Chiral Anomaly and Local Polarization Effect from Quantum Transport Approach

J.H. Gao, Z.T. Liang, S. Pu, Q. Wang, X.N. Wang, PRL 109, 232301(2012)201441823 Outline Introduction Chiral Anomalous Fluid Chiral Anomalous Fluid from Quantum Transport Approach SummaryQuantum Chromo Dynamics

QCD :Quark Confinement:Chiral Symmetry breaking:Asymptotic freedom:

Instanton and Sphaleron Gluon field configuration with topological winding number:

Lepton and baryon number non-conservation Strong CP violationAnomalous fluid in HICHydrodynamics with EM fields:Sphaleron Chirality imbalance:Chiral current:

Hydrodynamic equations with anomalous axial current :

Hydrodynamics with Chiral AnomaliesHydrodynamic Equation with Anomalies :

D.T. Son, P. Surowka PRL103:191601,2009 Requiring,

The new kinetic coefficients can be fixed uniquely:

From one current to two currents: Requiring S. Pu, J.H. Gao, Q. W. PRD83:094017,2011 Hydrodynamics with Chiral Anomalies

CME & CVEChiral magnetic effectChiral vortical effect

+_

STAR collaboration PRL 103 (2009) 251601 K.Fukushma, D.E.Kharzeev, H.J.Warringa PRD78:074033,2008

(A+A 200GeV)Classical transport approach

Gauge invariant Wigner operator:Gauge link

The ensemble average of Wigner operator:Probability density functionQuantum transport approach

Wigner functions

D.Vasak, M.Gyulassy, H. Elze Annals Phys. 173 (1987) 462-492From Macroscopic to MicroscopicWigner equations for massless collisionless particle system in homogeneous background EM field :

Wigner functions can be expanded as :

Quantum Transport EquationsVector parts:Scalar and tensor parts:

In order to find the solutions near the equilibrium, we can expand and in powers of and Perturbative Expansion SchemeThe equations can be solved in a very consistent iterative scheme !

Iterative equations:

0-th order:1-st order:One more operatorOne more orderThe 0-th Order Solution

The 0-th order solutions take the local equilibrium form:The 0-th order equations::Local flow 4-velocity

The 1-st Order SolutionConsider the local static solutionsThe first order solution can be generally made from

Constraint conditionsfor Vlasov equationEvolution equationsfor ideal fluidsIterative equations:

Chiral Anomaly

All the conservation laws and anomaly can be derived naturally:Integrate over the momentum CME , CVE, LPECME:CVE:

Local polarization effect Reversal chiral magnetic effect

LPE should be present in both high and low energy heavy-ion collisions witheither low baryonic chemical potential and high temperature or vice versa.

Approaches to CME/CVEGauge/Gravity Duality Erdmenger et.al., JHEP 0901,055(2009); Banerjee, et.al., JHEP 1101,094(2011); Torabian and Yee, JHEP 0908,020(2009); Rebhan, Schmitt and Stricher, JHEP1001,026(2010); Kalaydzhyan and Kirsch, et.al, PRL 106,211601(2011) Hydrodynamics with Entropy Principle Son and Surowka, PRL 103,191601(2009); Kharzeev and Yee, PRD 84,045025(2011); Pu,Gao and Wang, PRD 83,094017(2011)Quantum Field Theory Metlitski and Zhitnitsky, PRD 72,045011(2005); Newman and Son, PRD 73, 045006(2006); Lublinsky and Zahed, PLB 684,119(2010); Asakawa, Majumder and Muller, PRC81, 064912(2010);Landsteiner,Megias and Pena-Benitez, PRL 107,021601(2011); Hou, Liu and Ren, JHEP 1105,046(2011); Hou, Liu and Ren PRD86(2012)121703Quantum Kinetic Approach Stephanov and Yin PRL 109,(2012)162001, Son and Yamamoto PRD 87 (2013) 8, 085016;

Chen, Pu, Q.Wang and X.N. Wang, PRL 110 (2013)262301

Summary A consistent iterative scheme to solve quantum transport equations has been set up, in which transport approach, hydro expansion and chiral anomaly are totally consistent with each other.

Induced currents by vorticity and magnetic field are natural results of quantum transport theory.

A local polarization effect due to the vorticity can be expected in non-central heavy ion collisions.

The success of this approach urges us to go further: Non-interacting system Interacting system, QGP First order Second order, Constant EM field Arbitrary EM field