Quantum measurements and

chiral magnetic effectV.Shevchenko

Kurchatov Institute, Moscow

Workshop on QCD in strong magnetic fieldTrento, Italy, 15 November 2012

based on arXiv: 1008.4977 (with V.Orlovsky); 1208.0777

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

Experimental view: 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

Theoretical view:

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.

Moreover, 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…

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

Closer look at P-parity

A seminal suggestion for QCD: chiral magnetic effectVilenkin, ‘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

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. …

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:

CME can be seen as a consequence of correlation between the vector and (divergence of the) axial current

Another general comment

vanishing in the vacuum.

Another general comment 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.

Far from being intuitively clear …

Another general comment CME can be seen as a consequence of correlation between the vector and (divergence of the) axial current

…and one more comment It could be interesting to look on the lattice at nonlocal“order parameters” like

vanishing without external magnetic field. With nonzero field one would expect (for free fermions)

where there are no higher powers of magnetic field.

(Non)renormalization, temperature dependence etc.

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!

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

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 magnetic field in the vacuum do not force a freely moving charge to radiate

Standard Unruh – DeWitt detector coupled to vector current:

Amplitude to click:

Measurement of the electric current fluctuations in external magnetic field for free 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≠0B≠0

The asymmetry is small:

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

ALICE, arXiv: 1207.0900

Qualitative outcome of the aboveanalysis:

Data clearly indicate presence of both terms

(stronger current fluctuations alongthe field B than in reaction plane)

(if the asymmetry is caused by B)

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.

Classical pattern for strongly interacting many-body quantum system

Instead of conclusion…

Thank you for attention!