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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)
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
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
Outline
To explain you that
Magnetic Field + Topological charge =
Charge separation
+-
B
+-
Kharzeev ('06)Fluctuating EDM of QGP
Q < 0
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
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
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)
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?
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
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)
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)
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
+
+++-
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
⟨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=
