Towards a quantum theoryof chiral magnetic effect

V.Shevchenko (ITEP, Moscow)

QUARKS - 2010Kolomna, Russia

11/06/2010

based on a paper with V.Orlovsky, to appear

It is often useful to think about QFT vacuum as about a medium

Αἰθήρ

There is a huge hierarchy of dynamical scales in Naturecharacterizing the vacua of different sectors of the SM(and beyond).

To study the properties of these (and actually of any) media one uses two main approaches: • Send test particles• Put external conditions (fields, temperature, density etc)

τ, Fm

eB,

(MeV

)2

Kharzeev, McLerran, Warringa, ‘07

Heavy ions collision experiments provide an interesting interplay ofthese strategies because the matter created after the collision ofelectrically charged ions is hot (T ≠ 0), dense (µ ≠ 0) and experiencestrong abelian fields in the collision region (B ≠ 0).

B

This opens the window (or a chance, at least) for experimental studies of QCD in abelian magnetic fields with the magnitude of QCD dynamical scale.

Pro & contra

• Non-stationary nature of the problem• Fast field decay, time- integrated field is moderate• No clear experimental signature, “null test”

Asakawa, Majumder, Müller ‘10

A seminal suggestion:Kharzeev, Pisarski, Tytgat, ’98; Halperin, Zhitnitsky, ‘98;Kharzeev, ’04; Kharzeev, McLerran, Warringa ’07 …

Possible experimental manifestations of chiral magnetic effectin heavy ion collisions ?

µR

µL

Energy

Right-handedLeft-handed

Many complementary ways to derive (Chern-Simons,linear response, triangle loopetc)

Robust theoretical effect

Electric current along the magnetic field

Final particles charge distribution asymmetry?

(pictures from Ilya Seluzhenkov’s talk at RHIC@AGS Users’ Meeting)

(pictures from arXiv:0909.1717STAR Collaboration)

Important questions:

1. What is CME in real QCD?There is no such thing as µ5 in QCD Lagrangian

2. What is quantum meaning of CME?

3. Can CME be used to explain the observed charge asymmetries? There might be alternative explanations (see, e.g. Asakawa, Majumder, Müller ’10)

To answer the first question it is often argued that quark interaction with topologically non-trivial gluon fields generates “effective” chiral chemical potential in each single event.

It is worth reminding that for any volume!

Quantum dynamics of topological fluctuations is governedby Veneziano-Witten formula

and in stationary case for any Minkowski 4-volume all field configurations interfere in the sum over histories.

One needs true space-time fluctuation pattern!

We discuss three basic ways to address the CMEin quantum framework:

• P-parity violation probed by local order parameters

• CME in quantum measurement theory framework

• P-odd × P-odd contributions to P-even observables

Our world WonderlandDNA

Р-parity is 100% broken (as is in EW-sector of the SM)

P-parity violation probed by local order parameters

3. The medium with applied external field:

1. Macroscopic quantities out of microscopic ones”VIII LL volume out of II LL volume” ©

2. The medium:

Local parity violation:

and e.g.

In a medium with applied external field one can have

P-odd correlation between charge density and divergence of axial current in moving medium in magnetic field:

BIf ∂J5 is uniform in the volume of the fireball, charge density changes thesign crossing the reaction plane

v

v

P-parity violation induced by measurement

Simple example:

Event-by-event P-parityviolation?

In QM individual outcome (“event”) has no meaning

For conserved axial current

However, due to anomaly

where

We define

The formalism is based on partial partition functions

;

;

with the detector function

Taking into account that for singlet current at Nc=3

one gets in Gaussian approximation

Notice that as it should be.

where ;

Maximal current is reached by

Topological susceptibility sharply drops at T>Tc

Del Debbio, Panagopoulos, Vicari, ‘04

P-odd × P-odd contributions to P-even observables

The object of main interest is polarization operator

since it encodes information about where

Confinement phase, large distances, weak fields

Clear similarity with vector-axial mixing at finite T(Dey, Eletsky, Ioffe, ’90)

πj j

Confinement phase, strong fields:

If Larmor radius is much smaller than ΛQCD no quarkdegrees of freedom can propagate in transverse direction

η,ήj j

Thus correlations in transverse plane are entirely due to gluoncomponents of isoscalar currents

We are interested in transition matrix elements betweenstates of opposite parity

Tensor structure of polarization operator is fixed bycurrent conservation, Bose symmetry and generalizedFurry’s theorem

Perez Rojas,Shabad, ’79;Alexandre, ‘00

Of special interest for us is a tensor

With conventional notation

for the chosen background

For free fermions in strong field limit the formfactorbecomes dominant in temperature-independent part:

To make contact with charge fluctuation pattern we use

Let us consider

and expand

in harmonics:

The result reads:

where one is to assume particular time/temperature profile

It is worth reminding that quantum fluctuations is a finite volume effect (UV-protected by gauge invariance):

The large field limit

makes this fact manifest in another way.

Numerically relevant dimensionless parameter is

Conclusions

• Chiral magnetic effect is a robust theoreticalresult with possible applications in high energy and condensed matter physics

• At the moment there are no unequivocal arguments relating CME and charge asymmetry fluctuations in heavy ion collisions experiments at RHIC

• Future studies of heavy ion collisions (RHIC@BNL, ALICE@CERN, FAIR@GSI, NICA@JINR) have great discovery potential and will surely deepen our understanding of strong interaction physics