The Chiral Magnetic Effect: Measuring event-by-event P- and CP-violation with heavy-ion collisions Or from

Transcription

1 The Chiral Magnetic Effect: Measuring event-by-event P- and CP-violation with heavy-ion collisions Or from To Topological charge flucutations, D. Leinweber Tracks in TPC of STAR And back! Harmen Warringa, Institut für Theoretische Physik, Goethe Universität, Frankfurt Kharzeev, McLerran & HJW, Nucl. Phys. A803, 7 (008) HJW, J.Phys.G35, (008) Fukushima, Kharzeev & HJW, Phys.Rev.D78, (008)

2 The vacuum of the gluon sector of QCD In the classical vacuum: H YM = 0... the gauge fields are a pure gauge. i Ai x,t = U x i U x g U x SU 3 Pure gauge (and hence the vacuum) have winding number = complicated formula Ai = 0, ±1, ±... Winding number = Topological invariant. Smooth deformations cannot change winding number. Need to go out of pure gauge=energy to change winding number. mathworld.org

3 So then, how does the vacuum of the gluon sector of QCD look like? energy = Callan, Dashen, Gross ('76)

4 Transitions between vacua: g Q= d topological charge 3 a x F F a Sphaleron Q= 1 energy = N CS = Instanton Q=1 1 3 Instantons: Configuration with finite action. Tunneling through barrier Suppression of rate at finite temperature 't Hooft ('76), Pisarski and Yaffe ('80) =lim V, t 1 8 Q ~exp Vt g T =0 180 MeV 4 Sphaleron: Configuration with finite energy. Real time. Go over barrier. Only possible at finite temperature, rate not suppressed! Manton ('83), Manton and Klinkhamer ('84), McLerran, Mottola and Shaposhnikov ('88) ~385 5S T 4 Bödeker, Moore and Rummukainen ('00), several transitions per fm-3 per fm/c

5 QCD: Gluon fields can have g Q = d topological charge 3 4 a x F F a Belavin, Polyakov, Schwartz and Tyupkin ('75) Non-perturbative physics D. Leinweber, Topological charge flucutations Average over time and space vanishes Q = 0 But fluctuations not How does topological charge deal with quarks? Q 0

6 The Axial Anomaly (= quantum mech. sym. breaking) Steinberger ('49) Schwinger ('51) Bell, Jackiw ('69) Adler ('69) 5 j 5 x = x x Axial current in the chiral limit is not conserved QED e j = F F 8 5 Pion decay to two photons 0 QCD g a j 5 = F F a 16 Note: these relations are exact in chiral limit Axial U(1) symmetry breaking m ' m, m K

7 Topological charge induces chirality Chirality: difference between number of quarks + antiquarks with right- and left-handed helicity spin qr + # qr ql # # # N 5= ql momentum Integrating Axial Ward volume and time gives g a Identity = F F a 16 5 over N 5 [ N R N L ]t = [ N R N L ]t= = Q Axial Anomaly: Topological charge induces chirality m=0, N 5 =4 Q 1. Fluctuations in topological charge implies fluctuations in chirality.. No topological charge = no difference between number left- and right. 3. Fluctuations: number left- and right-handed fermions differ in each event. Event-by-event P- and CP-violation.

8 The Chiral Magnetic Effect: Measuring event-by-event P- and CP-violation with heavy-ion collisions Or from Q 0 N 5 0 And back!

9 What does a magnetic field do to quarks A magnetic field will align the spins, depending on their 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 A quark with right-handed helicity will have momentum opposite to a left-handed one In this way the magnetic field can distinguish between right and left

10 What does a magnetic field do with chirality (generated by topological charge) A magnetic field will align the spins, depending on their electric charge No Magnetic Field: No polarization Magnetic field: Polarization Positively charged particles move parallel the magnetic field Negatively charged particles move to antiparallel to magnetic field An electromagnetic current is created along the magnetic field B

11 The Chiral Magnetic Effect 1. Topological charge induces Chirality. In presence of Magnetic field this induces an Electromagnetic Current along Magnetic Field. 3. In finite volume this causes separation of positive from negative charge Kharzeev, McLerran & HJW ('07) B Q = -1 time Current as a function of magnetic field (B), temperature (T), quark chemical potential ( ) and topological charge (Q) at high temperature, small field. 3e Q 3 3 J 3 = d x B q f f T / Fukushima, Kharzeev & HJW ('08)

12 The Chiral Magnetic Effect: Measuring event-by-event P- and CP-violation with heavy-ion collisions Or from Q 0 5 N 0 And back! J z 0 B

13 The Chiral Magnetic Effect in Heavy Ion Collisions Event by event P- and CP-violation Kharzeev ('06) EDM of QGP Magnetic field + - Charge conserved in hadronization: Excess of Positive Charge on one side of Reaction Plane around = / Caused by top. charge in quark-gluon plasma In combination with Magnetic Field heavy ions = QCD + EM Excess of Negative Charge on other side of Reaction Plane around =3 / More positively charged quarks implies more positively charged hadrons Kharzeev ('06), Kharzeev & Zhitnitsky ('07), Kharzeev, McLerran & HJW ('07)

14 Magnetic Field in Heavy Ion Collisions B Computed numerically at origin in pancake approximation RHIC@BNL e B =0. fm =10 ~10 MeV ~10 G 100 GeV per Nucleon Kharzeev, McLerran & HJW ('07) Low energy quarks which are produced in early stages will be polarized in the direction perpendicular to reaction plane to some degree. Magnetic field falls off rapidly: early time dynamics

15 The Chiral Magnetic Effect in Heavy Ion Collisions reaction plane B Topological charge Q fluctuates anywhere in the QGP - Q Measure: variances -> nonzero Event-by-Event P- & CP-violation Q + The Chiral Magnetic Effect is a near the surface effect - Medium causes screening Variance of charge difference between upper and lower side reaction plane: tf = t d t V d x [ x x ] f q e B ± i Time & Volume integral Overlap region 3 Rate of creation Topological charge Screening Functions f Square of Change Charge difference Estimate magnitude asymmetry for large impact parameter 10-4 with 1- orders of magnitude uncertainty.

16 Chiral Magnetic Effect prediction: Correlators vs. Centrality Preferential emission of positively charged particles around = / or = / N + Most Central % Centrality Most peripheral A possible result of the Chiral Magnetic Effect in Gold-Gold collisions at 130 GeV per nucleon

17 Preliminary data Au & Cu 00 GeV minimum bias Red points: + Blue points: STAR detector Most Central % Centrality + +- Most peripheral Sergei Voloshin (STAR Collaboration) Quark Matter 008. more on this at Quark Matter 009. See also talk by Helen Caines at this meeting. Possible BACKGROUNDS? 1 d N± 1 = a± sin RP v cos[ RP ]... N± d

18 Features of the Chiral Magnetic Effect Order parameter for Confinement / Deconfinement Confined quarks cannot be separated. Order parameter for Chiral Symmetry Breaking / Restoration A nonzero chirality will be quickly removed by the chiral condensate. Friction term in anomaly. Hence no QGP implies: no Chiral Magnetic Effect Test: Energy scan The correlators are proportional to Z Chiral magnetic effect: QCD + EM Test: use nuclei with same A and different Z, isobars Work to do. More accurate beam energy dependence (what happens at LHC?), A dependence, correlations between different charged particles,... Kharzeev, McLerran & HJW ('07)

19 Conclusions The Chiral Magnetic Effect Or from Q 0 If QGP 5 B N 0 J z 0? + +± ±, cos i j RP 0 And back! ± 0, 0

20 Backup slides

21 Topological Susceptibility in Euclidean space-time 1 1 = lim V, t [ N CS t N CS t=0 ] = Q Vt V4 g 4 a Q= d x F F a = Q = d x q x q 0 V4 8 ~exp[ S ]~exp[ Q ] g Large suppression at large temperatures.. N f f = m ' m mk Del Debbio, Panagopolous & Vicari ('0) T =0 180 MeV 4

22 Topological susceptibiliy in Minkowski space-time Sphaleron energy N CS = Instanton 1 3 Callan, Dashen, Gross ('76) Sphaleron: Configuration with finite energy. Go over barrier. Only possible at finite temperature, rate not suppressed, look for it in QGP! Manton ('83), Manton and Klinkhamer ('84), McLerran, Mottola and Shaposhnikov ('88) ~385 5S T 4 Bödeker, Moore and Rummukainen ('00), several transitions per fm-3 per fm/c Winding in real-time is very different from winding in Euclidean space-time. See Arnold and McLerran ('88). The sphaleron strikes back for a nice discussion.

23 Chirality and Helicity ul 1 Left-handed chirality: L = 1 5 Left-handed helicity: p = 1 p 1 Right-handed chirality: R = 1 5 p =1 Right-handed helicity: p In the chiral limit Particle (P) with Left/Right-handed chirality has Left/Right-handed helicity Antiparticle (AP) with Left/Right-handed chirality has Right/Left-handed helicity N 5= d x = d x [ R R L L ] N 5= N R N L = 3 # (P - AP) with RH chirality - # (P - AP) with LH chirality # (P + AP) with RH helicity - # (P + AP) with LH helicity [ N R N L ]t= [ N R N L ]t= = N f Q

24 Relation between current and topological charge e B L3 J 3= 5 n5 = N 5= Q 5 =? 1 = log Z V 5 At large temperatures and small magnetic fields, We can take a free noninteracting gas of fermions. This can be improved. 5= 3n5 T / 3e Q J 3 B q f f T / Fluctuations in topological charge lead to fluctuations in the current 3e 1 J [ B q ] Q f f T / 3 Kharzeev, Fukushima & HJW ('08)

25 The chiral chemical potential Energy R= 5 L = 5 Lefthanded Righthanded If a system has Chirality, Fermi-surfaces Right- and Left-handed fermions differ. This can be described by a chiral chemical potential 5 Study equilibrium response to Magnetic Field

26 Computing the induced current Introduce Chiral Chemical Potential 5 to obtain nonzero Chirality Study equilibrium response to Magnetic Field J = d 3 x 1. Consider Parallel Electric and Magnetic Fields d N R N L e 3 = d xe B. Chirality is generated by the EM anomaly with rate dt d N R N L 3. Moving particles from one to other Fermi Surface e 3 = d xe B 5 5 costs energy per unit time dt e d x j E = 5 d 3 x E B 4. Energy has to be delivered by current, energy conservation gives 3 Nielsen and Ninomiya ('83) 5. Take limit Electric field -> 0 e B L3 J 3= 5 The Chiral Magnetic Effect: Kharzeev, Fukushima & HJW ('08) QCD anomaly provides chirality EM anomaly provides current See paper this and 4 other methods to arrive at this result

27 Current as a function of Chirality e B L3 J= 5 Express 5 in terms of N 5 (neglecting gluonic corrections) Fermions in a magnetic field without gluons.. Also large magnetic fields here. High temperature and small magnetic field approx. (dashed line) valid for QCD 5= 3n5 T / 3 e N 5 1 J= B q f f N T / f Relation between chirality and topological charge N = N 5 Current as a function of magnetic field zero temp (red) and T / n1/3 5 = (blue) f Q Kharzeev, Fukushima & HJW ('08)

28 Suppression of +/- correlations Suppression of correlations between positively charged particles on one side and negatively charged particles on other side of reaction plane due to screening. A possible result of the Chiral Magnetic Effect reaction plane

29 Chiral Magnetic Effect on the Lattice? The Chiral Chemical Potential 5 has no sign problem! Since 0 5 is anti-hermitian Dirac operator: D has purely imaginary eigenvalues which come in pairs det D m 0, real! Suggestion: Extract relation between chirality and chiral chemical potential from the lattice. With or withouth magnetic field. Need good chiral behavior of fermions. Kharzeev, Fukushima & HJW ('08)

30 Preliminary data Au & Cu 6 GeV Red points: + Blue points: + +Most Central % Centrality Most peripheral Voloshin (STAR Collaboration) Quark Matter 008

31 Measurements suggest Preferential emission of charged particles in one direction perpendicular to reaction plane. Correlations between positively charged particles and negatively charged particles on opposite sides. Existence of screening effect. About 1-3 % asymmetry Sergei Voloshin (STAR Collaboration) Quark Matter 008 Asymmetry increases for more peripheral collisions Magnitude asymmetry Cu-Cu and Au-Au very similar both at 6 GeV and 00 GeV for all centralities. Is it due to the Chiral Magnetic Effect or due to something else, and how to find out?

32 Features of the Chiral Magnetic Effect - Magnitude of asymmetry estimate: gold-gold at 130 GeV 4 at large impact parameter a ~10 with large uncertainty - Atomic Number (A) dependence is determined by initial time. A better computation (no pancake approximation) could give us this more accurately. For now it seems that for intermediate energies we have (Z/A) dependence, not completely certain: depends on dynamics - The correlators are proportional to Z Test: use nuclei with same A and different Z, isobars - Particle species dependence - Beam energy dependence is determined by initial time. A better computation (no pancake approximation) could give us this. At LHC smaller asymmetries. Magnetic field decays faster.