P- and CP-odd effects in hot quark matter

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1 P- and CP-odd effects in hot quark matter Goethe Denkmal, Opernring, Wien Harmen Warringa, Goethe Universität, Frankfurt Collaborators: Kenji Fukushima, Dmitri Kharzeev and Larry McLerran. Kharzeev, McLerran & HJW, Nucl. Phys. A 803, 7 (008) HJW, J.Phys.G 35, (008) Fukushima, Kharzeev & HJW, Phys. Rev. D 78, (008) HJW, arxiv: Kharzeev & HJW, Phys. Rev. D 80, (009)

2 P- and CP-odd effects in hot quark matter Hot quark matter is produced in heavy ion collisions Collided: heavy ions Observed: charged particle tracks For example Gold Gold at RHIC, BNL or Lead - Lead at SPS and LHC, CERN

3 P- and CP-odd effects in hot quark matter Hot quark matter is produced in heavy ion collisions P- and CP-odd effects possible in hot quark matter This talk: How P- and CP-odd effects lead to observable signatures

4 Observation I: Topological charge fluctuations present in hot quark matter The nontrivial vacuum structure of a SU(N) gauge theory Instanton with Q = 1 Energy N CS = Sphaleron with Q = g 4 a Q= d x F F a = N CS 3 Hot quark matter described by Quantum Chromodynamics (QCD) = SU(3) gauge theory + quarks

5 Observation I: Topological charge fluctuations present in hot quark matter The nontrivial vacuum structure of a SU(N) gauge theory Instanton with Q = 1 Energy N CS = Sphaleron with Q = g 4 a Q= d x F F a = N CS Rate= Q Minkowski ~385 S T Vt Topological susceptibility Bödeker, Moore and Rummukainen ('00) several transitions per fm-3 per fm/c

6 Observation II: Ultra high-energy heavy ion collisions = Ultra strong (EM) magnetic fields B, direction of mag. field. Gold Gold collision: two currents which carry 79 charges each

7 Observation II: Ultra high-energy heavy ion collisions = Ultra strong (EM) magnetic fields Au-Au 00 GeV Au-Au 00 GeV Pancake approximation Kharzeev, McLerran & HJW ('08) URQMD calculation Skokov, Illarionov, Toneev ('09) eb =0. fm /c 10 3 ~10 4 MeV G Yocto-second (10-4 s) pulses, see also the work of Ipp, Keitel and Evers ('09)

8 Outline To explain you that Magnetic Field + Topological charge = B Q < 0 - Fluctuating EDM of QGP P- and CP-odd effect Kharzeev ('06), Kharzeev and Zhitnitsky ('07) Kharzeev, Mclerran and Warringa ('08) Charge separation This can potentially be observed in experiment

9 Topological charge induces chirality This is the P- and CP-odd effect Chirality: difference between number of quarks + antiquarks with right- and left-handed helicity # qr + # _ qr spin _ # N 5= spin ql _ # momentum _ ql Relativistic fermions momentum Axial anomaly: topological charge induces chirality Steinberger ('49), Schwinger ('51), Alder ('69), Bell and Jackiw ('69) Change in chirality over time for each flavor = - x Topological charge N 5= Q

10 Magnetic field induces polarization Magnetic field aligns spins, depending on electric charge No Magnetic Field: No polarization ul dl Magnetic field: Polarization ul dl ul dl B The momenta of the quarks align along the magnetic field Quark with R-helicity obtains momentum opposite to one with L-helicity Hence magnetic field distinguishes between right and left

11 Topological Charge + Magnetic field = Chirality + Polarization = B Q = -1 N 5= Q < -1: Positively charged particles move parallel to magnetic field, negatively charged antiparallel... = Electromagnetic Current Chiral Magnetic Effect: Kharzeev, McLerran & HJW ('07)

12 Topological Charge + Magnetic field = Chirality + Polarization = B Q = -1 N 5= Size of Current: 3 J = d 3 x = Q f q f Valid for full polarization, what about smaller fields? Chiral Magnetic Effect: Kharzeev, McLerran & HJW ('07)

13 Topological Charge + Magnetic field = Chirality + Polarization = P- and CP-odd effect B Q = -1 time Completely dynamical proces. Top charge is configuration with characteristic size and life-time Size of Current: 3 J = d 3 x = Q f q f Valid for full polarization, what about smaller fields? Chiral Magnetic Effect: Kharzeev, McLerran & HJW ('07)

14 How chirality reacts to magnetic field Energy R = 5 L = 5 Lefthanded Righthanded Nonzero Chirality: Nonzero chiral chemical potential H H 5 d 3 x 0 5 Compute induced current in magnetic field 5

15 Magnitude of the induced current Alekseev, Cheianov, Fröhlich ('98), Fukushima, Kharzeev and HJW ('08) N c f q f 1. Energy conservation j= Nielsen and Ninomiya ('83) 5 B N c f q f. Density in Lowest Landau Level j= See also Metlitsky and Zhitnitsky ('06) N c f q f 3. Chern-Simons term j= 5 B N c f q f 4. Thermodynamic potential j= N c f q f 5 B 5. Linear reponse j= 5 B N c f q f 6. Propagator in magnetic field j= 5 B 5 B

16 Magnitude of the induced current Fukushima, Kharzeev and HJW ('08) Energy conservation derivation Nielsen and Ninomiya ('83) 1. Consider Parallel Electric and Magnetic Fields with E << B and a nonzero mu5. d N R N L e 3 = d xe B. Chirality is generated by the EM anomaly with rate dt 3. Moving particles from one to other Fermi surface d N N e R L costs energy per unit time 5 = 5 3 d xe B dt 4. Energy has to be delivered by current, energy conservation gives e d x j E = 5 d 3 x E B 3 5. Take limit E -> 0 e j= B 5 CM effect: QCD anomaly provides chirality, EM anomaly induces current.

17 Magnitude of the induced current in holographic model for QCD Rebhan, Schmitt and Stricker ('09) AdS/CFT correspondence gives access to strongly coupled regime of QCD-like theory Result general for strongly coupled theories or specific to Sagai-Sugimoto model? Rebhan, Schmitt and Stricker ('09)

18 Magnitude of the induced current Fukushima, Kharzeev and HJW ('08) j= N c f q f 5 B,... but what is mu5? n 5 = 5 Thermodynamic potential QCD computable at high T 5 = f N 5, T, B, Express mu5 in terms of chirality, etc. N 5 = Q Use relation between chirality and top. charge We should recover at strong B: J = d 3 x 3 = Q f q f

19 Magnitude of the induced current j= N c f q f Fukushima, Kharzeev and HJW ('08) n5 = 5 5 B N 5= Q Induced current by top. charge T =0 J e Q 1/3 5 T = n = small field approx.: J = = small field approx. 3 Q B q f f T / Chiral Magnetic Effect in lattice QCD: Buividovich, Chernodub, Luschevskaya and Polikarpov. (arxiv: )

20 Chiral Magnetic Effect in time-dep. field Kharzeev and HJW ('09) j= E E E = electrical conductivity j= B = chiral magnetic conductivity Compute induced current using linear response j x = d 4 x ' x x ' A x ' o A R = lim 1 ijk jk R, p p 0 i i p i Off diagonal, antisymmetric part of photon polarization tensor. Nonzero with mu5

21 CM conductivity: weak vs. strong coupling CM conductivity: = lim p i 0 1 i p i ijk R jk, p Weak coupling (1 loop pert. QCD) Strong coupling (holographic model of QCD) Kharzeev and HJW ('09) =0 = N c f q f 5 Ho-Ung Yee ('09)

22 Chiral Magnetic Effect in time-dep. field CM conductivity: = lim p i 0 1 i p i ijk R jk, p Kharzeev and HJW ('09) Current: const. chirality + time dep. mag. field B 0 B t = [1 t / ] 3/ Conclusion: also induced current in fast changing magnetic field

23 P- and CP-odd effects in Heavy Ion Collisions B Topological charge Q fluctuates anywhere in the QGP Q reaction plane Measure: variances = nonzero Q Medium causes screening Variance of charge difference between upper and lower side reaction plane: tf 3 ± = t d t V d x [ x x ] f i Time & Volume integral Overlap region Rate of creation Topological charge Screening Functions 3 q f e B T Square of Change Charge difference Estimate magnitude relative asymmetry for large impact parameter 10-4 with 1- orders of magnitude uncertainty.

24 Charge correlations at RHIC Red points: Au-Au and 00 GeV + Blue points: S. Voloshin (STAR Collaboration) Quark Matter 009, Knoxville TN arxiv: , arxiv: STAR detector Strong charge correlations observed at RHIC is it due to P- and CP-odd effects or something else?

25 Conclusions: P- and CP-odd effects in hot quark matter N CS= Q 0 B J z J x, y N 5 0? + +± ±, cos i j RP 0 ± 0, 0