В поисках кирального магнитного эффекта

В.И.Шевченко

НИЦ Курчатовский институт

Померанчук-100ИТЭФ, Москва, 06 / 06 / 2013

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

Matterdominance

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...

+ ≠ 0no Furry

theorem atµ ≠ 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>Tc : 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, ‘11B

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 ?

µR

µL

Energy

Right-handedLeft-handed

Many complementary ways to derive (Chern-Simons,linear response, triangle loopetc). At effective Lagrangian level

Robust theoretical result

~5

This CME current is non-dissipative

j σ EP - + -T - - +

j σχ B

P - - +T - + -

No arrow of time, no dissipation, no entropy production

Clear similarity with superconductivity, but temperature-independent!

py

px

ALICE @ LHC & (STAR&PHENIX) @ RHIC study new state of matter, sometimes referred to as quark-gluon plasma

It is not plasmaRHIC

strongly coupled(no obviousquasiparticles)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 stillbehaves 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 µ5 ?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 abelianfield 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”) onegets 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 quantumand classical objects.

Quantum fluctuations:all histories (fieldconfigurations) coexisttogether and simultaneously

Classical fluctuations(statistical, thermal etc):one random position (field configuration) at any given time

Interaction with the medium provides decoherence andtransition 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 thedirection of gradientof 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 asymmetryshows 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 µ5 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 parallelwith common wisdom about importance of (quasi)classical degrees of freedom in heavy ion collisions.

Superfluidity → macroscopically coherent quantum phase →non-dissipative (superconducting) current. Compare withnon-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:

Conclusion1. 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% brokenat 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 muchfrom 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)