Chiral Anomaly and Local Polarization Effect from the Quantum Kinetic Approach

Abstract

A power expansion scheme is set up to determine the Wigner function that satisfies the quantum kinetic equation for spin-1/2 charged fermions in a background electromagnetic field. Vector and axial-vector current induced by magnetic field and vorticity are obtained simultaneously from the Wigner function. The chiral magnetic and vortical effect and chiral anomaly are shown as natural consequences of the quantum kinetic equation. The axial-vector current induced by vorticity is argued to lead to a local polarization effect along the vorticity direction in heavy-ion collisions.PACS numbers: 25.75. Nq, 12.38.Mh, 13.88.+e Introduction. -Chiral anomaly is an important quantum effect which is absent at the classical level. Recently it has been shown that such a microscopic quantum effect can have a macroscopic impact on the dynamics of relativistic fluids, termed as the chiral magnetic and vortical effect (CME and CVE) [1][2][3] as manifested in currents induced by magnetic field and vorticity. Such effects and related topics have been investigated within a variety of approaches, such as AdS/CFT duality [4][5][6][7][8], relativistic hydrodynamics [9][10][11], and quantum field theory [2,[12][13][14][15][16][17]. However, it is still not clear how CME and CVE can emerge from a microscopic quantum kinetic theory.In this Letter we make a first attempt to derive both the CME and CVE from a quantum kinetic theory. A power expansion in space-time derivatives and weak external fields is used to determine the analytic form of vector and axial-vector components of the Wigner function that satisfies the quantum kinetic equation for spin-1/2 massless fermions. The CME and CVE appear naturally in the induced currents. Chiral anomaly and other conservation laws are also automatically satisfied. The axialvector current induced by vorticity depends quadratically on the temperature, baryonic and chiral chemical potential. So it should be present in both hot and dense matter, and can lead to a local polarization effect in heavy-ion collisions as proposed in earlier studies [18][19][20]. This provides another possible future experimental measurement of the CVE in high-energy heavy-ion collisions.The quantum kinetic approach can provide a bridge between the microscopic and macroscopic description of the CME and CVE and should be more suitable for future simulations of both effects in heavy-ion collisions. The power expansion method can also be applied to the calculation of other transport coefficients.

(Non)-renormalization of the chiral vortical effect coefficient

“…at strong coupling) coincides with its value at zero coupling, suggesting coupling-constant independence (For a different approach based on kinetic theory see [10]). In a theory with a single fermion of right-handed chirality, C 1 = 1/12.…”

Polarization of massive fermions in a vortical fluid

“…In other words, the axial current in a three-flavor quark matter is blind to the magnetic field and solely induced by the vorticity. Such an axial current leads to the Local Polarization Effect [19] which is also connected to the spin-vorticity coupling for chiral or massless fermions [20].…”

Hyperons polarization in heavy-ion collisions

“…The mechanism analogous to CVE (known as axial vortical effect, see [4] and references therein) leads to induced axial current of strange quarks which may be converted to polarization of Λ-hyperons [3,5,6]. Another mechanism of this polarization is provided by so-called thermal vorticity in the hydrodynamical approach [7].…”