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Nov 15, 2013 (3 years and 11 months ago)

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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)