Harmen J. Warringa

The Effects of topological charge change in heavy ion collisions: 'Event by event P and CP violation'

Abstract Quantum chromodynamics (QCD) contains field configurations which can be characterized by a topological invariant, the winding number Q w . Configurations with non-zero Q w break the charge-parity ( CP ) symmetry of QCD. We consider a novel mechanism by which these configurations can separate charge in the presence of a background magnetic field—the “chiral magnetic effect”. We argue that sufficiently large magnetic fields are created in heavy ion collisions so that the chiral magnetic effect causes preferential emission of charged particles along the direction of angular momentum. Since separation of charge is CP -odd, any observation of the chiral magnetic effect could provide a clear demonstration of the topological nature of the QCD vacuum. We give an estimate of the effect and conclude that it might be observed experimentally.

Chiral magnetic effect

Topological charge changing transitions can induce chirality in the quark-gluon plasma by the axial anomaly. We study the equilibrium response of the quark-gluon plasma in such a situation to an external magnetic field. To mimic the effect of the topological charge changing transitions we will introduce a chiral chemical potential. We will show that an electromagnetic current is generated along the magnetic field. This is the chiral magnetic effect. We compute the magnitude of this current as a function of magnetic field, chirality, temperature, and baryon chemical potential.

Chiral magnetic conductivity

Gluon field configurations with nonzero topological charge generate chirality, inducing P- and CP-odd effects. When a magnetic field is applied to a system with nonzero chirality, an electromagnetic current is generated along the direction of the magnetic field. The induced current is equal to the chiral magnetic conductivity times the magnetic field. In this article we will compute the chiral magnetic conductivity of a high-temperature plasma for nonzero frequencies. This allows us to discuss the effects of time-dependent magnetic fields, such as produced in heavy ion collisions, on chirally asymmetric systems.

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.

Real-Time Dynamics of the Chiral Magnetic Effect

In quantum chromodynamics, a gauge field configuration with nonzero topological charge generates a difference between the number of left- and right-handed quarks. When a (electromagnetic) magnetic field is added to this configuration, an electromagnetic current is induced along the magnetic field; this is called the chiral magnetic effect. We compute this current in the presence of a color-flux tube possessing topological charge, with a magnetic field applied perpendicular to it. We argue that this situation is realized at the early stage of relativistic heavy-ion collisions.

Electric-current Susceptibility and the Chiral Magnetic Effect

Abstract We compute the electric-current susceptibility χ of hot quark–gluon matter in an external magnetic field B. The difference between the susceptibilities measured in the directions parallel and perpendicular to the magnetic field is ultraviolet-finite and given by χ ∥ − χ ⊥ = V T N c ∑ f q f 2 | q f B | / ( 2 π 2 ) , where V denotes the volume, T the temperature, N c the number of colors, and q f the charge of a quark of flavor f. This non-zero susceptibility difference acts as a background to the Chiral Magnetic Effect, i.e. the generation of electric current along the direction of magnetic field in the presence of topological charge. We propose a description of the Chiral Magnetic Effect that takes into account the fluctuations of electric current quantified by the susceptibility. We find that our results are in agreement with recent lattice QCD calculations. Our approach can be used to model the azimuthal dependence of charge correlations observed in heavy ion collisions.

Dynamics of the Chiral Magnetic Effect in a weak magnetic field

We investigate the real-time dynamics of the chiral magnetic effect in quantum electrodynamics (QED) and quantum chromodynamics (QCD). We consider a field configuration of parallel (chromo)electric and (chromo)magnetic fields with a weak perpendicular electromagnetic magnetic field. The chiral magnetic effect induces an electromagnetic current along this perpendicular magnetic field, which we will compute using linear response theory. We discuss specific results for a homogeneous sudden switch-on and a pulsed (chromo)electric field in a static and homogeneous (chromo)magnetic field. Our methodology can be easily extended to more general situations. The results are useful for investigating the chiral magnetic effect with heavy ion collisions and with lasers that create strong electromagnetic fields. As a side result we obtain the rate of chirality production for massive fermions in parallel electric and magnetic fields that are static and homogeneous.

Implications of {\cal C}{\cal P} -violating transitions in hot quark matter on heavy-ion collisions

Quantum chromodynamics (QCD) predicts that topological charge changing transitions will take place in hot quark matter. Such transitions induce - and -violating effects. We will show that in the presence of a magnetic field these transitions can separate quarks according to their electric charge along the direction of the magnetic field. This is the so-called chiral magnetic effect. We will argue that it might be possible to observe the chiral magnetic effect in heavy-ion collisions.

Thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions

The thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, only the minimum of the effective potential can be rendered finite by temperature-independent renormalization. To obtain a finite effective potential away from the minimum requires an arbitrary choice of prescription, which implies that the temperature dependence is ambiguous. We show that the problem is linked to thermal infrared renormalons.

Pion condensation in a dense neutrino gas

We argue that using an equilibrated gas of neutrinos it is possible to probe the phase diagram of QCD for finite isospin and small baryon chemical potentials. We discuss this region of the phase diagram in detail and demonstrate that for large enough neutrino densities a Bose–Einstein condensate of positively charged pions arises. Moreover, we show that for non-zero neutrino density the degeneracy in the lifetimes and masses of the charged pions is lifted.