Topologically induced local P and CP violation in QCD x QED

TL;DR

The work addresses local P- and CP-odd phenomena arising from QCD topological fluctuations in strong electromagnetic fields by formulating Maxwell-Chern-Simons (axion) electrodynamics with a space-time dependent $\theta$. It derives the chiral magnetic effect as a current $\mathbf{J} = -\frac{e^2}{2\pi^2}\,\dot{\theta}\,\mathbf{B}$ and analyzes related charge-separation and chiral-vortical effects, including the Witten effect and domain-wall charges. Key results connect domain-wall physics, CME, and CVE to observable signatures in heavy-ion collisions, with lattice and holographic studies supporting the mechanism and STAR reporting charge-dependent azimuthal asymmetries. The findings have significant implications for understanding the QCD vacuum under extreme conditions and motivate further experimental programs to probe parity-odd domains and topological fluctuations in hotspots of hot QCD matter.

Abstract

The existence of topological solutions and axial anomaly open a possibility of P and CP violation in QCD. For a reason that has not yet been established conclusively, this possibility is not realized in strong interactions - the experimental data indicate that a global P and CP violation in QCD is absent. Nevertheless, the fluctuations of topological charge in QCD vacuum, although not observable directly, are expected to play an important role in the breaking of $U_A(1)$ symmetry and in the mass spectrum and other properties of hadrons. Moreover, in the presence of very intense external electromagnetic fields topological solutions of QCD can induce local P- and CP-odd effects in the $SU_c(3)\times U_{em}(1)$ gauge theory that can be observed in experiment directly. Here I show how these local parity-violating phenomena can be described by using the Maxwell-Chern-Simons, or axion, electrodynamics as an effective theory. Local P- and CP- violation in hot QCD matter can be observed in experiment through the "chiral magnetic effect" - the separation of electric charge along the axis of magnetic field. Very recently, STAR Collaboration presented an observation of the electric charge asymmetry with respect to reaction plane in relativistic heavy ion collisions at RHIC.

Figures (6)

• Figure 1: The quarks couple the topological Chern-Simons current to the electromagnetic field through the axial anomaly.
• Figure 2: Magnetic monopole at finite $\theta$ angle acquires an electric charge $\sim e\theta/\pi$ that is localized on the domain wall where the value of $\theta$ changes from zero in the core of the monopole to some value $\theta \neq 0$ away from the monopole (the domain wall is shown by the gray ring) -- the Witten effect Witten:1979ey.
• Figure 3: Charge separation effect -- domain walls that separate the region of $\theta \neq 0$ from the outside vacuum with $\theta = 0$ become charged in the presence of an external magnetic field, with the surface charge density $\sim e \theta/\pi \cdot eB/2\pi$. This induces an electric dipole moment signaling ${\cal P}$ and ${\cal CP}$ violation.
• Figure 4: The chiral magnetic effect -- inside a domain with $\dot\theta \neq 0$ an external magnetic field induces an electric current $\vec{J} \sim e \dot\theta/\pi \cdot e \vec{B}/2\pi$. $\dot \theta \neq 0$ indicates the change of the chiral charge inducing an asymmetry between the left-- and right-- handed fermions inside the domain. Note that the current $\vec{J} \sim \vec{B}$ is absent in Maxwell electrodynamics.
• Figure 5: Dirac cones of the left and right fermions. In the presence of the changing chiral charge there is an asymmetry between the Fermi energies of left and right fermions $\mu_L$ and $\mu_R$: $\mu_L - \mu_R = 2 \mu_5 = 2 \dot \theta$.