Chromomagnetic Field Research Articles

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

Gluon and quark contributions to the thermodynamic potential (free energy) of a (2+1)-dimensional QCD model at finite temperature in the background of a constant homogeneous chromomagnetic field H combined with A_0 condensate are calculated. The role of the tachyonic mode in the gluon energy spectrum is discussed. A possibility of the free energy global minimum generation at nonzero values of H and A_0 condensates is investigated.

Analytical properties of the polarization operator and dispersion relations for of a photon in an external non-abelian field

Thresholds of photoproduction of SU(2) color quarks in an external field are determined. Analyticity of the polarization operator in a chromomagnetic field is studied. The dispersion relation for the trace of the polarization operator of a photon with an internal quark loop is derived.

Probing the Nonperturbative Dynamics of Lattice Gauge Theories

We investigate the vacuum dynamics of lattice gauge theories by means of a gaugeinvariant effective action defined through the lattice Schrodinger functional. The vacuum is probed using external background fields. An external constant Abelian chromomagnetic field and an Abelian monopole background field are considered. Numerical simulations have been performed employing APE/Quadrics computers. In the case of the Abelian monopole background field we have simulated the U(1) lattice gauge theory at zero temperature and the SU(2) and SU(3) lattice gauge theories at finite temperature. Introducing a disorder parameter that signals the Abelian monopole condensation in the confined phase, a gaugeinvariant evidence of the monopole condensation in the vacuum has been found. In the case of the external Abelian chromomagnetic background field we performed numerical simulations both at zero and finite temperature. The results suggest that at zero temperature the external field is screened in the continuum limit. On the other hand at finite temperature it seems that confinement is restored by increasing the strength of the applied field.

Probing the nonperturbative dynamics of the SU(2) vacuum

The vacuum dynamics of SU(2) lattice gauge theory is studied by means of a gauge-invariant effective action defined using the lattice Schr\"odinger functional. Numerical simulations are performed both at zero and finite temperature. The vacuum is probed using an external constant Abelian chromomagnetic field. The results suggest that at zero temperature the external field is screened in the continuum limit. On the other hand at finite temperature it seems that confinement is restored by increasing the strength of the applied field.

Stability of large scale chromomagnetic fields in the early universe

It is well known that Yang-Mills theory in vacuum has a perturbative instability to spontaneously form a large scale magnetic field (the Savvidy mechanism) and that a constant field is unstable so that a possible ground state has to be inhomogenous over the non-perturbative scale Λ (the Copenhagen vacuum). We argue that this spontaneous instability does not occur at high temperature when the induced field strength gB ∼ Λ 2 is much weaker than the magnetic mass squared ( g 2 T) 2. At high temperature, oscillations of gauge fields acquire a thermal mass M ∼ gT and we show that this mass stabilizes a magnetic field which is constant over length scales shorter than the magnetic screening length ( g 2 T) −1. We therefore conclude that there is no indication for any spontaneous generation of weak non-abelian magnetic fields in the early universe.

THE EXPULSION OF CHROMOMAGNETIC FIELDS

The time evolution of a classical gauge field configuration of the form of a uniform chromomagnetic field plus an added perturbation propotional to the unstable zero mode in the uniform background is studied numerically by means of the classical lattice field equations. It turns out that the decay process has two distinct stages. In the first stage, the unstable mode grows with time exponentially, as expected from the linearized equations of motion. This stage comes to an end when the magnetic field in the perturbation region reaches zero and reverses direction, making the unstable zero mode stable and vice versa. The second phase is characterized by the oscillation of the magnetic field around the zero value in the region of the initial perturbation and its gradual expulsion from the surrounding region, with the boundaries between the low field region and the high field region moving out at the speed of light. The energy of the vanished magnetic field is converted into the energy of the electric field induced according to Faraday's law.

Nonlinear effects on Nielsen-Olesen instability

We have obtained an analytical solution of the nonlinear Nielsen-Olesen mode, which is known to be linearly unstable. We believe that our solution may be a nonlinear saturated state of the instability. It is different from the flux tube structure of chromomagnetic field as proposed by the Copenhagen group [1-3]. We have reanalysed their calculations, including a term, which they have neglected, and find it consistent with our result.

THERMODYNAMIC POTENTIAL WITH CONDENSATE FIELDS IN AN SU(2) MODEL OF QCD

We calculate the thermodynamic potential of the quark–gluon plasma in an SU(2) model of QCD, taking into account the gluon condensate configuration with a constant A4-potential and a uniform chromomagnetic field H. Within this scheme the interplay of condensate fields, as well as the role of quarks in the possible dynamical stabilization of the system is investigated.

Magnetic and thermodynamic stability of SU(2) Yang-Mills theory

SU(2) Yang-Mills theory at finite extension or, equivalently, at finite temperature is probed by a homogeneous chromomagnetic field. We use a recent modified axial gauge formulation which has the novel feature of respecting the center symmetry in perturbation theory. The characteristic properties of the Z_2-symmetric phase, an extension-dependent mass term and antiperiodic boundary conditions, provide stabilization against magnetic field formation for sufficiently small extension or high temperature. In an extension of this investigation to the deconfined phase with broken center symmetry, the combined constraints of thermodynamic and magnetic stability are shown to yield many of the high temperature properties of lattice SU(2) gauge theory.

UNSTABLE MODES AND CONFINEMENT IN THE LATTICE SCHRÖDINGER FUNCTIONAL APPROACH

We analyze the problem of the Nielsen–Olesen unstable modes in the SU(2) lattice gauge theory by means of a recently introduced gauge-invariant effective action. We perform numerical simulations in the case of a constant Abelian chromomagnetic field. We find that for lattice sizes above a certain critical length, the density of effective action shows a behavior compatible with the presence of the unstable modes. We put out a possible relation between the dynamics of the unstable modes and the confinement.

Finite temperature quark confinement via chromomagnetic fields

A natural mechanism for finite temperature quark confinement arises via the coupling of the adjoint.Polyakov loop to the chromamagnetic field. Lattice simulations and analytical results both support this hypothesis. Finite temperature SU(3) lattice simulations show that a large external coupling to the chromomagnetic field restores confinement at temperatures above the normal deconfining temperature. A one-loop calculation of the effective potential for SU(2) gluons in a background field shows that a constant chromomagnetic field can drive the Polyakov loop to confining behavior, and the Polyakov loop can in turn remove the well-known tachyonic mode associated with gluons in an external chromomagnetic field. For abelian background fields, tachyonic modes are necessary for confinement at one loop.

Temperature dependence of a gluon condensate in a model with a spherically symmetric non-Abelian field

The single-loop approximation is used to calculate a gluon condensate in an external spherically symmetric non-Abelian chromomagnetic field.

Derivative expansion of the effective action in Yang-Mills theory

The effective action model for mesons relies on the one-loop effective action in quantum chromodynamics in the presence of a constant background chromoelectric field in a fixed direction in group space. We extend this effective action so as to include those terms quadratic in the first derivate of the field, for both a chromoelectric and chromomagnetic background field. An instability arises in the chromoelectric case.

Limits on the monopole polarization magnetic field from measurements of the electric dipole moments of atoms, molecules, and the neutron

A radial magnetic field can induce a time invariance violating electric dipole moment (EDM) in quantum systems. The EDMs of the Tl, Cs, Xe and Hg atoms and the neutron that are produced by such a field are estimated. The contributions of such a field to the constants, $\chi$ of the T,P-odd interactions $\chi_e {\bf N} \cdot {\bf s}/s$ and $\chi_N {\bf N} \cdot {\bf I}/I$ are also estimated for the TlF, HgF and YbF molecules (where ${\bf s}$ (${\bf I}$) is the electron (nuclear) spin and ${\bf N}$ is the molecular axis). The best limit on the contact monopole field can be obtained from the measured value of the Tl EDM. The possibility of such a field being produced from polarization of the vacuum of electrically charged magnetic monopoles (dyons) by a Coulomb field is discussed, as well as the limit on these dyons. An alternative mechanism involves chromomagnetic and chromoelectric fields in QCD.

Exploring the unstable modes dynamics by the lattice Schrödinger functional

We analyze the problem of the Nielsen-Olesen unstable modes in the SU (2) lattice gauge theory by means of a recently introduced gauge-invariant effective action. We perform numerical simulations in the case of a constant Abelian chromomagnetic field. We find that for lattice sizes above a certain critical length the density of effective action shows a behaviour compatible with the presence of the unstable modes.

Role of the chromomagnetic vacuum background field in e+e--->2 jets and other reactions.

We propose a new type of a measurement which is sensitive to the QCD vacuum color-magnetic fluctuations: a measure of the axial asymmetry of the hadronic final states produced in the high energy ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ collisions which is related to the chromomagnetic vacuum field strength. \textcopyright{} 1996 The American Physical Society.

Dimensional reduction in Nambu-Jona-Lasinio model in external chromomagnetic field

The effective dimensional reduction of fermion-antifermion pairing dynamics in the Nambu-Jona-Lasinio model in an external chromomagnetic field is considered. It is shown that such a field causes the reduction of the space dimension by one unit in contrast to an ordinary magnetic field which reduces it by two units. The enhancement of the dynamical chiral symmetry breaking due to the reduction is discussed.

Infrared behavior of closed superstrings in strong magnetic and gravitational fields

A large class of four-dimensional supersymmetric ground states of closed superstrings with a non-zero mass gap are constructed. For such ground states we turn on chromo-magnetic fields as well as curvature. The exact spectrum as function of the chromo-magnetic fields and curvature is derived. We examine the behavior of the spectrum, and find that there is a maximal value for the magnetic field H max ∼ M 2 planck. At this value all states that couple to the magnetic field become infinitely massive and decouple. We also find tachyonic instabilities for strong background fields of the order O ( μM planck) where μ is the mass gap of the theory. Unlike the field theory case, we find that such ground states become stable again for magnetic fields of the order O ( M 2 planck). The implications of these results are discussed.

A model for the B → XS + γ decay in the chromomagnetic background

We calculate the shape of the photon spectrum for the B → X S + γ decay in the presence of a background chromomagnetic field for the case of an SU (2) gauge group. The effect of the external field resembles the Zeeman effect — the parton model peak is split into two slightly asymmetric peaks, located around the kinematic endpoint. We investigate the analytic properties of the spectrum and calculate the total decay rate. This decay may serve as a model for the investigation of gluon condensate effects and their influence on the shape of the spectrum.

ON THE POSSIBILITY OF CONSTRUCTING COVARIANT CHROMOMAGNETIC FIELD MODELS

Expressions for SO(4) invariant Euclidean QCD generating functionals are introduced which should produce nonvanishing gluon condensates. We consider first the loop expansion of the corresponding effectíve action searching for a description differing from the usual perturbation theory. At this level, we consider special free propagators which have off-diagonal long range order. The calculation of the polarization tensor leads to a gluon mass term which is proportional to the squared root of the finite value for <G2>. The summation of all the one-loop contributions to the energy having only mass insertions, indicates the spontaneous generation of the condensate from the perturbative ground state in a way resembling the similar effect in the case of chromomagnetic field models.