Pseudoscalar condensation induced by chiral anomaly and vorticity for massive fermions

Abstract

We derive the pseudoscalar condensate induced by anomaly and vorticity from the Wigner function for massive fermions in homogeneous electromagnetic fields. It has an anomaly term and a forcevorticity coupling term. As a mass effect, the pseudoscalar condensate is linearly proportional to the fermion mass in small mass expansion. By a generalization to two-flavor and three-flavor cases, the neutral pion and eta meson condensates are calculated from the Wigner function and have anomaly parts as well as force-vorticity parts, in which the anomaly part of the neutral pion condensate is consistent to the previous result. We also discuss about possible observables of the condensates in heavy ion collisions such as collective flows of neutral pions and eta mesons which may be influenced by the electromagnetic field and vorticity profiles.

Relativistic hydrodynamics for spin-polarized fluids

“…The 4×4 matrices ± in Eqs. (30) and (31) are defined as products of the relativistic Boltzmann distributions (Jüttner distributions [60]) and matrices ± , namely…”

“…In the present work, by discussing the quantum kinetic equation in the semi-classical expansion and by developing the hydrodynamic framework with a classical treatment of spin, we eventually conclude on the applicability range of Eqs. (30) and (31). Nonetheless, before concluding on this issue, we develop a formalism based on Eqs.…”

“…Nonetheless, before concluding on this issue, we develop a formalism based on Eqs. (30) and (31), as this allows us to build a necessary theoretical scheme and to introduce relevant definitions and concepts.…”

“…Theoretical studies analyzing the spin polarization and vorticity formation in heavy-ion collisions include several highly debated topics: the importance of the spin-orbit coupling [22,23], global equilibrium with a rigid rotation [24,25,26,27], kinetic models of spin dynamics [28,29,30,31], anomalous hydrodynamics [32,33], the Lagrangian formulation of hydrodynamics [34,35,36,37] and hydrodynamic treatment of the spin tensor using holographic techniques [38].…”

Wigner function approach to polarization-vorticity coupling and hydrodynamics with spin

“…Recent measurements of the Λ-hyperon spin polarization in heavy-ion collisions by the STAR experiment [1,2] have inspired a broad interest in the theoretical studies related to spin polarization and vorticity formation. The results of various investigations that refer to: the spin-orbit coupling [3,4,5,6,7], statistical properties of matter in global equilibrium [8,9,10,11,12,13], kinetic models of spin dynamics [14,15,16,17], hydrodynamics with triangle anomalies [18,19] and the Lagrangian formulation of hydrodynamics [20,21,22] have been reported in this context.…”