Perturbative versus lattice QCD energy density correlators at high temperatures

Correlators of magnetic and electric field energy density are investigated for SU(N_c) gauge theory at high temperatures T. A separations z ⩽ 2/T the correlators are shown to be dominated by a power-law behavior even for finite gluon screening masses. This continuum behavior is well approximated on current 4 × 16³-lattices in the perturbative limit and leads to a considerable overestimate of screening masses deduced from fitting the lattice correlators with conventional exponential forms. The use of extended sources and sinks to enhance the signal improves the situation for screening masses m ⪢ T but leads to a largely uncontrolled error for masses less than T. In fact, we show that recent lattice QCD data of Grossmann et al., from which a magnetic screening mass m_M ∼ 2.9T was deduced, may even be consistent with a vanishing actual magnetic screening mass.     

Behaviour of gluons at high temperature

The screening of colour electric and magnetic fields and plasma oscillations in a high-temperature gluon plasma are investigated using linear response theory and self-consistent nonperturbative solutions to the Schwinger-Dyson equation. Static electric fields are screened, with

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. This result is proven to be gauge invariant in two ways: by computing π₀₀ in temporal axial, Coulomb and covariant gauges, and by computing the physical free energy of a heavy quark pair in the plasma in temporal axial gauge. To order g³ static magnetic fields are not screened.     

Dynamical properties of the vacuum in non-abelian field theories with and without supersymmetry

In QCD with massless quarks, the effective potential for the color singlet operator (F_μν^a)² can be constructed by the use of the trace anomaly equation and tells us that magnetic gluon condensation, 〈0|(F_μν^a)²|0〉 > 0, occurs. When the method is applied to supersymmetric QCD, however, it gives us a puzzle; the gluons condense with negative energy density, and supersymmetry is broken in a pathological manner with the appearance of a negatively normed Nambu-Goldstone fermion. Spurred on by this observation, we examine in detail the properties of the vacuum for the super (and ordinary) O(N) non-linear σ model in two dimensions for which a similar puzzling situation occurs with regard to the lagrangian condensate. We find, in particular, that (i) the chiral condensate plays a crucial role in resolving the puzzle and that (ii) it is the nature of the response of the lagrangian condensate to the test charge, not the sign or the magnitude of the condensate itself, that determines the phase of the system. Implications of these results for (super) QCD, including an unconventional possibility of “electric” gluon condensation, are discussed.     

Expanding color flux tubes and instabilities

We present an analytic study of the physics of the glasma which is a strong classical gluon field created at early stage of high-energy heavy-ion collisions. Our analysis is based on the picture that the glasma just after the collision is made of color electric and magnetic flux tubes extending in the longitudinal direction with their diameters of the order of 1/Q_s (Q_s is the saturation scale of the colliding nuclei). We find that both the electric and magnetic flux tubes expand outwards and the field strength inside the flux tube decays rapidly in time. Next we investigate whether there exist instabilities against small rapidity-dependent perturbations for a fixed color configuration. We find that the magnetic background field exhibits an instability induced by the fluctuations in the lowest Landau level, and it grows exponentially in the time scale of 1/Q_s. For the electric background field we find no apparent instability while the possible relation to the Schwinger mechanism for particle pair creations is suggested.     

Estimates for Parameters and Characteristics of the Confining SU(3)-gluonic Field in ϕ-meson from Leptonic Widths

The paper is devoted to applying the confinement mechanism proposed earlier by one of the authors to estimate the possible parameters of the confining SU(3)-gluonic field in vector ?-meson. The estimates obtained are consistent with the leptonic widths of the given meson. The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of the meson under consideration.     

Synchrotron contribution to photon emission from a quark–gluon plasma

The influence of the magnetic field on the photon emission from the quark–gluon plasma created in AA collisions is studied. It is found that the effect of magnetic field is very small even for very optimistic assumption on the magnitude of the magnetic field for noncentral AA collisions.     

Free energy in the (2+1)-dimensional SU(2) QCD model against the background of a gauge-field condensate

The thermodynamic potential (free energy) for quarks and gluons in (2+1)-dimensional spacetime is calculated in the one-loop approximation at finite temperatures against the background of a constant uniform color magnetic field H and a constant uniform A ₀ condensate. The problem of interpreting the tachyon mode in the gluon energy spectrum is discussed. The question of whether the free energy may develop a minimum at nonzero values of H and A ₀ is analyzed.     

Quantum Chromodynamics in 1+3 Dimensions at High Temperature: Dimensional Reduction Revisited

The gluon sector of QCD in 1+3 dimensions in analyzed at high temperature (much larger than the critical ones) thereby generalizing previous results by other authors. The imaginary time formalism is used. The analysis is carried out to all orders in an improved perturbation theory which includes all second-order internal quark loops in the “free” gluon propagators. General results are given for the leading high temperature contributions to all renormalized connected gluon Green's functions (for fixed external threemomenta, much smaller than the temperature). The latter are generated by a new (dimensionally reduced) high-temperature partition function Z_HT, which corresponds to: i) the Yang-Mills (“magnetic”) gluon field coupled to a massive scalar (“electric”) gluon field, all in 3 spatial dimensions and at zero imaginary time, ii) the quark field, which continues to depend on imaginary time, coupled to the above gluon fields Z_HT also depends on the renormalized quark masses and gauge coupling constant at zero temperature, the second order quark-loop contributions to the zero-temperature renormalization constants for the gluon field and the three and four gluon vertices and on new gluon mass terms. The latter correspond to a finite number of diagrams in the improved perturbation theory at high temperature. Z_HT could be useful as the starting point for further non-perturbative studies. For the pure Yang-Mills plus ghosts theory (no quarks), it is conjectured that contributions to Green's functions depending on external momenta due to internal electric gluons could be regarded, as subdominant. Arguments are given in order to justify that conjecture. Then, the above Z_HT can be simplified and another high-temperature generating functional depending only on magnetic gluon fields is given. For the full theory including quarks, the possibility of neglecting contributions due to internal quark loops is discussed: certain infrared divergences beyond the oneloop level appear to imply that such a simplification, although not discarded, is rather hard to establish.     

Non-linear BFKL dynamics: Color screening vs. gluon fusion

A feasible mechanism of unitarization of amplitudes of deep inelastic scattering at small values of Bjorken x is the gluon fusion. However, its efficiency depends crucially on the vacuum color screening effect which accompanies the multiplication and the diffusion of BFKL gluons from small to large distances. From the fits to lattice data on field strength correlators the propagation length of perturbative gluons is R _c ? (0.2–0.3) fm. The probability to find a perturbative gluon with short propagation length at large distances is suppressed exponentially. It changes the pattern of (dif)fusion dramatically. The magnitude of the fusion effect appears to be controlled by the new dimensionless parameter ～ R _c ² /8B, with the diffraction cone slope B standing for the characteristic size of the interaction region. It should slowly ∝ 1/lnQ ₂ decrease at large Q ². Smallness of the ratio R _c ² /8B makes the non-linear effects rather weak even at lowest Bjorken x available at HERA. We report the results of our studies of the non-linear BFKL equation which has been generalized to incorporate the running coupling and the screening radius, R _c as the infrared regulator.     

Estimate of the screening corrections to gluon distributions in the smallx region

The screening corrections to gluon distributions in a proton corresponding to the triple gluonic ladder diagram are estimated. They are found to be relatively small: their values does not exceed 10% of the leading order QCD gluon distribution forx?10^?4 andQ ² ?100 GeV².     

The gluon propagator at finite temperature

The Landau gauge gluon propagator at finite temperature above and below the deconfinement transition is measured using lattice Monte Carlo simulation. The color electric and magnetic masses are determined. The most striking result of the calculation is that the time component of the gluon field appears to acquire a vacuum expected value in the deconfined region.     

Use and misuse of QCD sum rules,factorization and related topics

The purpose of this paper is twofold. First, we are prompted by some recent publications to reply to the criticism of the QCD sum-rules approach contained therein. Hopefully, some of the discussion is of wider interest. In particular, we point out that the multi-gluon operators unlike the multi-quark ones, relevant to the sum rules, do not factorize at large N_c. This implies that the masterfield, even if it is found, will be of no immediate help in evaluating the quarkonium spectrum. Second, we derive new sum rules for light quarks which are sensitive to the mean intensity of the gluon field in the vacuum (the so-called gluon condensate, or 〈vac|G²|vac〉). New sum rules confirm the standard value of 〈vac|G²|vac〉. Some casual remarks on the π⁰ transitions into two virtual photons, π⁰ → γ^*γ^*, are also presented. Finally, we enumerate (in sect. 7) basic points of the sum-rule approach and discuss, im brief, the unsolved problems.     

Chiral thermodynamics in a magnetic field

The phase structure of the QCD vacuum in a magnetic field H is investigated at low temperatures T. The free energy of the hadronic phase in a constant homogeneous magnetic field is calculated in the one-loop approximation of chiral perturbation theory. The quark and the gluon condensate are found as functions of temperature and the field strength. It is shown that the order parameter $\left\langle {\bar qq} \right\rangle $ for the chiral phase transition remains constant when the temperature T and the magnetic field H change in such a way that H=const×T ².     

Electric stimulation of magnetoplasticity and magnetic hardening in crystals

The effect of electric field E on the magnetoplastic effect (MPE) has been investigated in NaCl crystals with different impurities, which provide either the plasticization of the samples in the magnetic field (positive MPE) or their magnetic hardening (negative MPE). The mobility of individual dislocations under the joint action of the magnetic and electric fields and the mechanical load on the crystals has been studied. The sharp electric stimulation of the MPE of both signs has been revealed, i.e., an increase or a decrease in the mean free path of dislocations that is roughly proportional to exp(±E/E ₀) at E ? E ₀ ～ 1–10 kV/m. In particular, in the negative-MPE NaCl(Pb) crystals, the accompanying electric field enhances the magnetic suppression of plasticity. The results are attributed to the electrically induced transformation of the additional part of the pinning impurity ions Me⁺⁺ to the magnetically active state of Me⁺ on the dislocations. The subsequent magnetic transformation of the structure of these pinning centers should lead to a sharper variation of the dislocation pinning force (either an increase or a decrease, depending on the MPE sign).     

Fully quantum treatment of the Landau-Pomeranchik-Migdal effect in QED and QCD

A rigorous quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD is given for the first time. The rate of photon (gluon) radiation by an electron (quark) in a medium is expressed in terms of the Green’s function of a two-dimensional Schrödinger equation with an imaginary potential. In QED this potential is proportional to the dipole cross section for scattering of an e ⁺ e ^? pair off an atom, while in QCD it is proportional to the cross section of interaction of the color singlet quark-antiquark-gluon system with a color center.     

Nonneutral electron plasma with a 2.5 MeV mean energy

A pulsed magnetic mirror device is used to produce a nonneutral electron plasma (N_total = 8 × 10¹¹) with a mean kinetic energy of 2.5 MeV in a 26 kG field. This represents a substantial increase over previous results.     

Die Abhängigkeit innerer und äußerer Wechselwirkungen des TlF-Moleküls von der Schwingung,Rotation und Isotopie

The hyperfinestructure, Stark effekt and Zeeman effect of the TlF molecule have been measured with a molecular beam resonance apparatus. The apparatus uses electric four poles as deflecting fields and a homogeneous electric field parallel to a super-imposed magnetic field in the transition region. Electric dipole transitions withΔm _J =±1,ΔJ=0 (J rotational quantum number) were measured in the following (v, J) states (v vibrational quantum number): (0,1), (1,1), (2,1) and (0,2) of the molecule²⁰⁵Tl¹⁹F and (0,1) of the molecule²⁰³Tl¹⁹F. For these five states the following interaction constants were determined: The magnetic (and the electric) dipolemoment of the molecule, the scalar and the tensor nuclear dipole-dipole interaction, the nuclear spin-rotational interactions, the anisotropy of the diamagnetic susceptibility ξ_⊥?ξ_∥, the anisotropy of the diamagnetic shielding of the external field by the electrons at the position of the nuclei σ_⊥?σ_∥. From these quantities it was possible to calculate the quadrupole-moment of the electronic charge distribution. Furthermore, the dependence of the ratio of the isotopic electric dipolemoments on vibrational state was measured. A new method for determining the nuclear magnetic moments is described. The method consists of a molecular beam resonance apparatus with combined magnetic and electric transition fields and was used to measure the magnetic moments of the nuclei²⁰⁵Tl and¹⁹F. — On page 293 will be found a table of results.     

The electric screening mass in scalar electrodynamics at high temperature

We study the screening of static electric fields in massless scalar electrodynamics at high temperature and zero chemical potential. Effective field theory methods are used to separate the contributions from the momentum scales T and eT to the electric screening mass. The effects of the distance scale 1/T are encoded in the parameters of an effective three-dimensional field theory. The parameters of the effective Lagrangian can be written as a power series in e ². The contribution to physical quantities from the scale 1/eT can be calculated from perturbation theory in the effective theory and is an expansion in e starting at e ³. The electric screening mass squared is computed to order e ⁴.     

CGC formalism with two sources

In this work we extend the JIMWLK formalism to the two-source problem. The S-matrix for the forward scattering can be written in a double functional integral representation which involves the usual functional integral for the gluon field and the spin path integral for the external color sources. Modifications needed in the light-cone gauge are discussed. Using our source term we compute the produced gluon field and discuss the duality of the high energy evolution kernel in the pA collision.     

Entstehung und Eigenschaften des Halo bei Pinch-Plasmen

In pinch discharges a second plasma regime called halo^1,2 outside the central plasma column^1-4 has been observed. This surrounding plasma was investigated in the experiments with the 5.4 m long compression coil in the ISARI linear theta pinch because there it appears highly pronounced. The development of the discharge was observed side-on (stereoscopic) with image converters and a streak camera. It appears possible to resolve the space-time behaviour of the plasma, especially in the dynamic phase of the discharge where the halo shows a filament like structure, by using high-speed color reversal film (streak camera). Furthermore, the smear pictures show that after 6–8 μsec the halo region is frozen into the external magnetic field, that is from this time the halo is characterized by a high electrical conductivity. The boundary layer of the halo follows a magnetic flux tube. The parameters of the halo, such as electron densityn _e (< 10¹⁵ cm^?3), atomic temperatureT _a , and ion temperatureT _i (< 15 eV), were determined spectroscopically as a function of time and location from the broadening of the deuterium Balmer lines. The absolutely measured line intensities do not allow direct calculation of the electron temperature since the excited levels of the investigated Balmer lines are mainly populated from the ground level. By numerical solution of a system of rate equations describing the change of the levels a region for the electron temperature 5<T _e <10eV can be specified. Different mechanisms, such as photoionization, ionization by electron impact in a time varying magnetic field, ionizing collisions of high velocity neutral atoms with neutral gas at rest, transport processes in the plasma across the magnetic field, instabilities which may cause the development of the halo, are discussed by means of the experimental results. It is concluded that the halo region is caused by flute instabilities.