В поисках
кирального
магнитного эффекта
В.И.Шевченко
НИЦ Курчатовский институт
Померанчук

100
ИТЭФ, Москва, 06
/
06
/ 201
3
Vacuum
of any QFT (and the SM in particular)
is
often described as a special (relativistic etc)
medium
There are two main approaches to study properties
of this (and actually of any) media:
•
Send test particles and look how they move and interact
•
Put external conditions and study response
Of particular interest is a question about
the fate of symmetries
under this or that choice of external conditions
Macro
Micro
C
P
T
Matter
dominance
Arrows
of time
Chirality
Vacuum expectation value of any local
P

odd observable
has to vanish in vector

like theories such as QCD
(
C.Vafa
,
E.Witten
, ’84).
There can however be surprises at finite
T/B/µ/..
For example,
C

invariance is intact at finite temperature,
but gets broken at finite density...
+
≠
0
no Furry
theorem at
µ
≠ 0
or, magnetic catalysis of CSB at finite
B
…
Closer look at P

parity
A.B.Migdal
, ’71 :
M.Giovannini
,
M.E.Shaposhnikov
, ‘97
•
Electroweak sector
•
Strong sector
Pion
condensate
T.D.Lee
,
G.C.Wick
, ’66 :
P

odd bubbles
M.Dey
,
V.L.Eletsky
,
B.L.Ioffe
, ’90 :
ρ

π
mixing at
T ≠ 0
L.
McLerran
,
E.Mottola
,
M.E.Shaposhnikov
, ‘91
Hypercharge magnetic fields. At
T>
T
c
: U(1)
em
→ U(1)
Y
Sphalerons
and
axions
at high

T
QCD
0

+
j
j
LHC as a tester of symmetries
Electroweak gauge symmetry breaking pattern
:
Higgs boson and/or New Physics?
Space

time symmetries:
extra dimensions, black holes?
Supersymmetry
:
particles
–
superpartners
? Dark matter?
Enigma of
flavor
CP

violation: new sources?
Baryon asymmetry.
Indirect search of
superpartners
.
Chiral
symmetry of strong
interactions: pattern of restoration?
Deconfinement
.
P

parity violation?
New state of matter
General purpose experiments
Voronyuk
,
Toneev
,
Cassing
et al, ‘11
B
Heavy ions collision experiments → the matter created
after collision of electrically charged ions is hot (
T ≠ 0
),
dense (
µ ≠ 0
) and experience strong
abelian
fields in
the collision region (
B ≠ 0
) (and all is time

dependent!)
(slide from
D.Kharzeev
)
Idea:
electric current along the magnetic field
final particles charge distribution asymmetry with respect
to reaction plane for
noncentral
collisions
(pictures from
I.Seluzhenkov
)
chiral
magnetic effect
Vilenkin
, ‘80 (not in heavy ion collision context);
Kharzeev
,
Pisarski
,
Tytgat
, ’98;
Halperin
,
Zhitnitsky
, ‘98;
Kharzeev
, ’04;
Kharzeev
,
McLerran
,
Warringa
’07;
Kharzeev
, Fukushima,
Warringa
’08
Possible experimental manifestations of
chiral
magnetic effect
?
µ
R
µ
L
Energy
Right

handed
Left

handed
Many complementary ways
to derive (
Chern

Simons,
linear response, triangle loop
etc). At effective
Lagrangian
level
Robust theoretical result
~
5
This CME current is
non

dissipative
j
σ
E
P

+

T


+
j
σ
χ
B
P


+
T

+

No arrow of time, no dissipation, no entropy production
Clear similarity with superconductivity,
but temperature

independent!
p
y
p
x
ALICE
@ LHC
& (STAR&PHENIX) @ RHIC
study new state
of matter, sometimes referred to as
quark

gluon plasma
It is not plasma
RHIC
strongly coupled
(no obvious
quasiparticles
)
nearly ideal
(small viscosity)
liquid
(well described by
hydrodynamics)
I.Ya.Pomeranchuk
, 1950
«
You could think of it as of boiling operator liquid
»
(from PRL, 105 (2010) 252302)
The matter produced at LHC still
behaves as very low viscosity fluid
ALICE,
arXiv
: 1207.0900
Charge asymmetry
Questions worth to explore:
(the list is by definition subjective and incomplete)
1.
How
to
proceed
in
a
reliable
way
from
nice
qualitative
picture
of
CME
to
quantitative
predictions
for
charge
particle
correlations
measured
in
experiments?
2.
How
to
disentangle
the
genuine
nonabelian
physics
from
just
dynamics
of
free
massless
fermions
in
magnetic
field?
3.
How
is
the
fact
of
quantum,
anomalous
and
microscopic
current
non

conservation
encoded
in
equations
for
macroscopic,
effective
currents?
4.
What
is
quantum
dynamics
behind
µ
5
?
5.
…
CME can be seen as a consequence of correlation between
the vector and (divergence of the) axial current
vanishing in the vacuum.
CME can be seen as a consequence of correlation between
the vector and (divergence of the) axial current
vanishing in the vacuum. Not the case if external
abelian
field is applied:
and the coefficient is fixed by triangle (
abelian
) anomaly.
The
correlator
is the same regardless the physics behind
quantum fluctuations of the currents.
CME can be seen as a consequence of correlation between
the vector and (divergence of the) axial current
Measurement can induce symmetry violation
Event

by

event
P

parity violation?
In QM individual outcome has no meaning
Hamiltonian with
P

even potential
Measuring coordinate in a single experiment (“event”) one
gets sequence of generally nonzero values with zero mean
Law of Nature, not inefficiency of our apparatus
Device itself is P

odd!
Measurement is a story about interaction between quantum
and classical objects.
Quantum fluctuations:
all histories (field
configurations) coexist
together and simultaneously
Classical fluctuations
(statistical, thermal etc):
one random position
(field configuration) at
any given time
Interaction with the medium provides
decoherence
and
transition from quantum to classical fluctuations in the
process of continuous measurement.
Quantum fluctuations of electromagnetic field in the vacuum
do not
lead to radiation of freely moving charge
Standard Unruh
–
DeWitt detector coupled to vector current:
Amplitude to click:
Measurement of the electric current fluctuations in
external magnetic field for
massless
fermions.
Response function:
Usually one is interested in detector excitation rate in unit
time. For infinite observation time range it is determined by
the power spectrum of the corresponding Wightman function:
where
The detector is supposed to be at rest. Explicitly one gets
Usually one is interested in detector excitation rate in unit
time. For infinite observation time range it is determined by
the power spectrum of the corresponding Wightman function:
where
The detector is supposed to be at rest. Explicitly one gets
The result:
Asymmetry:
•
positive
, i.e. detector measuring currents along the field
clicks more often than the one in perpendicular direction
•
caused by
the same term in the Green’s function which is
responsible for triangle
anomaly
•
no higher orders
in magnetic field, the asymmetry is
quadratic in
В
for whatever field, weak or strong
•
inversion of statistics
from FD for elementary excitations to
BE for the observable being measured
T≠0
B≠0
Fluctuations
enhancement along the field
and
suppression perpendicular to it
by the same amount
At large magnetic fields
Same physics in the language of energy

momentum tensor:
B = 0
Strong magnetic field:
If the magnetic field is strong but slowly varied:
Magnetic
Arkhimedes
law
B≠0
T≠0
Buoyancy force in the
direction of gradient
of the magnetic field
Effects of finite time: detector is in operation for the time
λ
In particular,
Due to the energy

time uncertainty principle the asymmetry
shows up even in
chirally
symmetric case.
The result:
Measurement in the language of
decoherence
functionals
and filter functions
one can define distribution amplitude for the vector current
and some
P

odd quantity
CTP functional
Mean field current
In Gaussian approximation
Fluctuations are correlated due to
For the model Gaussian
Ansatz
•
the current flows only
inside
decoherence
volume
•
it is
odd in
κ
and
linear in
B
•
it has a
maximum value
(as a function of
κ
)
•
subtle
interplay
of
abelian
and
nonabelian
anomalies
the current is given by
Maximal effective
µ
5
in the model:
The filter field
κ
describes
classicalization
of some
P

parity
odd degrees of freedom in the problem. It is this
classicalization
that leads to electric current.
Classicalization
is caused by
decoherence
: clear parallel
with common wisdom about importance of (quasi)classical
degrees of freedom in heavy ion collisions.
Superfluidity
→ macroscopically coherent quantum phase →
non

dissipative (superconducting) current. Compare with
non

dissipative CME current flowing in
decohered
media.
Once
again
classical
pattern
for
strongly
interacting
many

body
quantum
system
–
in
more
than
50
years
after
Fermi

Pomeranchuk

Landau
.
Are there traces of CME at
central
collisions?
Fluctuation

dissipation theorem: yes, they should be.
Two ways to measure conductivity (in LR

approximation):
according to Ohm:
according to
Nyquist
:
Conclusion
1.
Experimentally
observed
effects
of
final
particle
charge
asymmetries
in
heavy
ion
collisions
can
be
caused
by
chiral
magnetic
effect
–
subtle
interplay
of
abelian
and
nonabelian
anomalies
.
2.
From
theoretical
side,
we
need
to
work
out
full
hydrodynamical
description
of
chiral
liquids
and
understand
the
role
of
decoherence
and
non

stationarity
.
3.
From
experimental
side,
systematic
measurements
of
various
correlators
is
foreseen
.
There are more things in heaven and earth, Horatio, Than
are dreamt of in your philosophy.
W.Shakespeare
, Hamlet
Act 1, scene 5
Спасибо за внимание
!
SM = EW + QCD
P

invariance
is
100
%
broken
at
Lagrangian
level
(lefts
are
doublets,
rights
are
singlets
)
.
CP

invariance
(and
hence
T
)
gets
broken
by
CKM
mechanism
(complex
phase)
Without
θ

term
QCD
Lagrangian
is
invariant
under
P

,
C

and
T

transformations
.
(from PRL, 107 (2011) 032301)
Higher harmonic
anisotropic flow
(from PRL, 105 (2010) 252302)
Elliptic flow does not change much
from RHIC to LHC
(
S.A.Voloshin
, ’04)
(ALICE, ’11)
1.
Energy scan for charge separation
STAR, arXiv:1210.5498 [
nucl

ex])
3. Charge asymmetry comparison between
Au
and
U
STAR, arXiv:1210.5498 [
nucl

ex]
4. Charge asymmetries of higher harmonics
Hydrodynamic description
:
Equation of motion
:
Equation of state
:
Emergent conformal symmetry for effective theory
:
with the “
chiral
current”
The crucial point is time dependence, not
masslessness
One general comment about
chiral
current
Not all currents of the form
results from the physics of
massless
degrees of freedom:
If one is monitoring
P

odd observable, e.g.
where the corridor width is given by
the result for another (correlated)
P

odd observable is
To consider less trivial example, lets us take
for but not invariant
under reflections of only one coordinate.
If the measuring device is switched off
Qualitative outcome of the above analysis:
Data clearly indicate presence of both terms
(stronger current fluctuations along the field
B
than in
reaction plane)
(if the asymmetry is caused by
B
only)
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