В поисках кирального магнитного эффекта

1. В поисках кирального магнитного эффекта В.И.Шевченко НИЦ Курчатовский институт Померанчук-100 ИТЭФ, Москва, 06/ 06 / 2013

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. Matter dominance Chirality Arrows of time

4. Closer look at P-parity 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... no Furry theorem at µ ≠ 0 + ≠ 0 or, magnetic catalysis of CSB at finite B…

5. Electroweak sector M.Giovannini, M.E.Shaposhnikov, ‘97 Hypercharge magnetic fields. At T>Tc : U(1)em → U(1)Y • Strong sector P-odd bubbles T.D.Lee, G.C.Wick, ’66 : Pion condensate A.B.Migdal, ’71 : M.Dey, V.L.Eletsky, B.L.Ioffe, ’90 : ρ-π mixing at T ≠ 0 0-+ j j L. McLerran, E.Mottola, M.E.Shaposhnikov, ‘91 Sphalerons and axions at high-T QCD

6. LHC as a tester of symmetries General purpose experiments Electroweak gauge symmetry breaking pattern: Higgs boson and/or New Physics? Space-time symmetries: extra dimensions, black holes? Supersymmetry:particles – superpartners? Dark matter? Enigma offlavor New state of matter CP-violation: new sources? Baryon asymmetry. Indirect search of superpartners. Chiral symmetry of strong interactions: pattern of restoration? Deconfinement.P-parity violation?

7. 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!) B Voronyuk, Toneev, Cassing et al, ‘11

8. (slide from D.Kharzeev)

9. Idea: electric current along the magnetic field final particles charge distribution asymmetry with respect to reaction plane for noncentral collisions chiral magnetic effect (pictures from I.Seluzhenkov)

10. 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 Energy µR Many complementary ways to derive (Chern-Simons, linear response, triangle loop etc). At effective Lagrangian level µL Left-handed Right-handed Robust theoretical result Possible experimental manifestations of chiral magnetic effect ?

11. This CME current is non-dissipative No arrow of time, no dissipation, no entropy production Clear similarity with superconductivity, but temperature-independent!

12. py px

13. ALICE@ LHC& (STAR&PHENIX) @ RHIC study new state of matter, sometimes referred to as quark-gluon plasma It is not plasma RHIC «You could think of it as of boiling operator liquid» I.Ya.Pomeranchuk, 1950 strongly coupled (no obvious quasiparticles) nearly ideal (small viscosity) liquid (well described by hydrodynamics)

14. The matter produced at LHC still behaves as very low viscosity fluid (from PRL, 105 (2010) 252302)

15. Charge asymmetry ALICE, arXiv: 1207.0900

16. Questions worth to explore: (the list is by definition subjective and incomplete) • How to proceed in a reliable way from nice qualitative picture of CME to quantitative predictions for charge particle correlations measured in experiments? • How to disentangle the genuine nonabelian physics from just dynamics of free massless fermions in magnetic field? • How is the fact of quantum, anomalous and microscopic current non-conservation encoded in equations for macroscopic, effective currents? • What is quantum dynamics behind µ5? • …

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

18. CME can be seen as a consequence of correlation between the vector and (divergence of the) axial current vanishing in the vacuum.

19. 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 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.

20. Measurement can induce symmetry violation Hamiltonian with P-even potential Measuring coordinate in a single experiment (“event”) one gets sequence of generally nonzero values with zero mean Device itself is P-odd! Event-by-event P-parity violation? In QM individual outcome has no meaning Law of Nature, not inefficiency of our apparatus

21. Measurement is a story about interaction between quantum and classical objects. Interaction with the medium provides decoherence and transition from quantum to classical fluctuations in the process of continuous measurement. Quantum fluctuations: all histories (field configurations) coexist together and simultaneously Classical fluctuations (statistical, thermal etc): one random position (field configuration) at any given time Quantum fluctuations of electromagnetic field in the vacuum do not lead to radiation of freely moving charge

22. Measurement of the electric current fluctuations in external magnetic field for masslessfermions. Standard Unruh – DeWitt detector coupled to vector current: Amplitude to click: Response function:

23. 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

24. 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

25. Asymmetry: The result: • 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 Вfor whatever field, weak or strong • inversion of statistics from FD for elementary excitations to • BE for the observable being measured

26. At large magnetic fields B≠0 T≠0 Fluctuations enhancement along the field and suppression perpendicular to it by the same amount

27. 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 Buoyancy force in the direction of gradient of the magnetic field T≠0

28. Effects of finite time: detector is in operation for the time λ In particular, The result: Due to the energy-time uncertainty principle the asymmetry shows up even in chirally symmetric case.

29. 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

30. In Gaussian approximation Fluctuations are correlated due to

31. For the model Gaussian Ansatz the current is given by Maximal effective µ5 in the model: • the current flows only inside decoherence volume • it is odd in κand linear in B • it has a maximum value (as a function of κ) • subtle interplay of abelian and nonabelian anomalies

32. The filter field κ describes classicalization of some P-parity odd degrees of freedom in the problem. It is this classicalizationthat 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. Once again classical pattern for strongly interacting many-body quantum system – in more than 50 years after Fermi-Pomeranchuk-Landau.

33. 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:

34. Conclusion 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. From theoretical side, we need to work out full hydrodynamical description of chiral liquids and understand the role of decoherence and non-stationarity. From experimental side, systematic measurements of various correlatorsis foreseen. There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.W.Shakespeare, Hamlet Act 1, scene 5

35. Спасибо за внимание!

37. 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.

38. Higher harmonic anisotropic flow (from PRL, 107 (2011) 032301)

39. Elliptic flow does not change much from RHIC to LHC (from PRL, 105 (2010) 252302)

40. (S.A.Voloshin, ’04) (ALICE, ’11)

41. Energy scan for charge separation STAR, arXiv:1210.5498 [nucl-ex])

42. 3. Charge asymmetry comparison between Au and U STAR, arXiv:1210.5498 [nucl-ex]

43. 4. Charge asymmetries of higher harmonics

44. Hydrodynamic description: Equation of motion: Equation of state: Emergent conformal symmetry for effective theory:

45. One general comment about chiral current Not all currents of the form results from the physics of massless degrees of freedom: with the “chiral current” The crucial point is time dependence, not masslessness

46. To consider less trivial example, lets us take for but not invariant under reflections of only one coordinate. 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 If the measuring device is switched off

47. Qualitative outcome of the above analysis: (stronger current fluctuations along the field B than in reaction plane) (if the asymmetry is caused by B only) Data clearly indicate presence of both terms