Chiral Magnetic Effect Kenji Fukushima (Yukawa Institute for - PowerPoint PPT Presentation

Chiral Magnetic Effect Kenji Fukushima (Yukawa Institute for Theoretical Physics) July 24 2010@Yukawa 1

Strong q Angle, Strong CP Problem and Heavy-Ion Collisions July 24 2010@Yukawa 2

P and CP Violation in the YM Theory Gauge Actions □ P - and CP - even ( T -even) terms  = 2 F 0 i F 0 i  F ij F ij F  F Even w.r.t. spatial and temporal indices □ P - and CP - odd ( T -odd) terms  = 2 F 01 F F   23  2 F 02 F 31  2 F 03 F 12 F Odd w.r.t. spatial and temporal indices Parallel E and B  = 2 E ⋅ B E B F   F vector axial vector July 24 2010@Yukawa 3

Terminology Topological Charge (Pontryagin Index) 1 4 x F  a  2 ∫ d a Q = F  32  a = 1  a 2    F  F  1 a  a =∂  K  2 F  F  32  2     A  c  1 a ∂  A  a  1 abc A  a A  b A  K  = 3  16  July 24 2010@Yukawa 4

Terminology Chern-Simons Number ijk  A i c  1 a  1 3 x  abc A i a A j b A k = ∫ d 2 ∫ d 3 x K 0 = a ∂ j A k 3  16  4 x ∂ 0 K 0 −∂ i K i = ∫ dt d 3 x K 0 = t =∞− t =−∞ Q = ∫ d dt ∫ d July 24 2010@Yukawa 5

q -Vacuum and Strong CP Problem Topological Structure and q -Vacuum Manton Faddeev Jackiw-Rebbi ∣  〉 = ∑ i  ∣  〉 e  (Bloch state) Strong CP Problem Spin 〈 ∣ 〉 S QCD = − 1 1    2 tr F    2 tr F  F F EDM 16  2 g + 2  ∣ d n ∣~ e m q / m N - No CP breaking (Why?) − 11 ∣∣ 0.7 × 10 July 24 2010@Yukawa 6

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 U  e Scalar meson i  5  ~ cos  0 sin  ~     e Pseudo-scalar meson i  5  i  5 ~ 0 cos  sin   0 ~  i  5     e h 0 condensates in addition to the chiral s condensate July 24 2010@Yukawa 7

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 the topological susceptibility Veneziano-Di Vecchia Susceptibility drops off at high temperature T ~ T c 2   exp [ −  ] n  T =  2  2 N c  N f 2 8  2 / g − 5 e − 8  2  2 T 2  3 g Gross-Pisarski-Yaffe Lattice Simulation Alles et al (1996) July 24 2010@Yukawa 8

Relativistic Heavy-Ion Collisions Kharzeev Finite- q Pisarski Tytgat Voloshin Baym Heavy-Ion (nucleus) Quark-Gluon Plasma Shuryak Au, Pb, Cu, ... Direct photon measurement  s NN = 200GeV , 62GeV , ... 0 , h ' etc) (not from p 12 K ~ GeV → Initial T ~ 4×10 c.f. T c ~ QCD ~ 0.3fm July 24 2010@Yukawa 9

Topological Contents in the QCD Vacuum and the Real-time Fluctuations July 24 2010@Yukawa 10

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 July 24 2010@Yukawa 11

Is the high-T QCD Vacuum Topologically Trivial? Yes … in terms of Instantons (Euclidean) Instantons are exponentially suppressed at high T . 2   exp [ −  ] n  T =  2  2 N c  N f 2 8  2 / g − 5 e − 8  2  2 T 2  3 g No … in terms of Sphalerons (Minkowskian) Sphalerons are parametrically enhanced at high T . 5 T 4  ~  s QCD sphalerons are abundant in hot and dense matter created in the relativistic heavy-ion collisions Arnold-McLerran (1987) July 24 2010@Yukawa 12

Topological Rate in Real- and Imaginary-Time Pendulum (Arnold-McLerran) Chern-Simons number x  t / 2  Topological charge n = 1  2  ∫ 0 d  ˙ x d   x  1 2  i   Finite- T Euclidean Action S E = ∫ 0 x 2 ˙ 2  ˙ Topological Susceptibility (Diffusion Rate) A  t = 〈 T  〉  2 x  t − x  0  2  2 2 Real-time (classical approx.) A  t ≃ t t 2 = v 2  2  4  4  2 〉≃ 2exp  − 2  2 /  cos  Imaginary-time A − i =〈 n July 24 2010@Yukawa 13

Analytical Continuation Diffusion Rate at High T A  t = 〈 T  〉  O  e  2  x  t − x  0  2 /  2  2  2 m  exp  m − 1   O  e exp − i m ∣ t ∣− 1 exp − m − 1 − exp  i m ∣ t ∣− 1 1 2 /  2  = 4  2   i t   O  e 2 1 t 2 /  2   4  2 /  2  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. July 24 2010@Yukawa 14

Topological Diffusion Rate = 1 4 x 〈 q  x  q  0  q  0  q  x 〉 V ∞ ∫ d 2 lim t  ∞ lim 2 〉= 2  V t 〈 Q Random Walk at Finite T In the strong-coupling AdS/CFT by Son and Starinets (hep-th/0205051) 2 2 = g YM N  4 3 T 256  In the weak-coupling perturbation by Arnold, Son, Yaffe, Bodeker, Moore, etc 1 2 5 ln 4 = const ⋅ g YM N  T 2 g YM N July 24 2010@Yukawa 15

Connection to the Heavy-Ion Collisions How to detect the topological effects? July 24 2010@Yukawa 16

Non-Central Collision Before Collision (seen from above) + + Centrality is determined by N part July 24 2010@Yukawa 17

Non-Central Collision After Collision + B + (Local) P and CP Violation July 24 2010@Yukawa 18

Estimated Magnetic Fields Classical (Pancake) Calcs (Kharzeev-McLerran-Warringa) 2 ] eB = 1 [ MeV 14 [ Gauss ]  B ≃ 1.7 × 10 UrQMD Calculations (Skokov-Illarionev-Toneev) July 24 2010@Yukawa 19

How Big? 2 → 10 18 Gauss eB ~ m p 3 ~ 10 6 × 10 Neutron Star (Magnetar) July 24 2010@Yukawa 20

Chiral Magnetic Effect Classical Picture Left-handed Quark = momentum parallel to spin B Right-handed Quark = momentum parallel to spin J ≠ 0 if N 5 = N R − N L ≠ 0 Kharzeev-McLerran-Warringa (2007) Kharzeev-McLerran-Warringa July 24 2010@Yukawa 21

Anomaly Relations Induced N 5 by Topological Effects 2 N f dN 5 = − g 3 x tr F   2 ∫ d  F QCD Anomaly Relation dt 8  Introduce m 5 to describe induced N 5 Induced J by the presence of N 5 and B 2  5 j = e 2 B QED Anomaly Relation 2   j = ∑ 2 B in QCD  2  5 q i 2  i = flavor Metlitski-Zhitnitsky (2005) Fukushima-Kharzeev-Warringa (2008) July 24 2010@Yukawa 22

Derivation (naïve calculation) Thermodynamic Potential ( UV divergent ) f ∫ ∣ q f B ∣ dp 3 ∞ 2  [  n , s  2 T ln  1  e − n ,s  ] =− V N c ∑ 2  ∑ s =± ∑  n, s f n = 0 2 =   p 3 2 2  2 ∣ q f B ∣ n  sgn  p 3  s  5  2  n, s  m Current ( UV finite ) Only surface terms! j 3 = e ∣ eB ∣ 2 ∑  n , s [  n, s  p 3 =− n , s  p 3 =− ] 4  s, n 2 B  5  n, s s  5 = e = e ∣ eB ∣ 2 ∑ 2 2  2  s ,n July 24 2010@Yukawa 23

Derivation (energy conservation) Energy Conservation (Nielsen-Ninomiya 1983) Electric field E → Energy shift (Fermi energy) Landau Levels Density of states Energy cost E B N N R L July 24 2010@Yukawa 24

CME from Inhomogeneous q Space-time Dependent q -angle i  5 / 2 N f  ⋅∂ i ⋅∂/ 2 N f  5   i  5 / 2 N f   = e ⋅∂ ⋅∂  e ∂ 0 / 2 N f = 5 Schematic Picture CME ≠ 0  in-medium  No CME 〈〉≠ 0 〈 0 〉≠ 0 Kharzeev, Pisarski, = 0  vacuum  Tytgat, Krasnitz, 〈〉≠ 0 〈 0 〉= 0 Venugopalan, Voloshin, ... No CME July 24 2010@Yukawa 25

Witten Effect and CME Maxwell-Chern-Simons Theory B −∂  E  j  c  ˙ E  ∇×   B − P × ∂ t =   ∇⋅ E =  c  P ⋅ B P  = ∂   E ∂  B  ∇× ∂ t = 0  ∇⋅ B = 0 Induced Electric Current j = c  ˙ E    B − P × Induced Electric Charge q = c  P ⋅ B =− c  g Witten, Wilczek July 24 2010@Yukawa 26

CME from AdS/QCD Models Chiral Magnetic Current Sakai-Sugimoto Model: Rebhan et al, JHEP 0905, 084 (2009) Lifshytz-Lippert, PRD80, 066005 (2009) Sakai-Sugimoto Model & Reissner-Nordstrom BH: Yee, JHEP 0911, 085 (2009) Soft-wall AdS/QCD: Gorsky-Kopnin-Zayakin, 1003.2293 Confusion and (maybe) a Resolution S CS 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 (2010) July 24 2010@Yukawa 27

Experimental Status July 24 2010@Yukawa 28

Relativistic Heavy-Ion Collisions Nucleus (Au) Collision Energy per nucleon-nucleon collision = 200GeV p 0 =100GeV, M =1GeV → g ~ 100 Same as the kinetic energy by flying mosquitoes M ~3mg, v ~10cm/s July 24 2010@Yukawa 29

Experimental Observation Brookhaven National Laboratory (Gallery) STAR Detector PHENIX Detector ×~ 100M events July 24 2010@Yukawa 30