Chiral anomaly, Berry phase, and chiral kinetic theory from worldlines in quantum field theory

Abstract

We outline a novel chiral kinetic theory framework for systematic computations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ion collisions. The real part of the fermion determinant in the QCD effective action is expressed as a supersymmetric world-line action of spinning, colored, Grassmanian point particles in background gauge fields, with equations of motion that are covariant generalizations of the Bargmann-Michel-Telegdi and Wong equations. Berry's phase is obtained in a consistent non-relativistic adiabatic limit. The chiral anomaly, in contrast, arises from the phase of the fermion determinant; its topological properties are therefore distinct from those of the Berry phase. We show that the imaginary contribution to the fermion determinant too can be expressed as a point particle world-line path integral and derive the corresponding anomalous axial vector current. Our results can be used to derive a covariant relativistic chiral kinetic theory including the effects of topological fluctuations that has overlap with classical-statistical simulations of the CME at early times and anomalous hydrodynamics at late times.

Mapping the phases of quantum chromodynamics with beam energy scan

“…During the last several years, such a kinetic chiral kinetic theory has been developed using a variety of approaches, see e.g. [139][140][141][142][143][144][145][146][147][148][149]. Also, several phenomenological attempts to study out-of-equilibrium anomalous chiral transport have been proposed [63,[150][151][152].…”

Structure functions at small x from worldlines: Unpolarized distributions

“…Finally, the world-line approach is ideally suited to address the subtle issues regarding the role of non-perturbative effects at small x [13,14]. In particular, it can potentially provide insight into the role of the chiral anomaly in polarized DIS at small x [64][65][66].…”

“…The first integral therefore has no auxiliary Grassmann integrations 13. For simplicity, we will suppress the indices µ 1 .…”

Relativistic quantum kinetic theory for massive fermions and spin effects

“…Because the hot and dense system produced in heavy-ion collisions expands and cools down very fast, the natural and promising theoretical framework to deal with these novel collective quantum effects is the relativistic quantum kinetic theory (RQKT). In recent years there has been a considerable amount of works and significant progresses on the chiral kinetic theory (CKT), i.e., RQKT for massless fermions [27][28][29][30][31][32][33][34][35][36][37][38]. With the running of the beam energy scan program at RHIC and especially the discovery of global polarization at relatively lower energies [1,2], it becomes indispensable to develop a consistent and practical framework of RQKT to be capable of treating various spin effects mentioned above for massive fermions.The covariant Wigner function formalism is a powerful and systematic quantum kinetic approach [39][40][41][42][43], which is very successful to derive CKT and describe CME and CVE consistently.…”