chiral kinetic theory for quark matter 高建华 山东大学(威海) j.h. gao and q. wang,...
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Chiral Kinetic Theory for Quark Matter
高建华
山东大学(威海)
J.H. Gao and Q. Wang, arXiv:1504.07334J.H. Gao, Z.T. Liang, S. Pu, Q. Wang and X.N. Wang, PRL 109, 232301(2012)
“2015手征有效场论研讨会”, 2015年 8月 14日 -18日,山东威海
Outline• Introduction• Vector and Axial Currents Induced by
Magnetic fields and Vorticity• Magnetic Moment and Spin-Vorticity Coupling of Chiral Fermions• Summary
Quantum Chromo Dynamics
QCD :
Quark Confinement:
Chiral Symmetry breaking:
Asymptotic freedom:
Instanton & Sphaleron Gluon field configuration with topological winding number:
PRD 28,2019; PRD 30,2212; PLB 155,36; PRD 36,581; NPB 308,885; PRD 37,1020; PRD 43,2027; PLB 326,118 …
CME & CVE
Chiral Magnetic Effect (CME) Chiral Vortical Effect (CVE)
Strong magnetic fields:
Chirality imbalance:
Large OAM:A+A 200GeV
PRD22,3080(1980);78:074033(2008);NPA803,227 PRL106, 062301(2011); PRL109, 232301(2012)
Approaches to CME/CVE
• Gauge/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)121703……
• Quantum 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, J.Y. Chen, Son and Stephanov PRL115, 021601 (2015)
Classical transport theory:
Wigner Functions
Wigner operator for the spin-1/2 fermion is given by:
Gauge link
The ensemble average of Wigner operator:
Probability density function
Quantum transport theory: Wigner functions
D.Vasak, M.Gyulassy, H. Elze Annals Phys. 173 (1987) 462-492
The equation satisfied by Wigner operator or function:
Wigner equations for massless collisionless particle system in constant EM field:
Wigner functions can be expanded as :
Quantum Transport Equations
Vector and axial vector parts: Scalar, pseudoscalar and tensor parts:
Rewrite Wigner equations by left-hand (s= +1) and right-hand (s= -1) parts
Perturbative Expansion Scheme
The equations can be solved in a very consistent iterative scheme !
Iterative Equation:
One more operator One more order
Derivative and weak field expansion:
The Solution up to the First Order
The 0-th order solutions take the local equilibrium form:
The 0-th order equations:
:Local flow 4-velocity
The first order solution can be given by :
:Temperature
Currents and Energy-Momentum Tensor
All the conservation laws and anomaly can be derived naturally:
Integrate over the momentum
Recall:
CME , CVE, CSE and LPE
CME: CVE:
Local polarization effect:
Chiral separation effect:
LPE should be present in both high and low energy heavy-ion collisions!
STAR collaboration PRL 103 (2009) 251601
Azimuthal Charged-Particle Correlations
Chiral Magnetic Effect
+_
PRD22,3080(1980);78:074033(2008) NPA803,227
Chiral vorticity effect:
Chiral Vorticity Effect
PRL106, 062301(2011); PRL109, 232301(2012)
Consider 3-flavor quark matter (u,d,s), Electric current:
Baryon current:
Chiral Magnetic Conductivity
Chiral Magnetic Conductivity:
HTL/HDL results from chiral kinetic theory:
PRD87,034028(2009), NPB337,569(1990), JHEP0510,056(2005), PRD89,096002(2013)
Wigner equations for massless collisionless system in arbitrary EM field:
Wigner Functions in Arbitrary EM Fields
Triangle Operator:
only act on EM fields
Wigner function Decomposition:
Spherical Bessel Functions
Left-hand (s= +1) and right-hand (s= -1) parts
Linear Response Theory for Wigner Functions
Weak Field Approximation:
Zero-th Order Equation:
Linear Response Theory for Wigner Functions
The first Order Equation:
Formal solution:
Parity –odd part of the Wigner function in momentum space:
Chiral Magnetic Conductivity
HTL / HDL result:
Induced currents:
Chiral Magnetic or Parity –odd Conductivity:
Energy Shift and Magnetic Moment
Effective Energy of Chiral Fermion:
Spin Vector:
Energy Shift:
Magnetic moment of massless fermion:
Son and Yamamoto, PRD87,085016(2013) Gao and Wang 1504.07334
Energy Shift and Magnetic Moment I
Particle density with :
Phase-space measure with the Berry curvature:
Effective energy: Berry curvature
Energy shift: Magnetic moment
Energy Shift and Magnetic Moment IIEnergy density with :
Phase-space measure with the Berry curvature:
Effective energy: Berry curvature
Energy shift: Magnetic moment
Energy Shift from Spin-Vorticity CouplingParticle density and energy density with :
Effective energy:
Energy shift: Spin vector
Summary• A consistent iterative scheme to solve Wigner
equations has been set up.• Wigner functions can describe CME, CVE, LPE,
magnetic energy shift and spin-vorticity coupling in a very consistent way,
• Up to now, it is the only chiral kinetic approach that could give the result of one-loop parity-odd conductivity.
• All these successes demonstrate that Wigner functions capture comprehensive aspects of physics for chiral fermions in EM fields.
• More interesting results are expected from Wigner functions.
Thanks for your attention!