Chiral kinetic theory and magnetic effect. Yoshimasa Hidaka (RIKEN)

Transcription

1 Chiral kinetic theory and magnetic effect Yoshimasa Hidaka (RIKEN)

2 What is chiral kinetic theory? Relativistic Boltzmann equation (v µ + v µ F p )f = C[f] widely used in plasma physics Transport coefficient: shear viscosity, etc..

3 What is chiral kinetic theory? Relativistic Boltzmann equation (v µ + v µ F p )f = C[f] widely used in plasma physics Transport coefficient: shear viscosity, etc.. Relativistic Boltzmann equation with quantum anomaly?

4 Anomaly matching and effective theory If UV theory has an anomaly, t Hooft ( 80) IR theory has the same anomaly.

5 Anomaly matching and effective theory If UV theory has an anomaly, t Hooft ( 80) IR theory has the same anomaly. UV theory QCD Chiral anomaly: μ j 3μ 5 = CE B

6 Anomaly matching and effective theory If UV theory has an anomaly, t Hooft ( 80) IR theory has the same anomaly. UV theory QCD Chiral anomaly: μ j 3μ 5 = CE B Effective theory

7 Anomaly matching and effective theory If UV theory has an anomaly, t Hooft ( 80) IR theory has the same anomaly. UV theory QCD Chiral anomaly: μ j 3μ 5 = CE B Effective theory Vacuum Chiral perturbation theory Wess-Zumino term π 0 2γ

8 Anomaly matching and effective theory If UV theory has an anomaly, t Hooft ( 80) IR theory has the same anomaly. UV theory QCD Chiral anomaly: μ j 3μ 5 = CE B Effective theory Vacuum Manybody systems Chiral perturbation theory Wess-Zumino term π 0 2γ Hydrodynamics Anomalous transport Chiral magnetic effect (CME) Chiral vortical effect (CVE) Kinetic theory Berry curvature Equilibrium: CME, CVE Nonequilibrium:?

9 Chiral Kinetic theory H = σ p Son, Yamamoto ( 12) Stephanov, Yin ( 12) cf. Chang and Niu ( 95)

10 Chiral Kinetic theory H = σ p Son, Yamamoto ( 12) Stephanov, Yin ( 12) cf. Chang and Niu ( 95) Hu ± = ± p u ±

11 Chiral Kinetic theory H = σ p Son, Yamamoto ( 12) Stephanov, Yin ( 12) cf. Chang and Niu ( 95) Hu ± = ± p u ± p ψ(t) = e i p t u +

12 Chiral Kinetic theory H = σ p Son, Yamamoto ( 12) Stephanov, Yin ( 12) cf. Chang and Niu ( 95) Hu ± = ± p u ± p ψ(t) e i p t i t dt a pu + a := u + i p u +

13 Chiral Kinetic theory Son, Yamamoto ( 12) Stephanov, Yin ( 12) cf. Chang and Niu ( 95) S = dt( x p + x A p A 0 p a) Action with Berry connection: a := u + i p u +

14 Chiral Kinetic theory Son, Yamamoto ( 12) Stephanov, Yin ( 12) cf. Chang and Niu ( 95) S = dt( x p + x A p A 0 p a) Action with Berry connection: a := u + i p u + x = p + p Ω p = x B + E Ω = p a = p 2p 2

15 Chiral Kinetic theory Son, Yamamoto ( 12) Stephanov, Yin ( 12) Chiral kinetic equation (CKE) ( t + x x + p p )f = 0

16 Chiral Kinetic theory Son, Yamamoto ( 12) Stephanov, Yin ( 12) Chiral kinetic equation (CKE) ( t + x x + p p )f = 0 Current j = p f p + E p fω+b p f p Ω

17 Chiral Kinetic theory Son, Yamamoto ( 12) Stephanov, Yin ( 12) Chiral kinetic equation (CKE) ( t + x x + p p )f = 0 Current j = p f p + E p fω+b p f p Ω

18 Chiral Kinetic theory Son, Yamamoto ( 12) Stephanov, Yin ( 12) Chiral kinetic equation (CKE) ( t + x x + p p )f = 0 Current j = p f p + E p fω+b p f p Ω Anomaly μ j μ = 1 4π 2 E B

19 S = dt( x p + x A p A 0 p a)

20 S = dt( x p + x A p A 0 p a) p p (1 Ω B)

21 S = dt( x p + x A p A 0 p a) p p (1 Ω B) δx = βt+ p β Ω δp = βϵ+ p (β Ω) B

22 Son, Yamamoto ( 12) Stephanov, Yin ( 12) World line formalism: Mueller, Venugopalan ( 17) ( 18) High density effective theory: On-shell effective theory: Wigner function: Son, Yamamoto ( 13) Gao,Liang,Pu,Wang,Wang ( 12), Chen, Pu, Wang, Wang ( 13) CVE: Gao, Pang, Wang ( 18) Kadanoff-Baym: YH, Shi Pu, Yang ( 16) ( 17), YH, Yang ( 18)

23 QFT approach Propagator (Wigner function) S < (p, X) = d 4 se is p ψ (y)ψ(x) U(x, y) S > (p, X) = d 4 se is p ψ(x)ψ (y) U(x, y) where X = x + y 2 s = x y

24 QFT approach Propagator (Wigner function) S < (p, X) = d 4 se is p ψ (y)ψ(x) U(x, y) S > (p, X) = d 4 se is p ψ(x)ψ (y) U(x, y) where X = x + y 2 s = x y EOM (Schwinger-Dyson equation) = + σ μ (p A ) S < = iħ μ μ 2 (Σ< S > Σ > S < )

25 EOM Up to order hbar σ μ ( p μ + iħ 2 Δ μ) S< = iħ 2 (Σ< S > Σ > S < ) where Δ μ = μ + F νμ p ν

26 EOM Up to order hbar σ μ ( p μ + iħ 2 Δ μ) S< = iħ 2 (Σ< S > Σ > S < ) where Δ μ = μ + F νμ p ν Chiral kinetic equation (CKE) Δ S <μ = Σ < μ μ S>μ Σ > μ S<μ where S <μ = 1 2 trσμ S <

27 EOM Up to order hbar σ μ ( p μ + iħ 2 Δ μ) S< = iħ 2 (Σ< S > Σ > S < ) where Δ μ = μ + F νμ p ν Chiral kinetic equation (CKE) Δ S <μ = Σ < μ μ S>μ Σ > μ S<μ where S <μ = 1 2 trσμ S < S <μ = 2πϵ(p n) [ δ(p 2 )(p μ +ħs μν n D ν )+ħp ν F μν δ (p 2 ) ] f S μν n = 1 p 2 ϵμναβ α n β p n YH, Shi Pu, Yang ( 16) ( 17) D μ f = Δ μ f + Σ < μ f Σ> μ f Talk by Amping Huang (Parallel II.3)

28 Talk by Jian-Hua Gao (Parallel II.1) S <μ = 2πϵ(p n) [ δ(p 2 )(p μ +ħs μν n D ν )+ħp ν F μν αβ δ (p2 ) ] f S <μ

29 Talk by Jian-Hua Gao (Parallel II.1) S <μ = 2πϵ(p n) [ δ(p 2 )(p μ +ħs μν n D ν )+ħp ν F μν αβ δ (p2 ) ] f S <μ f f f+ħ ϵνμαβ p α n β n μ 2(p n)(p n ) D ν f

30

31 J μ d 4 p = 2 (2π) 4 S<μ (p, X) J = nu + σ B B + σ ω ω

32 μ, T δj = C E μ + C E T + C μ T C τ i R

33 μ, T δj = C E μ + C E T + C μ T C τ i R E

34 μ, T δj = C E μ + C E T + C μ T C τ i R E J

35 δj i = C 4 π ij B j + C 5 π ij ω j +C 6 ( u)b i + C 7 ( u)ω i

36 δj i = C 4 π ij B j + C 5 π ij ω j +C 6 ( u)b i + C 7 ( u)ω i B u

37 δj i = C 4 π ij B j + C 5 π ij ω j +C 6 ( u)b i + C 7 ( u)ω i B J J u

38 σ(ω) = σ 0 ( ω ω + iτr 1 )

39 Dilepton production Gongyo, YH, Tachibana ( 18) QGP X q p 1 p 2 Lepton pair Photon polarization funciton Π <μν (X, q) = d 4 se iq s j ν (X s/2)j μ (X + s/2) Dilepton production rate dγ d 4 q = α 24π 4 Π<μ (q, X) μ

40 Di-lepton production Gongyo, YH, Tachibana( 18) dγ d 4 q = dγ 0 d 4 q + dγ ω d 4 q ω θ q dγ ω dγ 0 d 4 q )/( d 4 q ) ( 0 2 with angle dependence T = 200 MeV μ 5 = 20 2 ω = 10 MeV MeV dγ ω d 4 q = (Ω γ ω)c(q) Ω γ = q q 2 q 0 = 4GeV q = 2 GeV θ

41 Puzzle? CKE from on-shell effective theory Carignano, Manuel, Torres-Rincon ( 18) ( Δ 0 + (1 + B Ω) q i 1 Δ i + ( 2 ϵijk E j Ω k 1 4 Bi ) Δ i) f = 0 reproduces consistent anomaly μ j μ 5 = π 2 E B CKE by Son, Yamamoto ( 12), YH, Pu, Yang ( 17) ( Δ 0 + (1 + B Ω) q i Δ i + ϵ ijk E j Ω k Δ i ) f = 0 reproduces covariant anomaly μ j μ 5 = 1 2π 2 E B where Δ μ = μ + F νμ p ν

42 Summary Chiral kinetic theory: Effective theory reproducing chiral anomaly Novel dissipative anomalous transports are found. Application to HIC and cond-mat Quarks have mass. What is mass correction to CKE? Mass correction to CVE cf. Flachi, Fukushima ( 17), Lin, Yang ( 18) j μ 5 = ( T 2 6 m2 4π 2 ) ωμ Talk by Lixin Yang (Parallel II.1) Analysis with collisions without relaxation time approximation