperature and density. This paper focuses on heavy ion collisions in order to get an understanding of the interaction of high momentum partons. It is these highly sophisticated interactions that probe quantum chromodynamics theorem at very high temperatures and densities. This results in the QGP phase of NP via propagation of very energetic Gluon Jets.

Effective potential of the Polyakov loop in the Hamiltonian approach to QCD

We investigate the effective potential of the Polyakov loop, which is the order parameter for the deconfinement phase transition in finite temperature QCD. Our work is based on the Hamiltonian approach in Coulomb gauge where finite temperature $T$ is introduced by compactifying one space direction. We briefly review this approach and extend earlier work in the Yang-Mills sector by including dynamical quarks. In a first approximation, we follow the usual functional approach and include only 1-loop contributions to the energy, with the finite temperature propagators replaced by their $T=0$ counterparts. It is found that this gives a poor description of the phase transition, in particular for the case of full QCD with ${N}_{f}=3$ light flavors. The physical reasons for this unexpected result are discussed, and pinned down to a relative weakness of gluon confinement compared to the deconfining tendency of the quarks. We attempt to overcome this issue by including the relevant gluon contributions from the 2-loop terms to the energy. We find that the 2-loop corrections have indeed a tendency to strengthen the gluon confinement and weaken the unphysical effects in the confining phase, while slightly increasing the (pseudo)critical temperature ${T}^{*}$ at the same time. To fully suppress artifacts in the confining phase, we must tune the parameters to rather large values, increasing the critical temperature to ${T}^{*}\ensuremath{\approx}340\text{ }\text{ }\mathrm{MeV}$ for $G=SU(2)$.

Impact of dynamical fermions on the center vortex gluon propagator

The impact of $SU(3)$ center vortices on the Landau-gauge gluon propagator is calculated in the presence of dynamical fermions and compared to the pure Yang-Mills case. The presence of dynamical fermions is found to alter the behavior of the center vortex propagator when compared to the established pure-gauge result. The gluon spectral representation is also explored from the center vortex perspective, where center vortices are shown to exhibit clear signs of positivity violation, which is an indicator of confinement. Vortex removal subsequently restores positivity, demonstrating the crucial role center vortices play in the confinement of gluons.

NANOGrav signal from first-order confinement-deconfinement phase transition in different QCD-matter scenarios

Recently, an indicative evidence of a stochastic process, reported by the NANOGrav Collaboration based on the analysis of 12.5-year pulsar timing array data which might be interpreted as a potential stochastic gravitational wave signal, has aroused the keen interest of theorists. The first-order color charge confinement phase transition at the QCD scale could be one of the cosmological sources for the NANOGrav signal. If the phase transition is flavor dependent and happens sequentially, it is important to find that what kind of QCD matter in which the first-order confinement-deconfinement phase transition happens is more likely to be the potential source of the NANOGrav signal during the evolution of the universe. In this paper, we would like to illustrate that the NANOGrav signal could be generated from confinement-deconfinement transition in either heavy static quarks with a zero baryon chemical potential, or quarks with a finite baryon chemical potential. In contrast, the gluon confinement could not possibly be the source for the NANOGrav signal according to the current observation. Future observation will help to distinguish between different scenarios.

High energy evolution for Gribov-Zwanziger confinement: Solution to the equation

In this paper, we solve the new evolution equation for high energy scattering amplitude that stems from the Gribov-Zwanziger approach to the confinement of quarks and gluons. We found that (1) the energy dependence of the scattering amplitude turns out to be the same as for QCD Balitsky, Fadin, Kuraev and Lipatov (BFKL) evolution, (2) the spectrum of the new equation does not depend on the details of the Gribov-Zwanzinger approach, and (3) all eigenfunctions coincide with the eigenfunctions of the QCD BFKL equation at large transverse momenta $\ensuremath{\kappa}\ensuremath{\ge}1$. The numerical calculations show that there exist no new eigenvalues with the eigenfunctions which decrease faster than solutions of the QCD BFKL equation at large transverse momenta. The structure of the gluon propagator in the Gribov-Zwanziger approach, that stems from the lattice QCD and from the theoretical evaluation, results in the exponential suppression of the eigenfunctions at long distances and in the resolution of the difficulties, which the color glass condensate and some other approaches, based on perturbative QCD, face at large impact parameters. We can conclude that the confinement of quark and gluons, at least in the form of the Gribov-Zwanziger approach, does not influence on the scattering amplitude except for solving the long-standing theoretical problem of its behavior at large impact parameters.

Gribov-Zwanziger confinement, high energy evolution, and large impact parameter behavior of the scattering amplitude

In this paper we derive the high energy evolution equation in the Gribov-Zwanziger approach for the confinement of quarks and gluons. We demonstrate that the new equation generates an exponential decrease of the scattering amplitude at large impact parameter and resolves the main difficulties of color glass condensate high energy effective theory. Such behavior occurs if the gluon propagator in Gribov-Zwanziger approach does not vanish at small momenta. Solving the nonlinear equation for deep inelastic scattering, we show that the suggested equation leads to a Froissart disc with radius (${R}_{F}$), which increases as ${R}_{F}\ensuremath{\propto}Y=\mathrm{ln}(1/x)$, and with a finite width for the distribution over $|b\ensuremath{-}{R}_{F}|$.

QUARKS and GLUONS CONFINEMENT: a POSSIBLE PHYSICAL EXPLANATION

The rules established by Quantum Mechanics (QM) play a crucial role, through the Heisenberg Uncertainty Principle (HUP), in the spatial Confinement of Quarks and Gluons, which have remained eternally confined, since the down of time, in an extremely narrow space by the Strong Interaction.The enormous amount of energy the Q borrows in favor of the emitted G, prevents it from covering a long way. According to HUP the energy debt has to be paid immediately, and the G flow path, i.e. of its range, will be determined by the short existence that QM gives to the G. Consequently, the very short range of G implies that, according to Yukawa Principle, but in disagreement with gauge theories and Quantum Fields Theory, its mass cannot be = 0, but very high. Our calculations, in fact, show that the range of G should correspond approximately to 8.44[±1.44] 10-16[cm]. This value, therefore, indicates the maximum distance that can separate a Q from the other two inside of a hadron.

Strong QCD from Hadron Structure Experiments

The topical workshop Strong QCD from Hadron Structure Experiments took place at Jefferson Lab from November 6–9, 2019. Impressive progress in relating hadron structure observables to the strong QCD mechanisms has been achieved from the ab initio QCD description of hadron structure in a diverse array of methods in order to expose emergent phenomena via quasi-particle formation. The wealth of experimental data and the advances in hadron structure theory make it possible to gain insight into strong interaction dynamics in the regime of large quark–gluon coupling (the strong QCD regime), which will address the most challenging problems of the Standard Model on the nature of the dominant part of hadron mass, quark–gluon confinement, and the emergence of the ground and excited state hadrons, as well as atomic nuclei, from QCD. This workshop aimed to develop plans and to facilitate the future synergistic efforts between experimentalists, phenomenologists, and theorists working on studies of hadron spectroscopy and structure with the goal to connect the properties of hadrons and atomic nuclei available from data to the strong QCD dynamics underlying their emergence from QCD. These results pave the way for a future breakthrough extension in the studies of QCD with an Electron–Ion Collider in the U.S.

Reflection positivity and complex analysis of the Yang\u2013Mills theory from a viewpoint of gluon confinement

In order to understand the confining decoupling solution of the Yang–Mills theory in the Landau gauge, we consider the massive Yang–Mills model which is defined by just adding a gluon mass term to the Yang–Mills theory with the Lorentz-covariant gauge fixing term and the associated Faddeev–Popov ghost term. First of all, we show that massive Yang–Mills model is obtained as a gauge-fixed version of the gauge-invariantly extended theory which is identified with the gauge-scalar model with a single fixed-modulus scalar field in the fundamental representation of the gauge group. This equivalence is obtained through the gauge-independent description of the Brout–Englert–Higgs mechanism proposed recently by one of the authors. Then, we reconfirm that the Euclidean gluon and ghost propagators in the Landau gauge obtained by numerical simulations on the lattice are reproduced with good accuracy from the massive Yang–Mills model by taking into account one-loop quantum corrections. Moreover, we demonstrate in a numerical way that the Schwinger function calculated from the gluon propagator in the Euclidean region exhibits violation of the reflection positivity at the physical point of the parameters. In addition, we perform the analytic continuation of the gluon propagator from the Euclidean region to the complex momentum plane towards the Minkowski region. We give an analytical proof that the reflection positivity is violated for any choice of the parameters in the massive Yang–Mills model, due to the existence of a pair of complex conjugate poles and the negativity of the spectral function for the gluon propagator to one-loop order. The complex structure of the propagator enables us to explain why the gluon propagator in the Euclidean region is well described by the Gribov–Stingl form. We try to understand these results in light of the Fradkin–Shenker continuity between confinement-like and Higgs-like regions in a single confinement phase in the complementary gauge-scalar model.

Evolution of Colour in QCD and Informational Approach to Quantum Measurement

Quantum chromodynamics (QCD) introduces the quantum characteristic of colour in order to satisfy the Pauli exclusion principle and symmetric considerations for wavefunctions of hadrons. However, the particles that possess colour charge (quarks and gluons) are not directly observed in experiment – the effect which is often referred to as confinement. Confinement of quarks and gluons represents a theoretical challenge, as the dynamics of underlying fields is non-perturbative and therefore is problematic to be described analytically. One possible way is to use non-perturbative approaches and derive analogies with other well-established branches of physics. In this work we describe the use of the method of vacuum correlators – to analyze the confinement and other non-perturbative dynamics of quarks. The discussion of the acquired results is then given on the basis of quantum information and measurement description. It is shown that the confinement of quarks might be associated with the decoherence of colour state due to the interaction of colour charges with the environment of colour fields (QCD stochastic vacuum).

Complex poles and spectral function of Yang-Mills theory

We derive general relationships between the number of complex poles of a propagator and the sign of the spectral function originating from the branch cut in the Minkowski region under some assumptions on the asymptotic behaviors of the propagator. We apply this relation to the mass-deformed Yang-Mills model with one-loop quantum corrections, which is identified with a low-energy effective theory of the Yang-Mills theory, to show that the gluon propagator in this model has a pair of complex conjugate poles or "tachyonic" poles of multiplicity two, in accordance with the fact that the gluon field has a negative spectral function, while the ghost propagator has at most one "unphysical" pole. Finally, we discuss implications of these results for gluon confinement and other non-perturbative aspects of the Yang-Mills theory.

Finite temperature gluon propagator in Landau gauge: non-zero Matsubara frequencies and spectral densities

We report on the lattice computation of the Landau gauge gluon propagator at finite temperature, including the non-zero Matsubara frequencies. Moreover, the corresponding Källén-Lehmann spectral density is computed, using a Tikhonov regularisation together with the Morozov discrepancy principle. Implications for gluon confinement are also discussed.

Nonperturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST-invariant two-point correlation function

In order to construct a gauge invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge invariant transverse configurations A^h. Such configurations can be obtained through the minimization of the functional A^2_{min} along the gauge orbit within the BRST invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of non-perturbative aspects of the theory in a BRST invariant and gauge parameter independent way. In particular, it turns out that the poles of <A^h A^h> are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST invariant formulation introduced before. Moreover, the correlator <A^h A^h> enables us to attach a BRST invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of <A^h A^h> as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use <A^h A^h> to probe the pole structure of the massive gauge boson in a gauge invariant fashion.

Probing QCD perturbation theory at high energies with continuum extrapolated lattice data

Precision tests of QCD perturbation theory are not readily available from experimental data. The main reasons are systematic uncertainties due to the confinement of quarks and gluons, as well as kinematical constraints which limit the accessible energy scales. We here show how continuum extrapolated lattice data may overcome such problems and provide excellent probes of renormalized perturbation theory. This work corresponds to an essential step in the ALPHA collaboration's project to determine the $\Lambda$-parameter in 3-flavour QCD. I explain the basic techniques used in the high energy regime, namely the use of mass-independent renormalization schemes for the QCD coupling constant in a finite Euclidean space time volume. When combined with finite size techniques this allows one to iteratively step up the energy scale by factors of 2, thereby quickly covering two orders of magnitude in scale. We may then compare perturbation theory (with $\beta$-functions available up to 3-loop order) to our non-perturbative data for a 1-parameter family of running couplings. We conclude that a target precision of 3 percent for the $\Lambda$-parameter requires non-perturbative data up to scales where $\alpha_s\approx 0.1$, whereas the apparent precision obtained from applying perturbation theory around $\alpha_s \approx 0.2$ can be misleading. This should be taken as a general warning to practitioners of QCD perturbation theory.

Lattice Landau Gauge Gluon Propagator at Finite Temperature: Non-zero Matsubara Frequencies and Spectral Densities

The lattice Landau gauge gluon propagator at finite temperature is computed including the non-zero Matsubara frequencies. Furthermore, the Kallen-Lehmann representation is inverted and the corresponding spectral density evaluated using a Tikhonov regularisation together with the Morozov discrepancy principle. Implications for gluon confinement are discussed.

World-Line Formalism: Non-Perturbative Applications

This review addresses the impact on various physical observables which is produced by confinement of virtual quarks and gluons at the level of the one-loop QCD diagrams. These observables include the quark condensate for various heavy flavors, the Yang-Mills running coupling with an infra-red stable fixed point, and the correlation lengths of the stochastic Yang-Mills fields. Other non-perturbative applications of the world-line formalism presented in the review are devoted to the determination of the electroweak phase-transition critical temperature, to the derivation of a semi-classical analogue of the relation between the chiral and the gluon QCD condensates, and to the calculation of the free energy of the gluon plasma in the high-temperature limit. As a complementary result, we demonstrate Casimir scaling of k-string tensions in the Gaussian ensemble of the stochastic Yang-Mills fields.

Color confinement from fluctuating topology

QCD possesses a compact gauge group, and this implies a non-trivial topological structure of the vacuum. In this contribution to the Gribov-85 Memorial volume, we first discuss the origin of Gribov copies and their interpretation in terms of fluctuating topology in the QCD vacuum. We then describe the recent work with E. Levin that links the confinement of gluons and color screening to the fluctuating topology, and discuss implications for spin physics, high energy scattering, and the physics of quark-gluon plasma.

Matter confinement in light of the Gribov horizon

The procedure of quantization of Landau-gauge Yang-Mills theories that takes into account the presence of Gribov copies has led to the construction of a scenario of gluon confinement via an infrared effective action, the (refined) Gribov-Zwanziger theory. Here we briefly review and discuss a possible extension of this picture to the matter sector of confining Yang-Mills theories.