The spontaneous generation of magnetic fields at high temperature in a supersymmetric theory

The spontaneous generation of magnetic and chromomagnetic fields at high temperature in the minimal supersymmetric standard model is investigated. The consistent effective potential including the one-loop and the daisy diagrams of all bosons and fermions is calculated and the magnetization of the vacuum is observed. The mixing of the generated fields due to the quark and s-quark loop diagrams and the role of superpartners are studied in detail. It is found that the contribution of these diagrams increases the magnetic and chromomagnetic field strengths as compared with the case of a separate generation of fields. The magnetized vacuum state is found to be stable due to the magnetic masses of gauge fields included in the daisy diagrams. Applications of the results obtained are discussed. A comparison with the standard model case is given. Received: 18 October 2002 / Revised version: 23 December 2002 / Published online: 3 March 2003 RID="a" ID="a" e-mail: vadimdi@yahoo.com RID="b" ID="b" e-mail: skalozub@ff.dsu.dp.ua     

On the generation of Abelian magnetic fieldsin SU(3) gluodynamics at high temperature

The vacuum state of SU(3) gluodynamics at high temperature is investigated. A consistent approach including the calculation of the spontaneously generated constant chromomagnetic isotopic H₃ and hypercharge H₈ fields and the polarization operator of charged gluons in this background is applied. It is shown within the effective potential, taking into consideration the one-loop plus daisy diagrams, that the specific values of the fields yield a global minimum to the free energy. The spectrum of the transversal charged modes is stable at high temperature due to the calculated gluon magnetic mass which accounts for the fields. This leads to stable chromomagnetic fields in the deconfinement phase of QCD. A comparison with results of other approaches is made.Received: 10 September 2003, Revised: 4 December 2003, Published online: 29 January 2004     

Chromomagnetic catalysis of color superconductivity

The effect of an external chromomagnetic field on the phase structure of the extended Nambu-Jona-Lasinio model with two quark flavors is examined. It is shown that, depending on the relationship between the quark coupling constants in the q? and qq channels, chromomagnetic fields of certain types induce spontaneous breaking of chiral, color, or both symmetries simultaneously.     

Quark and pion condensation in a chromomagnetic background field

The general features of quark and pion condensation in dense quark matter with flavor asymmetry have been considered at finite temperature in the presence of a chromomagnetic background field modeling the gluon condensate. In particular, pion condensation in the case of a constant abelian chromomagnetic field and zero temperature has been studied both analytically and numerically. Under the influence of the chromomagnetic background field the effective potential of the system is found to have a global minimum for a finite pion condensate even for small values of the effective quark coupling constant. In the strong field limit, an effective dimensional reduction has been found to take place.     

Pion condensation in a medium with massive quarks in the external chromomagnetic field

Pion condensation in a flavor-asymmetric quark medium with massive quarks in the external chromomagnetic field is considered. It is shown that the external field catalyzes pion condensation while the finite quark mass does not impede the onset of this phenomenon.     

Pion condensation in a medium with massive quarks in an external spherically symmetrical non-Abelian chromomagnetic field

We consider pion condensation in a flavor asymmetric quark medium with massive quarks in the external spherically symmetric non-Abelian chromomagnetic field. It is shown that the external field is a catalyzing factor for the occurrence of pion condensation, while the finite quark masses prevent the emergence of this phenomenon.     

Magnetic fields boosted by gluon vortices in color superconductivity

We investigate the effects of an external magnetic field in the gluon dynamics of a color superconductor with three massless quark flavors. In the framework of gluon mean-field theory at asymptotic densities, we show that the long-range component H[over ] of the external magnetic field that penetrates the color-flavor locked phase produces an instability when its strength becomes larger than the Meissner mass of the charged gluons. As a consequence, the magnetic field causes the formation of a vortex state characterized by the condensation of charged gluons and the creation of magnetic flux tubes. Inside the flux tubes, the magnetic field is stronger than the applied one. This antiscreening effect is connected to the anomalous magnetic moment of the gluon field. We suggest how this same mechanism could serve to remove the chromomagnetic instabilities existing in gapless color superconductivity.     

Photon polarization operator and quantum transitions in QCD vacuum

The analytical properties of the photon polarization operator in the quark vacuum was analyzed. Branching points of the polarization operator were found and its imaginary part was calculated. Quantum transitions between quark states and the turning over of a quark's color spin in a chromomagnetic field were predicted. The negative values of the photon energy and the contribution of the photon zero energy to the branching point were taken into account Received: 20 July 2000 / Published online: 21 December 2000     

Cooper pairs? magnetic moment in MCFL color superconductivity

We investigate the effect of the alignment of the magnetic moments of Cooper pairs of charged quarks that form at high density in three-flavor quark matter. The high-density phase of this matter in the presence of a magnetic field is known to be the Magnetic Color-Flavor-Locked (MCFL) phase of color superconductivity. We derive the Fierz identities of the theory and show how the explicit breaking of the rotational symmetry by the uniform magnetic field opens new channels of interactions and allows the formation of a new diquark condensate. The new order parameter is a spin-1 condensate proportional to the component in the field direction of the average magnetic moment of the pairs of charged quarks. The magnitude of the spin-1 condensate becomes comparable to the larger of the two scalar gaps in the region of large fields. The existence of the spin-1 condensate is unavoidable, as in the presence of a magnetic field there is no solution of the gap equations with nonzero scalar gaps and zero magnetic moment condensate. This is consistent with the fact that the extra condensate does not break any symmetry that has not already been broken by the known MCFL gaps. The spin-1 condensate enhances the condensation energy of pairs formed by charged quarks and the magnetization of the system. We discuss the possible consequences of the new order parameter on the issue of the chromomagnetic instability that appears in color superconductivity at moderate density.     

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.     

Color superconducting matter in a magnetic field

We investigate the effect of a magnetic field on cold dense quark matter using an effective model with four-Fermi interactions. We find that the gap parameters representing the predominant pairing between the different quark flavors show oscillatory behavior as a function of the magnetic field. We point out that due to electric and color neutrality constraints the magnetic fields as strong as presumably existing inside magnetars might induce significant deviations from the gap structure at a zero magnetic field.     

Chromomagnetism in Nuclear Matter

Quarks are color charged particles. Due to their motion there is a strong possibility of generation of color magnetic field. It is shown that however hadrons are color singlet particles they may have non-zero color magnetic moment. Due to this color magnetic moment hadrons can show color interaction. In this paper we have studied the chromomagnetic properties of nuclear matter.     

Quark-Gluon Interactions at High Temperature and Large Distances

Continuum fourdimensional Quantum Chromodynamics (QCD) including quarks in the regime of high temperature and large distances (the HT regime) is studied to all perturbative orders. The imaginary time (τ) formalism is used. Then, as shown in previous works, QCD is described by a new generating functional Z_HT, in which quark fields retain their dependences on τ, while gluon and ghost fields are τ-independent. The invariance of Z_HT under BRST transformations in the HT regime is exhibited: it closed quark and electric gluon loops in the HT regime are obtained. The electric mass terms in Z_HT. Infinite sets of non-abelian Ward identities for the closed quark and electric gluon loops in the HT regime are obtained. The electric mass terms in Z_HT are shown to be infrared finite. We prove to all perturbative orders that one can regard as subdominant, and, hence, neglect consistently the contributions of :i) all closed electric gluon loops, ii) all closed quark loops with three or more vertices in diagrams having an even number of electric gluons (or none) in the external lines. In the HT regime, the axial anomalies are obtained: their expressions in terms of τ-independent gluon fields are similar to those for zero temperature. A non-trivial renormalization group (RG) equation in the HT regime, specifically due to the quark-gluon interaction, is presented. A positive beta function is obtained, and it is argued that interactions are not weak in that regime. The RG and the perturbative analysis to all orders appear to indicate that quarks and gluons may be confined in the HT regime (and, in particular in the Early Universe), due to the infrared divergent magnetic gluon sector. Other possibilities are also discussed.     

Investigation of the helicity of magnetic fields on the Sun within the Parker dynamo model

Construction of the butterfly diagrams for the magnetic helicity in several approximations of a Parker dynamo has been carried out. The diagrams are constructed both for the cases of efficient generation of the magnetic field (large dynamo numbers) and for the weak generation (a small dynamo number). The corresponding asymptotic solution to the solar dynamo is used in the first case. The butterfly diagrams for different values of the meridional circulation were studied due to this solution. The butterfly diagrams are constructed and based on the few-mode approximation, which is valid for moderate dynamo numbers. The issue of which butterfly diagram features are common in all these approximations and can be compared with observational data is discussed.     

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. M. E. Rasulzade Baku State University; M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 11–16, June, 2000.     

Quark matter influence on observational properties of compact stars

Densities in compact stars may be such that quarks are no longer confined in hadrons, but instead behave as weakly interacting particles. In this regime perturbative calculations are possible. Yet, due to high pressures and an attractive channel in the strong force, condensation of quarks in a superfluid state is likely. This can have interesting consequences for magnetic fields, especially in relation to the discovery of slow-period free precession in a compact star. In this proceedings there will be a discussion of the mass-radius relations of compact stars made from quark matter and magnetic field behaviour in compact stars with a quark matter core.     

Quark condensates in non-Abelian fields at finite temperature

The properties of quark condensates in static non-Abelian fields of the chromomagnetic types are investigated. The dependence of the condensate on the field strength and the temperature is discussed. It is shown that the principal term of the asymptotic expansion for all the investigated field types has the form v^–2 in the high-temperature limit. An expansion is obtained for the quantity in the limit of an arbitrary, uniform, weak field for T=0 and at finite temperature.M. V. Lomonosov State University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 39–52, January, 1994.     

Neutron star in the presence of strong magnetic field

Compact stars such as neutron stars (NS) can have either hadronic or exotic states like strange quark or colour superconducting matter. Stars can also have a quark core surrounded by hadronic matter, known as hybrid stars (HS). The HS is likely to have a mixed phase in between the hadron and the quark phases. Observational results suggest huge surface magnetic field in certain NS. Therefore, we study here the effect of strong magnetic field on the respective equation of states (EOS) of matter under extreme conditions. We further study the hadron–quark phase transition in the interiors of NS giving rise to HS in the presence of strong magnetic field. The hadronic matter EOS is described based on RMF theory and we include the effects of strong magnetic fields leading to Landau quantization of the charged particles. For quark phase, we use the simple Massachusetts Institute of Technology (MIT) bag model, assuming density-dependent bag pressure and magnetic field. The magnetic field strength increases from the surface to the centre of the star. We construct the intermediate mixed phase using Glendenning conjecture. The magnetic field softens the EOS of both the matter phases. We finally study, the mass–radius relationship for such types of mixed HS, calculating their maximum mass, and compare them with the recent observations of pulsar PSR J1614-2230, which is about 2 solarmass.     

Photon polarization operator in an external non-Abelian field

The contribution of massive spin-0, isospin-1/2 particles to the photon polarization operator in the background non-Abelian constant field is calculated. We have considered the spherically symmetric chromomagnetic field B _a ⁱ =λδ _a ⁱ . Such model vacuum is shown to be gyrotropic in spite of the fact that it is stable with respect to creation of pairs of real particles. At large Euclidean photon momentum the leading power term in the polarization operator is exactly determined by the value of scalar quark condensate. Its contribution to the scale-breaking correction to the deep inelastic scattering cross-section is also calculated in the paper. The gauge- and Lorentz-invariant averaging of the polarization operator over the ensemble of vacuum fields of various orientations is performed.     

Testing the chiral magnetic effect with central U+U collisions

A quark interaction with topologically nontrivial gluonic fields, instantons and sphalerons, violates P and CP symmetry. In the strong magnetic field of a noncentral nuclear collision such interactions lead to the charge separation along the magnetic field, the so-called chiral magnetic effect (CME). Recent results from the STAR collaboration on charge dependent correlations are consistent with theoretical expectations for CME but may have contributions from other effects, which prevents definitive interpretation of the data. Here I propose to use central body-body U+U collisions to disentangle correlations due to CME from possible background correlations due to elliptic flow. Further, more quantitative studies can be performed with collision of isobaric beams.