1. Quantum measurements and chiral magnetic effect V.Shevchenko Kurchatov Institute, Moscow Workshop on QCD in strong magnetic field Trento, Italy, 15 November 2012 based on arXiv: 1008.4977 (with V.Orlovsky); 1208.0777

2. 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

3. 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

4. Theoretical view: 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.

5. 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... +≠ 0 no Furry theorem at µ ≠ 0 or, magnetic catalysis of CSB at finite B…

6. 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 Closer look at P-parity

7. A seminal suggestion for QCD: 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 ? µRµR µLµL Energy Right-handedLeft-handed Many complementary ways to derive (Chern-Simons, linear response, triangle loop etc). At effective Lagrangian level Robust theoretical result

8. 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.…

9. 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:

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

11. 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

12. 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. 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

13. …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.

14. 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!

15. 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

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

17. 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:

18. 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

19. 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

20. 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

21. T≠0 B≠0 The asymmetry is small: Fluctuations enhancement along the field and suppression perpendicular to it by the same amount At large magnetic fields

22. 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

23. ALICE, arXiv: 1207.0900 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)

24. 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

25. In Gaussian approximation Fluctuations are correlated due to

26. 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:

27. 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. Classical pattern for strongly interacting many-body quantum system

28. Instead of conclusion… Thank you for attention!