Color Electric Field Research Articles

Exploring quantum entanglement in chiral symmetry partial restoration with 1+1 string model

Within the confining color flux tube picture, we assess the color electric field generated by quark-antiquark pairs within the framework of the Schwinger model and estimate its impact on the chiral condensate. We observe differences in the distribution of the color flux tube generated by quark-antiquark pairs at different separation distances, leading to discrepancies in the partial restoration of chiral symmetry. Furthermore, we suggest incorporating the color magnetic field in the calculation of chiral condensate, leading to quantum entanglement effects, and proceed to compute the entanglement entropy. We observe that the entanglement entropy increases with the distance of the color source (the separation distance between quark and anti-quark), and the magnitude of the color electric field and chiral condensate restoration after spatial integration also increases with the distance of the color source. Then, we try to provide a qualitative explanation for the existence of these phenomena.

Charge gap in SU(3) Yang–Mills-plus-nonlinear-spinor-field theory

Particlelike solutions in SU(3) gauge Yang–Mills theory with color magnetic and electric fields sourced by a nonlinear spinor field are obtained. The asymptotic behavior of these fields is studied. It is shown that the electric field exhibits the Coulomb asymptotic behavior, and one of the color components of the magnetic field behaves asymptotically as the field of a magnetic dipole. This allows one to determine the corresponding charge and magnetic moment. It is shown that profiles of the color charge and magnetic moment have global minima, which may be called charge and magnetic moment gaps. The relationship between the total energy of the system and the color charge is obtained. The physical reason for the appearance of the mass, charge, and magnetic moment gaps in the theory under consideration is discussed.

QCD Effects in Non-QCD Theories

It is shown that, in some non-QCD theories, there are effects shared by QCD: (i)~in SU(2) Yang-Mills theory containing a nonlinear spinor field, there is a mass gap; (ii)~in SU(3) Proca-Higgs theory, there are flux tube solutions with a longitudinal electric field required for producing a force binding quarks; (iii)~in non-Abelian Proca-Higgs theories, there exist flux tube solutions with a momentum directed along the tube axis and particlelike solutions with a nonvanishing total angular momentum created by crossed color electric and magnetic fields; in QCD, such configurations may contribute to the proton spin. We discuss the conjecture that such non-QCD theories might be a consequence of approximate solution of an infinite set of Dyson-Schwinger equations describing the procedure of nonperturbative quantization. The phenomenon of dimensional transmutation for nonperturbative quantization and the analogy between nonperturbative quantization and turbulence modeling are also discussed.

Abelian Dirac-type monopoles and the dual Meissner effect in QCD

We investigate the Abelian dual Meissner effect due to violation of the non-Abelian Bianchi identity in SU (3) gauge thoery without gauge fixing. To decide the vacuum type, we evaluate the Ginzburg-Landau parameter from the spatial distribution of color electric fields and squared monopole density. Although the study is done only on 24 (40)3 × 4 lattice at β = 5.6, the SU (3) vacuum is found to be of the type 1 near the border of type 1 and type 2. We also confirm the dual Ampere’s law directly.

Linear Energy Density and the Flux of an Electric Field in Proca Tubes

In this work, we study cylindrically symmetric solutions within SU(3) non-Abelian Proca theory coupled to a Higgs scalar field. The solutions describe tubes containing either the flux of a color electric field or the energy flux and momentum. It is shown that the existence of such tubes depends crucially on the presence of the Higgs field (there are no such solutions without this field). We examine the dependence of the integral characteristics (linear energy and momentum densities) on the values of the electromagnetic potentials at the center of the tube, as well as on the values of the coupling constant of the Higgs scalar field. The solutions obtained are topologically trivial and demonstrate the dual Meissner effect: the electric field is pushed out by the Higgs scalar field.

Nonperturbative and Thermal Dynamics of Confined Fields in Dual QCD

In order to study the detailed dynamics and associated nonperturbative features of QCD, a dual version of the color gauge theory based on a topologically viable homogeneous fibre bundle approach has been analysed taking into account its magnetic symmetry structure. In the dynamically broken phase of magnetic symmetry, the associated flux tube structure on a S2 sphere in the magnetically condensed state of the dual QCD vacuum has been analyzed for the profiles of the color electric field using flux quantization and stability conditions. The color electric field has its intimate association with the vector mode of the magnetically condensed QCD vacuum, and such field configurations have been analyzed to show that the color electric flux gets localized towards the poles for a large sphere case while it gets uniformly distributed for the small sphere case in the infrared sector of QCD. The critical flux tube densities have been computed for various couplings and are shown to be in agreement with that for lead-ion central collisions in the near infrared sector of QCD. The possible annihilation/unification of flux tubes under some typical flux tube density and temperature conditions in the magnetic symmetry broken phase of QCD has also been analyzed and shown to play an important role in the process of QGP formation. The thermal variation of the profiles of the color electic field is further investigated which indicates the survival of flux tubes even in the thermal domain that leads the possibility of the formation of some exotic states like QGP in the intermediate regime during the quark-hadron phase transition.

Impact of the pre-equilibrium stage of ultra-relativistic heavy ion collisions: isotropization and photon production

We present a model in which gluon and quark pairs are produced by means of the Schwinger mechanism from the decay of color-electric flux tubes, which are expected to be produced in the early stage of ultra-relativistic heavy ion collisions. The evolution equations of the initial field are coupled to the relativistic transport equation which describes the dynamics of the many particle system and is formulated in terms of a fixed viscosity over entropy density ratio $ \eta$ /s. This self-consistent solution of the problem allows to take into account the backreaction of the color currents on the classical field. We study isotropization and thermalization of the plasma produced by the field decay for a expanding geometry in $ 1+1{\rm D}$ and in $ 3+1{\rm D}$ . We find that the initial color-electric field decays within 1fm/c ; in the case of large $ \eta$ /s oscillations of the field appear along the whole temporal evolution of the system, affecting also the ratio between longitudinal and transverse pressure. In the case of small viscosities ( $ \eta/s\lesssim3/4\pi$ ) we find an equilibration time less than 1 fm/c, in agreement with the common lore of hydrodynamics. Including the pertinent scattering processes into the collision integral of the Boltzmann equation we investigate photon production within our model for the pre-equilibrium dynamics and with simulations starting with equilibrium initial conditions. Thus, we are able to identify the contribution of the early-stage to the photon spectrum in Au-Au collisions at RHIC $\sqrt{s_{NN}}=200$ GeV and in Pb-Pb collisions at LHC $ \sqrt{s_{NN}}=2.76$ TeV. We find that there is no dark age in relativistic heavy ion collisions: early-stage photons enhance the direct photon spectrum in the intermediate transverse momentum region ( $ p_{T}\gtrsim 1.5$ -2 GeV depending on the collision energy) and their abundance is comparable with that produced by a thermalized quark-gluon plasma.

The motion of color-charged particles as a means of testing the non-Abelian dark matter model

A possibility is discussed to experimentally test a dark matter model supported by a classic non-Abelian SU(3) Yang–Mills gauge field. Our approach is based on the analysis of the motion of color-charged particles in the background of color electric and magnetic fields using the Wong equations. Estimating the magnitudes of the color fields near the edge of a galaxy, we employ them in obtaining the general analytic solutions to the Wong equations. Using the latter, we calculate the magnitude of the extra acceleration of color-charged particles related to the possible presence of the color fields in the neighborhood of Earth.

Color field densities of the quark-antiquark excited flux tubes in SU(3) lattice QCD

We combine techniques previously utilized to study flux tube field density profiles and to study the excited spectrum of the gluonic fields produced by a static quark-antiquark pair. Working with pure gauge SU(3) fields discretized in a lattice, we utilize Wilson loops with a large basis of gluonic spacelike Wilson lines to include different excitations of the quark-antiquark flux tube. To increase the signal over noise ratio, we use the multihit technique in the temporal Wilson lines and the APE smearing in spatial Wilson lines. The number of gluonic operators combined with the space points where we compute the flux tube densities turns out to be very large, and we resort to GPUs and to CUDA codes. Computing the effective mass plot from the diagonalized correlation matrix, we separate the excitations with different two-dimensional angular momentum, parity, and radial quantum numbers. We then compute the color field density profiles for all the components of the colour electric and colour magnetic fields. We analyze our results for the first excitations of the flux tube and search for signals of novel phenomena beyond the Nambu-Goto string model, such as a longitudinal mode or an explicit gluon.

Observation of a Coulomb flux tube

In Coulomb gauge there is a longitudinal color electric field associated with a static quark-antiquark pair. We have measured the spatial distribution of this field, and find that it falls off exponentially with transverse distance from a line joining the two quarks. In other words there is a Coulomb flux tube, with a width that is somewhat smaller than that of the minimal energy flux tube associated with the asymptotic string tension. A confinement criterion for gauge theories with matter fields is also proposed.

Schwinger effect for non-Abelian gauge bosons

We investigate the Schwinger effect for the gauge bosons in an unbroken non-Abelian gauge theory (e.g. the gluons of QCD). We consider both constant “color electric” fields and “color magnetic” fields as backgrounds. As in the Abelian Schwinger effect we find there is production of “gluons” for the color electric field, but no particle production for the color magnetic field case. Since the non-Abelian gauge bosons are massless there is no exponential suppression of particle production due to the mass of the electron/positron that one finds in the Abelian Schwinger effect. Despite the lack of an exponential suppression of the gluon production rate due to the masslessness of the gluons, we find that the critical field strength is even larger in the non-Abelian case as compared to the Abelian case. This is the result of the confinement phenomenon on QCD.

Quark and gluon production from a boost-invariantly expanding color electric field

Particle production from an expanding classical color electromagnetic field is extensively studied, motivated by the early stage dynamics of ultra-relativistic heavy ion collisions. We develop a formalism at one-loop order to compute the particle spectra by canonically quantizing quark, gluon and ghost fluctuations under the presence of such an expanding classical color background field; the canonical quantization is done in the $\tau$-$\eta$ coordinates in order to take into account manifestly the expanding geometry. As a demonstration, we model the expanding classical color background field by a boost-invariantly expanding homogeneous color electric field with lifetime $T$, for which we obtain analytically the quark and gluon production spectra by solving the equations of motion of QCD non-perturbatively with respect to the color electric field. In this paper we study (i) finite lifetime effect which is found to modify significantly the particle spectra from those expected from the Schwinger formula; (ii) the difference between the quark and gluon production; and (iii) the quark mass dependence of the production spectra. Implications of these results to ultra-relativistic heavy ion collisions are also discussed.

Impact of early stage non-equilibrium dynamics on photon production in relativistic heavy ion collisions

In this study we discuss our results on the spectrum of photons emitted from the quark-gluon plasma produced in heavy ion collisions at RHIC energies. Simulating the space-time evolution of the fireball by solving the relativistic Boltzmann transport equation and including two-particle scattering processes with photon emission allows us to make a first step in the description of thermal photons from the QGP as well as of those produced in the pre-equilibrium stage. Indeed, we consider not only a standard Glauber initial condition but also a model in which quarks and gluons are produced in the very early stage through the Schwinger mechanism by the decay of an initial color-electric field. In the latter approach relativistic kinetic equations are coupled in a self-consistent way to field equations. We aim at spotting the impact of early stage non-equilibrium dynamics on the photon production.

Plasmon mass scale in classical nonequilibrium gauge theory

Classical lattice Yang-Mills calculations provide a good way to understand different nonequilibrium phenomena in nonperturbatively overoccupied systems. Above the Debye scale the classical theory can be matched smoothly to kinetic theory. The aim of this work is to study the limits of this quasiparticle picture by determining the plasmon mass in classical real time Yang-Mills theory on a lattice in 3 spatial dimensions. We compare three methods to determine the plasmon mass: a hard thermal loop expression in terms of the particle distribution, an effective dispersion relation constructed from fields and their time derivatives, and by measuring oscillations between electric and magnetic field modes after artificially introducing a homogeneous color electric field. We find that a version of the dispersion relation that uses electric fields and their time derivatives agrees with the other methods within 50%.

Nonperturbative quantization ‘a la Heisenberg for non-Abelian gauge theories: two-equation approximation. Applications: a flux tube solution and a scalar model of glueball

The nonperturbative quantization technique a la Heisenberg is applied for the SU(3) gauge theory. The operator Yang-Mills equation and corresponding infinite set of equations for all Green’s functions are considered. Gauge degrees of freedom are splitted into two groups: (1) A μ a ∈ SU (2) × U (1) ⊂ SU (3); (2) coset degrees of freedom SU (3)/SU (2) × U (1). Using some assumptions about 2- and 4-point Green’s functions, the infinite set of equations is truncated to two equations. The first equation is the SU (2) × U (1) Yang-Mills equation, and the second equation describes a gluon condensate formed by coset fields. A flux tube solution describing longitudinal color electric fields stretched between quark and antiquark located at the ± infinities is obtained. It is shown that the dual Meissner effect appears in this solution: the electric field is pushed out from the gluon condensate.

Initial state azimuthal anisotropies in small collision systems

Strong multiparticle azimuthal correlations have recently been observed in high energy proton-nucleus collisions. While final state collective effects can be responsible for many of the observed effects, the domain structure in the classical color field of a high energy nucleus, naturally also leads to such multiparticle correlations. We describe recent calculations of the momentum space 2-particle cumulant azimuthal anisotropy coefficients νn{2}, n=2,3,4 from fundamental representation Wilson line distributions describing the high energy nucleus. We find significant differences between Wilson lines from the MV model and from JIMWLK evolution. We also discuss the relation of this calculation to earlier work on the ridge correlation obtained in the “glasma graph” approximation, and to the “color electric field domain model.”

Modeling early time dynamics of relativistic heavy ion collisions

We studied isotropization and thermalization of the quark-gluon plasma produced by decaying color-electric flux tubes created at the very early stages of relativistic heavy ion collisions. We coupled the dynamical evolution of the initial field, which decays to a plasma by the Schwinger mechanism, to the dynamics of the many particles system produced by the decay. The evolution of such a system is described by relativistic transport theory at fixed values of the viscosity over entropy density ratio. Within a single self-consistent calculation scheme we computed quantities which serve as indicators of the equilibration of the plasma for a 1+1 dimensional expanding geometry. We find that the initial color-electric field decays within 1 fm/c and particles production occurs in less than 1 fm/c; however, in the case of large viscosity oscillations of the field appear along the entire time evolution of the system, affecting also the behaviour of the ratio between longitudinal and transverse pressure. In case of small viscosity we find that the isotropization time is about 0.8 fm/c and the thermalization time is about 1 fm/c, in agreement with the common lore of hydrodynamic approaches.

Perturbative renormalization of the electric field correlator

The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ~12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.

Temperature dependence of dimension-6 gluon operators and their effects on charmonium

Starting from an earlier representation of the independent dimension 6 gluon operators in terms of color electric and magnetic fields, we estimate their changes near the critical temperature $T_c$ using the temperature dependence of the dimension 4 electric and magnetic condensates extracted from pure gauge theory on the lattice. We then improve the previous QCD sum rules for the $J/\psi$ mass near $T_c$ based on dimension 4 operators, by including the contribution of the dimension 6 operators to the OPE. We find an enhanced stability in the sum rule and confirm that the $J/\psi$ will undergo an abrupt change in the property across $T_c$.

Flavoured aspects of the QCD thermodynamics

We discuss recent progress in lattice QCD studies on various aspects involving strange and heavy quarks. Appropriate combinations of conserved net strange and net charm fluctuations and their correlations with other conserved charges provide evidence that in the hadronic phase so far unobserved hadrons contribute to the thermodynamics and need to be included in hadron resonance gas models. In the strange sector this leads to significant reductions of the chemical freeze-out temperature of strange hadrons. We have found that a description of the thermodynamics of open strange and open charm degrees of freedom in terms of an uncorrelated hadron gas is valid only up to temperatures close to the chiral crossover temperature. This suggests that in addition to light and strange hadrons also open charm hadrons start to dissolve already close to the chiral crossover. Further indications that open charm mesons start to melt in the vicinity of Tc is obtained from an analysis of screening masses, while in the charmonium sector these screening masses show a behavior compatible with a sequential melting pattern. In the last section we discuss resent progress in extracting a transport coefficient, the heavy quark momentum diffusion coefficient, based on continuum extrapolated color-electric field correlation functions and estimate the time scale associated with the kinetic equilibration of heavy quarks. Close to Tc this suggests that charm quark kinetic equilibration appears almost as fast as that of light partons in agreement with qualitative discoveries at RHIC and LHC that charm quarks appear to flow about as effectively as light quarks.