Towards a quantum theory of chiral magnetic effect V.Shevchenko (ITEP, Moscow) QUARKS Kolomna, 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 Α ἰ θήρ There is a huge hierarchy of dynamical scales in Nature characterizing 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 of these strategies because the matter created after the collision of electrically charged ions is hot (T ≠ 0), dense (µ ≠ 0) and experience strong 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 effect in heavy ion collisions ? µRµR µLµL Energy Right-handedLeft-handed Many complementary ways to derive (Chern-Simons, linear response, triangle loop etc) Robust theoretical effect

Electric current along the magnetic field Final particles charge distribution asymmetry? (pictures from Ilya Seluzhenkov’s talk at Users’ Meeting)

(pictures from arXiv: STAR Collaboration)

Important questions: 1.What is CME in real QCD? There is no such thing as µ 5 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 governed by 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 CME in 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 Wonderland DNA 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: ande.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: B If ∂J 5 is uniform in the volume of the fireball, charge density changes the sign crossing the reaction plane v v

P-parity violation induced by measurement Simple example: Event-by-event P-parity violation? 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 N c =3 one gets in Gaussian approximation Notice that as it should be. where; Maximal current is reached by

Topological susceptibility sharply drops at T>T c 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) π jj

Confinement phase, strong fields: If Larmor radius is much smaller than Λ QCD no quark degrees of freedom can propagate in transverse direction η,ήη,ή jj Thus correlations in transverse plane are entirely due to gluon components of isoscalar currents We are interested in transition matrix elements between states of opposite parity

Tensor structure of polarization operator is fixed by current conservation, Bose symmetry and generalized Furry’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 formfactor becomes 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 theoretical result 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 have great discovery potential and will surely deepen our understanding of strong interaction physics