Chiral Magnetic EffectKenji Fukushima(Department of Physics, Keio University)
May 10, 2012 @ HIP

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Talk Plan
Chiral Magnetic Effect ~ conventional explanation
Current from infinity – What really flows?
Chiral Magnetic Effect in a hadronic phaseIs there a current... or not? Signature of what??
Experimental challenges and theories
May 10, 2012 @ HIP

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Chiral Magnetic Effect~ conventional explanation ~May 10, 2012 @ HIP

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Basic Formula
Chiral Magnetic Effectj= N c ∑2fq μ5flavor

May 10, 2012 @ HIP

2πB
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Basic Formula
Chiral Magnetic EffectHard to understand2fq μ5j= N c ∑flavor

2πB2

Easy to understand
Very hard to understandMay 10, 2012 @ HIP

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Origin of the Magnetic Field
Moving almost at the speed of light
Au, Pb, Cu, ...

+Au, Pb, Cu, ...

Quark-Gluon Plasma
Impact parameter ~ b

May 10, 2012 @ HIP+
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Origin of the Magnetic Field
Strong B generated due to Electrodynamics+

B+

on top of the Quark-Gluon Plasma
May 10, 2012 @ HIP

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Point-charge Approximation
Lienard-Wiechert potentialeB (t)=eB 02 3/2[1+(t /t 0 ) ]1 fm
eB 0=( 47.6 MeV)b2

2~g( ) Z sinh (Y ) ,bt0 =2 sinh (Y )Discussed by Rafelski, Mueller, … (~1976)
May 10, 2012 @ HIP

8Physics of the Strong Magnetic Field
Magnetic field looks like a “medium”
A photon becomes massive.
Generally, the dispersion relations of photons withrespective polarizations are distorted (Birefringence)
A photon on top of B decays into pair particles.
Chiral symmetry breaking is enhanced.
Not known how the phase diagram is affected.
Pion structural change is hardly understood...
May 10, 2012 @ HIPFukushima-Hidaka

9Origin of the Chiral Chemical Potential
Generation of the chiral charge
2dN 5g Nf3μν̃= −d x tr F μ ν F2 ∫dt8π
Chirality

Topological charge density

Topologically non-trivial gauge configuration

N5
Derek's visual QCD

May 10, 2012 @ HIP

μ510

Origin of the Topological Charge Qw
Topologically non-trivial gauge configurations
Instanton (tunneling under barrier)Lives only in Euclidean space-time
Makes the h' meson heavy
Suppressed at high temperature χ ∼ exp [−c ρ2 T 2 ]Sphaleron (excitations over barrier)Lives in Minkowski space-time
Breaks the baryon and lepton numbers (in the weak int.)
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Arnold-McLerranEnhanced at high temperature Γ ∼ T
Kharzeev-McLerran-Warringa

Sphalerons get excited (~1fm/c) only after B decays
May 10, 2012 @ HIP

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Origin of the Topological Charge
Difference between instanton and sphaleron

Instantons (Euclidean windings) are suppressed at high T
but communications in real time are not and dominatedby the contribution from the zero-winding sector.
May 10, 2012 @ HIP

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Origin of the Topological Charge
Color Glass Condensate
QED field (RHIC)
2
∼m π
18
∼10 gauss
QCD field (RHIC)
2∼Q s2∼100 mπE⋅B≠0Fukushima-Kharzeev-Warringa
May 10, 2012 @ HIP

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Local Parity Violation (LPV)

+Qw>0
Qw<0

Qw<0
Qw>0

Qw>0
Qw<0+

Physics Impact
Experimental evidence for the quantum anomaly
Origin of the mass – QCD instanton never detected
Particle production from the CGC initial condition
May 10, 2012 @ HIP

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Charge Separation
Without B Fields

Spin

Net Current 〈 J 〉=0Momentum
RR

Topological Domain
Qw > 0RR

May 10, 2012 @ HIP

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Charge Separation
With B Fields

Spin

Net Current 〈 J 〉≠0〉=0Momentum
RRBRR
Kharzeev-McLerran-Warringa

May 10, 2012 @ HIP

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Caution!

Such a classical picture is not correct!
With the B-effect many phenomena (related tothe Landau quantization) look classical, but
their origin is purely quantum!

May 10, 2012 @ HIP

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Caution!

Such a classical picture may easily
lead people to a wrong interpretationof the chiral magnetic effect!
Deconfined and light (chiral-symmetric) quarks
are seemingly necessary... but really so?

May 10, 2012 @ HIP

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Current from infinity– What really flows?

May 10, 2012 @ HIP

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Landau Quantization
Energy dispersion relation in B
22z2

ω = p +2∣g B∣(n+1/ 2)+m −2 s g B
Transverse motion = Harmonic Oscillator- Light fermions (s=1/2) have zero mode.
(Nearly) massless quarks at high T and/or m- Light vector bosons have (Nielesen-Olesen) instability.
Gluons in the chromo-B / r in a superstrong B (Chernodub)- Charged scalar bosons are all massive.
p+, p-, … Explicit breaking of isospin symmetryEtc, etc...
May 10, 2012 @ HIP

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Quantum Anomaly
Formula insensitive to M, T, m ← IR scales∞∞ dp∣qB∣
Zero-pointfz
α n , s∫−∞ωn, sOscillation Γ=−N c ∑2 ∑∑2πflavor 2 πs n =0
Landauspin
degeneracy

ω

2n,s

Landaulevel

Chirality2=( √ p +2∣q f B∣n+sgn ( p z ) s μ 5 ) +M2z2dΓdΓjz==q f=# [ ω n , s ( p z =∞)−ω n , s ( p z =−∞) ]d Az
d pz
2∣q f B∣q f B μ5
=N c ∑ q fα n , s s μ 5=N c ∑2 ∑2
2 π nMay, s 10, 2012 @ HIP
2πflavorflavor21

(1+1)-dimensional Anomaly
Anomaly is a “surface” effectParticlesfrom momenta
at infinity!

Peskin-Schroeder
May 10, 2012 @ HIP

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Current from the Chiral Magnetic EffectParticles from infinitely large momentum
components in virtual excitations of quarks!?
All soft scales (M, T, m) are irrelevant!?
What would be seen in real experiments?
Let's take another example of quantum anomaly
for a better intuition!
May 10, 2012 @ HIP

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Triangle Anomaly
Anomaly Matching Condition ('t Hooft)j(q)=i ∫ d x e 〈 j (x ) j (0)〉 Be B qμ q̃ν 1 AB∼−N cδ
222π q 2
Equivalent to the chiral magnetic effect

Kj5BABμν4i q⋅xA5μB
ν

If quarks are confined, how can be this singularity saturated?

jB

p

j5

In the confined world there must be
massless NG bosons (chiral broken).
For Nf =2, massless proton and neutron
could saturate the IR singularity...
May 10, 2012 @ HIP24

p 0 → 2g
Typical example of the anomalous processγπ0γ
May 10, 2012 @ HIP

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B+p0→ g
Typical example of the anomalous process

Current!

π0γdΓ
jz=d Az

B

Asakawa-Majumder-Mueller
May 10, 2012 @ HIP

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Current on top of pions
If p 0 distributes coherently (with condensation),
microscopic currents in p 0 make a macroscopic
current (similar to the Josephson current in SC).
* p 0 domain wall and the current(Son-Stephanov)* Skyrmion and induced charge(Eto-Hashimoto-Iida-Ishii-Maezawa)May 10, 2012 @ HIP

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Chiral Magnetic Effectin a hadronic phase

May 10, 2012 @ HIP28

Chiral LagrangianN f χ top
f 2πμ†††2L= tr [ ∂μ U ∂ U +U χ+χ U ] −(−i ln det U −θ )42(i ϕ1eCondensate: U = 000iϕe0200iϕe3)2π(2m1 0Mass: χ= 0 m 220000m23)

N f χ top
2f2Potential: V (ϕ)=− ∑ m i cos ϕi+ϕi−θ∑2 i2i(Physics is periodic in terms of q (Dashen's phenomena)
May 10, 2012 @ HIP)

Witten29q = Pseudo-scalar Condensatef 1, f 2, f 3=-f 1-f 2 describe h 0 and h 8
N f χ top2f 2π2Potential: V (ϕ)=− ∑ m i cos ϕi+ϕi−θ
∑2 i2i()If any of flavors is massless, q -dependence is gone;
Absorbed by the pseudo-scalar condensate
If any of flavors is massless, q and the pseudo-scalarcondensate are simply identifiable.

May 10, 2012 @ HIP

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Local Parity Violation (LPV) again+h 0>0h 0<0h 0<0h 0>0

h 0>0
h 0<0+

Disoriented Chiral Condensate in not only the pion direction
but also the iso-singlet direction.
Pionic DCC would also exhibit the LPV.
Spatially and temporally fluctuating h0 condensates→ Inhomogeneous (and non-zero) q
May 10, 2012 @ HIP

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Question

Calculate a current with B and q (t)Do not use deconfined and massless quarks
but just stick to the Chiral Lagrangian!

May 10, 2012 @ HIP

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Anomaly in the Chiral LagrangianWess-Zumino-Witten Action−−π →e ̄νe γ
N c μ ν ρσ†̂̂L WZW =−ϵtr
Ur̂Ul−r̂
[{μνμlν232 π2†̂+i Σμ (U ̂r ν U + l ν ) ] tr ( vρ σ )+ tr( Σμ Σ ν Σ ρ) tr (v σ )30+ −π0 → 2 γγπ →π π†̂r̂ μ =̂v μ+ â μ , l μ= v̂ μ− â μ , Σμ =U ∂μ U

Axial vector field (traceless)
Kaiser-Leutwyler

Vector field (traceless)May 10, 2012 @ HIP33}

Another WZW (Contact Term)
WZW term without dynamical U fields
LP=

Nc
8N f π2ϵμ νρ σ{[ ()]itr v μ ∂ ν v ρ− [v ν , vρ ] ∂ σ θ3]}Nc
4+tr ( aμ D ν aρ ) tr ( a σ )+∂ σ θ −tr (aμ ) tr (∂ ν a ρ)∂ σ θ2 2312 N f π[()2 /30QED fields: vμ =eQ Aμ =e
Aμ0 −1/3
Kaiser-Leutwyler
May 10, 2012 @ HIP

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Current from the WZW Action

Γ p =∫

Ncμ νσρ

8N f π2ϵtr [v μ ∂ ν v ρ ]∂ σ θ+⋯d ΓpNc
zxyt
2jz==ϵ tr (Q ) B z ∂ t θ2d Az 4 N f π2fq B z ∂t θ=N c ∑⋅2f2π 2 N f
May 10, 2012 @ HIP

Time-dependent
DCC in the singlet channelμ535

Full Computation
Non-anomalous+−Currents from π , π flows
Non-singlet anomalous (conventional DCC)

Currents from inhomogeneous π condensation
Singlet anomalous (CME)

Currents from inhomogeneous η0 condensation
In completion (Fukushima-Mameda)
May 10, 2012 @ HIP36

Similar Effectsνj μ =ϵ μ ν σ ρ (∂ θ) FσρDerivative of a scalar quantity
h ' condensate
Pseudo-scalar condensate
2nd-rank tensor
Strong q angle
Field strength tensor
Angular momentum
Angular velocity

Chiral separation / vortical / … / effect
May 10, 2012 @ HIP37

Is there a current... or not?
Signature of what?

May 10, 2012 @ HIP38

What is necessary for the CME?
Is “quark deconfinement” necessary?

May 10, 2012 @ HIP39

What is necessary for the CME?
Is “quark deconfinement” necessary?

NO!?
Anomaly should be saturated with quarks and hadrons
This is realized by the Wess-Zumino-Witten action.
WZW is used for similar phenomena (Son-Stephanov)and can be for the CME.
What flows microscopically in a hadronic phase?
Through high-momentum quark component inthe h 0 condensate??
May 10, 2012 @ HIP

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What is necessary for the CME?
Is “quark deconfinement” necessary?

NO!?
Anomaly should be saturated with quarks and hadrons
This is realized by the Wess-Zumino-Witten action.
WZW is used for similar phenomena (Son-Stephanov)and can be for the CME.
Dima says sphaleron transitions enhancedin the deconfined phase at high temperature...
May 10, 2012 @ HIP

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What is necessary for the CME?
Is “chiral symmetry restoration” necessary?

May 10, 2012 @ HIP

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What is necessary for the CME?
Is “chiral symmetry restoration” necessary?

Probably Yes!?
WZW action does not require the chiral limit.
CME current is insensitive to the quark mass.
To form the DCC, far off-equilibrium matter fromchiral symmetric (and U(1)A symmetric) state is
implicitly assumed.
Picture in a hadronic phase
May 10, 2012 @ HIP43

What is necessary for the CME?
Is “chiral symmetry restoration” necessary?

Probably Yes!?
IF, topological gauge configurations (sphaleron)are given, not m 5 but N5 is generated.
N5 decays with the quark mass term.
(Chirality makes sense only for massless quarks)
Picture in a deconfined phase
May 10, 2012 @ HIP

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Experimental Challenges
and Theories

May 10, 2012 @ HIP

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Difficulty

P-odd quantity is zero on average
What we can observe in physics
of the strong interaction is:
NOT P (and CP) Violation
BUT Local P (and CP) Violation
Not qualitative but quantitative
May 10, 2012 @ HIP

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Difficulty〈 (P-odd Observable) 〉=02〈 (P-odd Observable) 〉=Large or Small?
Even if we find the latter large,
can we really say that we findthe local parity violation?
Theoretical prediction needed...
May 10, 2012 @ HIP

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Fluctuation of Charge Separation

 : Azimuthal angle
v1 : Directed flow
v2 : Elliptic flow
“Looking for parity violationin heavy-ion collisions”
by Berndt Müller
Physics 2, 104 (2009)
May 10, 2012 @ HIP

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Interpretation
Parity-Odd (Charge Separation)(α , β=+ , −)May 10, 2012 @ HIPCancel? NO!

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Famous (Infamous?) Results
3-Particle Correlation (fluctuation measurement)

STAR Results

VoloshinSTAR
May 10, 2012 @ HIP

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Followed up by RHIC (PHENIX)
Qualitative agreement with STAR

Figures froma talk by Laceyin CPODD

May 10, 2012 @ HIP

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Further confirmation from ALICE

Data from ALICEMay 10, 2012 @ HIP

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What really happens?

Theoretical fit I made three years ago
but didn't publish and just threw away!
May 10, 2012 @ HIP

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What really happens?

To fit the date, the CME is not necessary.
If going to peripheral, less particles andlarger fluctuations....
all!
May 10, 2012that's@ HIP

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Systematic fit possible?

Species dependence

Pt dependence
May 10, 2012 @ HIP

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Difficulty

Theoretical fit is always possible.
But... so what?
We cannot conclude anything!

May 10, 2012 @ HIP

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Decomposition (Background)〈 cos (Δ ϕα +Δ ϕβ )〉=〈 cos Δ ϕα cos Δ ϕβ 〉−〈 sin Δ ϕα sin Δ ϕβ 〉〈 cos (Δ ϕα −Δ ϕβ )〉=〈 cos Δ ϕα cos Δ ϕβ 〉+〈 sin Δ ϕα sin Δ ϕβ 〉Bzdak-Koch-Liao (2009)

Not ruled out (yet?)No longer considered as
an evidence of anything...

May 10, 2012 @ HIP

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Multi-Particle Correlation
Two Distribution Functionsh〈 S p =sin   p 〉h−〈 Sn 〉h∓〈S p 〉h∓〈 Sn 〉PHENIXTalk by Laceyin CPODD

May 10, 2012 @ HIP

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Summary
Theory of the Chiral Magnetic Effect is robust, but
phenomenological inputs have uncertainties...
Parity Violation itself cannot be seen, and only its
fluctuations are observed which are parity even!
Subtraction of backgrounds is very hard...
Important to look at physics observables with whichflow effects are distinguishable (multi-particle corr.)More from forthcoming conferences:
CPODD (BNL – June) QM (Washington D.C. – Aug.)QCD in a Strong B (ECT*– Nov.)
May 10, 2012 @ HIP

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