Chiral Magnetic Effect

Transcription

1 Chiral Magnetic Effect Kenji Fukushima (Yukawa Institute for Theoretical Physics) 1

2 Strong q Angle, Strong CP Problem and Heavy-Ion Collisions

3 P and CP Violation in the YM Theory Gauge Actions P- and CP- even (T-even) terms 0i ij F F = F 0 i F F ij F Even w.r.t. spatial and temporal indices P- and CP- odd (T-odd) terms = F 01 F 3 F 0 F 31 F 03 F 1 F F Odd w.r.t. spatial and temporal indices Parallel E and B F F = E B E B vector axial vector 3

4 Terminology Topological Charge (Pontryagin Index) 1 4 a a Q= d x F F 3 1 a a F = F 1 a a F F = K 3 K = 1 1 abc a b c a a A A A A A

5 Terminology Chern-Simons Number 1 3 ijk = d 3 x K 0= d x 16 4 Q= d x 0 K 0 i K i = dt 1 Aia j Aak abc Aai Abj Ack 3 d 3 d x K 0 = t= t= dt 5

6 q -Vacuum and Strong CP Problem Topological Structure and q -Vacuum Manton Faddeev Jackiw-Rebbi = e i (Bloch state) Strong CP Problem S QCD 1 1 = tr F F tr F F g 16 d n ~ e mq /mn Spin 11 No CP breaking (Why?) EDM + - 6

7 Finite-q Hadronic World q can be eliminated by U(1)A rotation One solution to the strong CP problem is the presence of massless quarks (almost excluded...) Effect of strong q-angle to hadron physics i U e U Scalar meson i ~ e ~ cos 0 sin Pseudo-scalar meson i 0 ~ i e i 5 ~ 0 cos sin h0 condensates in addition to the chiral s condensate 7

8 Possibility for Finite h Condensate If U(1)A symmetry is NOT broken s and h are degenerate (h may have a chance as much as the s condensate develops) U(1)A is broken but can be effectively restored U(1)A breaking effective interaction is induced by Veneziano-Di Vecchia the topological susceptibility Susceptibility drops off at high temperature T ~ Tc / g n T = e g Lattice Simulation Alles et al (1996) [ exp T N c N f 3 ] Gross-Pisarski-Yaffe 8

9 Relativistic Heavy-Ion Collisions Finite-q Heavy-Ion (nucleus) Au, Pb, Cu,... s NN =00 GeV, 6 GeV,... Kharzeev Pisarski Tytgat Voloshin Quark-Gluon Plasma Baym Shuryak Direct photon measurement (not from p0, h' etc) Initial T ~ K ~ GeV c.f. T c ~ QCD ~0.3fm 9

10 Topological Contents in the QCD Vacuum and the Real-time Fluctuations 10

11 Lattice Simulation Topological Charge Distribution at T =0 This is not a function of Real-Time but of the simulation step. Derek's Visual QCD 11

12 Is the high-t QCD Vacuum Topologically Trivial? Yes in terms of Instantons (Euclidean) Instantons are exponentially suppressed at high T / g n T = e g [ exp T N c N f 3 ] No in terms of Sphalerons (Minkowskian) Sphalerons are parametrically enhanced at high T. ~ 5s T 4 QCD sphalerons are abundant in hot and dense matter created in the relativistic heavy-ion collisions Arnold-McLerran (1987) 1

13 Topological Rate in Real- and Imaginary-Time Pendulum (Arnold-McLerran) Chern-Simons number x t / 1 Topological charge n= d x 0 Finite- T Euclidean Action S E = 0 d 1 x i x Topological Susceptibility (Diffusion Rate) A t = T x t x 0 t t Real-time (classical approx.) A t v= 4 4 Imaginary-time A i = n exp / cos 13

14 Analytical Continuation Diffusion Rate at High T x t x 0 A t = T O e / 1 exp i m t 1 exp i m t 1 / = O e exp m 1 4 m exp m 1 1 t / i t O e 4 A t = i O e / Instantons (Euclidean windings) are suppressed at high T but communications in real time are not and dominated by the contribution from the zero-winding sector. 14

15 Topological Diffusion Rate 1 4 = lim lim d x q x q 0 q 0 q x t V Q = V t Random Walk at Finite T In the strong-coupling AdS/CFT by Son and Starinets (hep-th/005051) = g YM N 56 3 T 4 In the weak-coupling perturbation by Arnold, Son, Yaffe, Bodeker, Moore, etc =const g YM N ln T g YM N 15

16 Connection to the Heavy-Ion Collisions How to detect the topological effects? 16

17 Non-Central Collision Before Collision (seen from above) + + Centrality is determined by Npart 17

18 Non-Central Collision After Collision + B (Local) P and CP Violation + 18

19 Estimated Magnetic Fields Classical (Pancake) Calcs (Kharzeev-McLerran-Warringa) eb=1[ MeV ] B [Gauss ] UrQMD Calculations (Skokov-Illarionev-Toneev) 19

20 How Big? eb ~ m 3 p Gauss 6 10 ~10 Neutron Star (Magnetar) 0

21 Chiral Magnetic Effect Classical Picture Left-handed Quark = momentum parallel to spin B Right-handed Quark = momentum parallel to spin Kharzeev-McLerran-Warringa (007) J 0 if N 5= N R N L 0 Kharzeev-McLerran-Warringa 1

22 Anomaly Relations Induced N5 by Topological Effects dn 5 g N f 3 = d x tr F F dt 8 QCD Anomaly Relation Introduce m5 to describe induced N5 Induced J by the presence of N5 and B j = j = e 5 B i=flavor QED Anomaly Relation q i 5 B in QCD Metlitski-Zhitnitsky (005) Fukushima-Kharzeev-Warringa (008)

23 Derivation (naïve calculation) Thermodynamic Potential (UV divergent) q f B dp 3 f = V N c T ln 1 e ] [ n, s n,s n,s f s=± n =0 = p q f B n sgn p3 s 5 m n, s 3 Current (UV finite) Only surface terms! eb n, s p 3= n, s p 3= ] n,s [ 4 s,n e B 5 eb =e s 5= n, s s,n j 3=e 3

24 Derivation (energy conservation) Energy Conservation (Nielsen-Ninomiya 1983) Electric field E Energy shift (Fermi energy) Landau Levels Density of states Energy cost E B NR NL 4

25 CME from Inhomogeneous q Space-time Dependent q -angle i / N e 5 f i / N =e i / N f 5 5 f 0 / N f = 5 Schematic Picture No CME 0 in-medium Kharzeev, Pisarski, Tytgat, Krasnitz, Venugopalan, Voloshin,... CME =0 vacuum 0 0 =0 No CME 5

26 Witten Effect and CME Maxwell-Chern-Simons Theory E B = j c B P E t E = c P B B E = 0 t B = 0 P = Induced Electric Current j=c B P E Induced Electric Charge q=c P B = c g Witten, Wilczek 6

27 CME from AdS/QCD Models Chiral Magnetic Current Sakai-Sugimoto Model: Rebhan et al, JHEP 0905, 084 (009) Lifshytz-Lippert, PRD80, (009) Sakai-Sugimoto Model & Reissner-Nordstrom BH: Yee, JHEP 0911, 085 (009) Soft-wall AdS/QCD: Gorsky-Kopnin-Zayakin, Confusion and (maybe) a Resolution SCS and Bardeen's counter terms change the CME currents? Axial gauge fields are not dynamical ones so the counter terms should not be applied. Rubakov (010) 7

28 Experimental Status 8

29 Relativistic Heavy-Ion Collisions Nucleus (Au) Collision Energy per nucleon-nucleon collision = 00GeV p0 =100GeV, M =1GeV g ~ 100 Same as the kinetic energy by flying mosquitoes M ~3mg, v ~10cm/s 9

30 Experimental Observation Brookhaven National Laboratory (Gallery) STAR Detector ~100 M events PHENIX Detector 30

31 Charge Separation Looking for parity violation in heavy-ion collisions by Berndt Müller Physics, 104 (009) 31

32 Observable by Voloshin Measured Multiplicity : Azimuthal angle v1 : Directed flow v : Elliptic flow 3

33 Observable by Voloshin Observable (fluctuation measurement) STAR Results 33

34 Confirmation by PHENIX Good agreement between STAR and PHENIX Not conclusive Backgrounds from Flow, Decay, etc 34

35 Multi-Particle Correlation Two Distribution Functions h S p =sin p h Sn h S p h Sn PHENIX Talk by R.Lacey Simulation 35

36 Preliminary Data (talk by R. Lacey) 36

37 Some Attempts to the Current Fluctuations 37

38 Charge Asymmetry by Currents Induced Charge Induced Charge Fluctuation 38

39 CME and Non-CME Contributions Electric-current Correlation Function Disconnected Part CME (known) Connected Part non-cme background 39

40 Susceptibility Computation Expression (Ritus' method) 40

41 Susceptibility Difference UV-Finite Results Only the Landau zero-mode contributes to the final result. The longitudinal and transverse difference is UV finite and insensitive to any IR scales. 41

42 Heuristic Argument Current generation rate = Chirality (Schwinger process) rate c.f. Iwazaki KF-Kharzeev-Warringa Linear response theory Integration by parts in the gauge (d/dx0)az = Ez 4

43 Heuristic Argument Current generation rate = Chirality (Schwinger process) rate c.f. Iwazaki KF-Kharzeev-Warringa Linear response theory Integration by parts in the gauge (d/dx0)az = Ez 43

44 Comparison with Lattice QCD Buividovich, Chernodub, Luschevskaya, Polikarpov (009) 44

45 More Attempts from Lattice QCD Polikarpov et al (Instanton + Magnetic Field) Current Squared Chiral fermions are crucial Overlap fermion 45

46 More Attempts from Lattice QCD Blum et al (Instanton + Magnetic Field) Charge Separation QCD+QED simulations are ongoing 46

47 Instead of Conclusions Please visit: 47