I review the origin and properties of electromagnetic fields produced in heavy-ion collisions The field strength immediately after a collision is proportional to the collision energy and reaches &#x7e; at RHIC and &#x7e; at LHC I demonstrate by explicit analytical calculation that after dropping by about one-two orders of magnitude during the first fm/c of plasma expansion, it freezes out and lasts for as long as quark-gluon plasma lives as a consequence of finite electrical conductivity of the plasma Magnetic field breaks spherical symmetry in the direction perpendicular to the reaction plane, and therefore all kinetic coefficients are anisotropic I examine viscosity of QGP and show that magnetic field induces azimuthal anisotropy on plasma flow even in spherically symmetric geometry Very strong electromagnetic field has an important impact on particle production I discuss the problem of energy loss and polarization of fast fermions due to synchrotron radiation, consider photon decay induced by magnetic field, elucidate dissociation via Lorentz ionization mechanism, and examine electromagnetic radiation by plasma I conclude that all processes in QGP are affected by strong electromagnetic field and call for experimental investigation

https://downloads.hindawi.com/journals/ahep/2013/490495.pdf

Particle production in strong electromagnetic fields in relativistic heavy-ion collisions

theta dependence of SU(N) gauge theories in the presence of a topological term

I review the origin and properties of electromagnetic fields produced in heavy ion collisions. The field strength immediately after a collision is proportional to the collision energy and reaches eB\sim(m_\pi)^2 at RHIC and eB\sim10 (m_\pi)^2 at LHC. I demonstrate by explicit analytical calculation that after dropping by about one-two orders of magnitude during the first fm/c of plasma expansion, it freezes out and lasts for as long as quark-gluon plasma exists as a consequence of finite electrical conductivity of the plasma. Magnetic field breaks spherical symmetry in the direction perpendicular to the reaction plane and therefore all kinetic coefficients are anisotropic. I examine viscosity of QGP and show that magnetic field induces azimuthal anisotropy on plasma flow even in spherically symmetric geometry. Very strong electromagnetic field has an important impact on particle production. I discuss the problem of energy loss and polarization of fast fermions due to synchrotron radiation, consider photon decay induced by magnetic field, elucidate J/Psi dissociation via Lorentz ionization mechanism and examine electromagnetic radiation by plasma. I conclude that all processes in QGP are affected by strong electromagnetic field and call for experimental investigation.

We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief discussion of spontaneous symmetry breaking and the role of a magnetic field in its a dynamics. This is followed by a detailed presentation of the essential features of the phenomenon. In particular, we emphasize that the dimensional reduction plays a profound role in the pairing dynamics in a magnetic field. Using the general nature of underlying physics and its robustness with respect to interaction types and model content, we argue that magnetic catalysis is a universal and model-independent phenomenon. In support of this claim, we show how magnetic catalysis is realized in various models with short-range and long-range interactions. We argue that the general nature of the phenomenon implies a wide range of potential applications: from certain types of solid state systems to models in cosmology, particle and nuclear physics. We finish the review with general remarks about magnetic catalysis and an outlook for future research.

Magnetic Catalysis: A Review

https://www.springer.com/cda/content/document/cda_downloaddocument/9783642373046-c2.pdf?SGWID=0-0-45-1393306-p175064717

The one-loop quark contribution to the QCD effective potential for the homogeneous Abelian gluon field in the presence of an external strong electromagnetic field is evaluated. The structure of extrema of the potential as a function of the angles between chromoelectric, chromomagnetic, and electromagnetic fields is analyzed. In this setup, the electromagnetic field is considered as an external one while the gluon field represents domain structured nonperturbative gluon configurations related to the QCD vacuum in the confinement phase. Two particularly interesting gluon configurations, (anti-)self-dual and crossed orthogonal chromomagnetic and chromoelectric fields, are discussed specifically. Within this simplified framework it is shown that the strong electromagnetic fields can play a catalyzing role for a deconfinement transition. At the qualitative level, the present consideration can be seen as a highly simplified study of an impact of the electromagnetic fields generated in relativistic heavy ion collisions on the strongly interacting hadronic matter.

Impact of the strong electromagnetic field on the QCD effective potential for homogeneous Abelian gluon field configurations

An approach to QCD vacuum as a medium describable in terms of a statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is briefly reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral $S{U}_{\mathrm{L}}({N}_{f})\ifmmode\times\else\texttimes\fi{}S{U}_{\mathrm{R}}({N}_{f})$ and ${U}_{A}(1)$ symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic, and weak interactions of mesons are represented in the action in terms of nonlocal $n$-point interaction vertices given by the quark-gluon loops averaged over the background ensemble. New systematic results for the mass spectrum and decay constants of radially excited light, heavy-light mesons, and heavy quarkonia are presented. The interrelation between the present approach, models based on ideas of soft-wall anti--de Sitter/QCD, light-front holographic QCD, and the picture of harmonic confinement is outlined.

Regge spectra of excited mesons, harmonic confinement and QCD vacuum structure

A qualitative mechanism for the emergence of domain structured background gluon fields due to singularities in gauge field configurations is considered, and a model displaying a type of mean field approximation to the QCD partition function based on this mechanism is formulated. Estimation of the vacuum parameters (gluon condensate, topological susceptibility, string constant and quark condensate) indicates that domain-like structures lead to an area law for the Wilson loop, nonzero topological susceptibility and spontaneous breakdown of chiral symmetry. Gluon and ghost propagators in the presence of domains are calculated explicitly and their analytical properties are discussed. The Fourier transforms of the propagators are entire functions and thus describe confined dynamical fields.

/pdf/confinement-and-chiral-symmetry-breaking-via-domainlike-46u75j29up.pdf

Confinement and chiral symmetry breaking via domainlike structures in the QCD vacuum

The ensemble of Euclidean gluon field configurations represented by the domain wall network is considered. A single domain wall is given by the sine-Gordon kink for the angle between chromomagnetic and chromoelectric components of the gauge field. The domain wall separates the regions with Abelian self-dual and anti-self-dual fields. The network of the domain wall defects is introduced as a combination of multiplicative and additive superpositions of kinks. The character of the spectrum and eigenmodes of color-charged fluctuations in the presence of the domain wall network is discussed. Conditions for the formation of a stable thick domain wall junction (the chromomagnetic trap) during heavy-ion collisions are discussed, and the spectrum of color-charged quasi-particles inside the trap is evaluated. An important observation is the existence of the critical size $ L_{c}$ of a single trap stable against gluon tachyonic modes. The size $ L_{c}$ is related to the value of gluon condensate $ \langle g^{2} F^{2}\rangle$. The growth of large lumps of merged chromomagnetic traps and the concept of the confinement-deconfinement transition in terms of the ensemble of domain wall networks are outlined.

Domain wall network as QCD vacuum and the chromomagnetic trap formation under extreme conditions

The domain model for the QCD vacuum has previously been developed and shown to exhibit confinement of quarks and strong correlation of the local chirality of quark modes and duality of the background domain-like gluon field. Quark fluctuations satisfy a chirality violating boundary conditions parametrized by a random chiral angle $\alpha_j$ on the $j-th$ domain. The free energy of an ensemble of $N\to\infty$ domains depends on $\{\alpha_j, j=1... N\}$ through the logarithm of the quark determinant. Its parity odd part is given by the axial anomaly. The anomaly contribution to the free energy suppresses continuous axial U(1) degeneracy in the ground state, leaving only a residual axial Z(2) symmetry. This discrete symmetry and flavour $SU(N_f)_L\times SU(N_f)_R$ chiral symmetry in turn are spontaneously broken with a quark condensate arising due to the asymmetry of the spectrum of Dirac operator. In order to illustrate the splitting between the $\eta'$ from octet pseudoscalar mesons realised in the domain model, we estimate the masses of light pseudoscalar and vector mesons.

/pdf/realization-of-chiral-symmetry-in-the-domain-model-of-qcd-3jjmcuoq2h.pdf

Sergei N. Nedelko

Papers

Impact of the strong electromagnetic field on the QCD effective potential for homogeneous Abelian gluon field configurations

Regge spectra of excited mesons, harmonic confinement and QCD vacuum structure

Confinement and chiral symmetry breaking via domainlike structures in the QCD vacuum

Domain wall network as QCD vacuum and the chromomagnetic trap formation under extreme conditions

Realization of chiral symmetry in the domain model of QCD