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Implications of topological charge fluctuations on heavy ion collisions Harmen Warringa, Goethe Universität, Frankfurt Collaborators: Kenji Fukushima, Dmitri Kharzeev and Larry McLerran. Kharzeev, McLerran & HJW, Nucl. Phys. A 803, 227 (2008) HJW, J.Phys.G 35, 104012 (2008) Fukushima, Kharzeev & HJW, Phys. Rev. D 78, 074033 (2008) HJW, arXiv:0906.2803 Kharzeev & HJW, Phys. Rev. D 80, 034028 (2009)

Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

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Page 1: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Implications of topological chargefluctuations on heavy ion collisions

Harmen Warringa, Goethe Universität, Frankfurt

Collaborators: Kenji Fukushima, Dmitri Kharzeev and Larry McLerran.

Kharzeev, McLerran & HJW, Nucl. Phys. A 803, 227 (2008)HJW, J.Phys.G 35, 104012 (2008) Fukushima, Kharzeev & HJW, Phys. Rev. D 78, 074033 (2008)HJW, arXiv:0906.2803Kharzeev & HJW, Phys. Rev. D 80, 034028 (2009)

Page 2: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Observation I:

Ultra high-energy heavy ion collisions = Ultra strong (EM) magnetic fields

Pancake approximationKharzeev, McLerran & HJW ('08)

URQMD calculationSkokov, Illarionov, Toneev ('09)

Au-Au200 GeV Au-Au

200 GeV

eB =0.2 fm /c ≈ 103~104 MeV2≈1017G

Page 3: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Observation II:

Topological charge fluctuations presentin QCD and hence in produced matter

-3 -2 -1 0 1 2 3 NCS=

Q =g 2

322∫d4 x F

a F a

=N CS

Rate=1Vt

⟨Q2⟩Minkowski~385S

5 T 4 Bödeker, Moore and Rummukainen ('00)several transitions per fm-3 per fm/c

Instantonwith Q = 1

Sphaleronwith Q = -1Energy

Page 4: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Outline

To explain you that

Magnetic Field + Topological charge =

Charge separation

+-

B

+-

Kharzeev ('06)Fluctuating EDM of QGP

Q < 0

Page 5: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Topological charge induces chirality

qLq

RN 5= # +

#

qR#

_ qL

# __ _ Relativisticfermions

Chirality: difference between number of quarks + antiquarks withright- and left-handed helicity

momentum

spin

Axial anomaly: topological charge induces chirality

N 5=−2Q

Generation of chirality is a P- and CP-odd effect

See also Kharzeev, Pisarski and Tytgat ('98)

Change in chirality over time for each flavor = - 2 x Topological charge

Page 6: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Magnetic field induces polarizationMagnetic field aligns spins, depending on electric charge

uR d

Lu

R

dRu

L

uL

uR d

Lu

R

dRu

L uR

B

dL

dR

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

Magnetic field: PolarizationNo Magnetic Field: No polarization

Page 7: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Topological Charge + Magnetic field =Chirality + Polarization =

uRuR

dRu

R

B

dR

Q < -1: Positively charged particles move parallel to magnetic field,negatively charged antiparallel

... = Electromagnetic Current

Q = -1N 5=2

Chiral Magnetic Effect: Kharzeev, McLerran & HJW ('07)

Page 8: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Topological Charge + Magnetic field =Chirality + Polarization =

uRuR

dRu

R

B

dR

Size of Current:

Q = -1N 5=2

Chiral Magnetic Effect: Kharzeev, McLerran & HJW ('07)

J=∫d3 x ⟨ 3⟩=−2Q∑ f

∣q f∣

Valid for full polarization, what about smaller fields?

Page 9: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

5Nonzero Chirality: Nonzero chiral chemical potential

Compute induced current in magnetic field

Energy

Left-handed

Right-handed

L=−5

R=5

How chirality reacts to magnetic field

Page 10: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Magnitude of the induced current

1. Energy conservation

2. Density in Lowest Landau Level

3. Chern-Simons term

4. Thermodynamic potential

5. Linear reponse

6. AVV triangle diagram

j=N c∑ f

q f2

22 5B

j=N c∑ f

q f2

22 5B

j=N c∑ f

q f2

22 5B

j=N c∑ f

q f2

22 5B

j=N c∑ f

q f2

22 5B

j=N c∑ f

q f2

22 5B

Nielsen and Ninomiya ('83)

See also Metlitsky and Zhitnitsky ('06)

Fukushima, Kharzeev and HJW ('08)

Page 11: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Magnitude of the induced current

, .... but what is mu5?j=N c∑ f

q f2

22 5B

Fukushima, Kharzeev and HJW ('08)

J2e∣Q∣ T=2n5

1/3

T=0

−−−−= small field approx.

N 5=−2Q

n5=∂

∂5

J=−3

2

Q

T 2

2/

2 B∑ fq f

2

−−−−= small field approx.:

Induced current by top. charge

In QCD compu-table at high T

Chiral Magnetic Effect in lattice QCD: Buividovich, Chernodub, Luschevskaya and Polikarpov. (arXiv:0907.0494)

Page 12: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

Chiral Magnetic Effect in time-dep. fieldKharzeev and HJW ('09)

= lim pi 0

1

2 i piijk R

jk , p

=0 =N c∑ f

q f2

22

5

Results for one-loop pert. QCD valid at high temperature

CM conductivity:

B t =B0

[1t /2]3/ 2

Current: const. chirality + time dep. mag. fieldCM Conductivity

Page 13: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

+

+++-

Red points:

Blue points:

STAR detector

S. Voloshin (STAR Collaboration)Quark Matter 2009, Knoxville TN

Charge correlations at RHICAu-Au and Cu-Cu @ 200 GeV

Page 14: Implications of topological charge fluctuations on heavy ......R= 5 How chirality reacts to magnetic field. Magnitude of the induced current 1. Energy conservation 2. Density in Lowest

⟨N 52⟩≠0

⟨Q2⟩≠0

⟨ J z2⟩⟨ J x , y

2⟩

+++-

⟨±

2⟩0, ⟨ −⟩0⟨cosi

± j

± ,∓−2RP⟩≠0

uRuR

uRuR

dR

uR

dR

Bu

RuR

uRuR d

R

uR

dR

Implications of topological chargefluctuations on heavy ion collisions

?

NCS=