1. Strong CP violation in hot QCD: from heavy ion collisions to cosmology D. Kharzeev BNL Winter Workshop on Nuclear Dynamics, La Jolla, 2006 Phys.Lett.B633 (2006) 260, + work in progress

2. QCD and the U A (1) problem.i Invariant under chiral transformations in the limit of massless quarks U L (N f )xU R (N f ) chiral symmetry parity doubling in the hadron spectrum (not seen!) If broken spontaneously, N f 2 = 9 Goldstone bosons. Only 8 exist; the ninth,  ’ is heavier than the proton! Left Right => Something is wrong with the flavor-singlet U A (1)…

3. Axial anomaly Consider the flavor singlet current It is not conserved even in the m -> 0 limit due to quantum effects: Divergence can be written down as a surface term, and so is seemingly irrelevant:

4. Instantons and the U A (1) problem But: sometimes, surface terms are important Instantons: classical Euclidean solutions of QCD which map color SU(2) onto the sphere S 3 ; in Minkowski space, describe quantum tunneling between degenerate vacua with different topological Chern-Simons numbers As a result, chiral charge is no longer conserved

5. QCD vacuum as a Bloch crystal “quasi-momentum” “coordinate” “  - vacuum”

6. The lost symmetries of QCD The prescription with the “Bloch” weight is equivalent to adding to the Lagrangian a new piece which is odd under P, T, CP symmetries !

7. The strong CP problem Unless  =0, P, T and CP invariances are lost! Experiment: (e.d.m. of the neutron) Why  is so small? Axions? - PVLAS - recent evidence? Will assume  =0 for the rest of the talk

8. The strong CP problem and the structure of QCD vacuum Vafa-Witten theorem: P and CP cannot be broken spontaneously in QCD But: 1. it does not constrain metastable states 2. it does not apply at finite temperature, finite baryon density, finite isospin density

9. CP-odd domains in heavy ion collisions: how to look for them? v.e.v. of the  field is equivalent to non-zero  DK, Pisarski, Tytgat ‘98

10. Diffusion of Chern-Simons number in QCD: real time lattice simulations DK, A.Krasnitz and R.Venugopalan, Phys.Lett.B545:298-306,2002 P.Arnold and G.Moore, Phys.Rev.D73:025006,2006 What are the experimental signatures?

11. What are the observable signatures of strong CP violation? rotate all CP violating phase into the quark piece of the Lagrangian: is a complex mass parameter In a CP-odd domain, This leads to the asymmetry between “left” and “right” quarks What is “left” and what is “right”? Quarks are massive, so the definition of chirality depends on the frame…

12. Azimuthal anisotropy: collective flow of strongly interacting matter Hydro limit STAR PHOBOS Hydro limit STAR PHOBOS Description in terms of relativistic hydrodynamics

13. A.Nakamura and S.Sakai, hep-lat/0406009 Quark-gluon plasma: more fluid than water? KSS bound: strongly coupled SUSY QCD = classical supergravity Superfluid helium

14. Azimuthal anisotropy = angular momentum What happens if a superfluid is rotated?

15. Magnetic vortices in rotating super-fluids J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Observation of Vortex Lattices in Bose-Einstein Condensates, Science 292, 476 (2001). E.J. Yarmchuk, M.J.V. Gordon, and R.E. Packard, Observation of Stationary Vortex Arrays in Rotating Superfluid Helium, Phys. Rev. Lett. 43, 214 (1979).

16. Magnetic vortices “Higgs” field Energy density

17. Magnetic vortices in QCD superfluid and CP violation E PzPz Left quarks Right anti-quarks Fluctuation of chromo-electric field in the presence of chromo-magnetic vortex produces left quarks and right anti-quarks (level crossing at the 0th Landau level)

18. Magnetic vortices in QCD superfluid and CP violation Left quarks: in the electric field, energy increases: Decreases by the same amount for right anti-quarks. Density of states = longitudinal x transverse: Rate of chirality generation: Analogous to cosmic strings, except not 1D

19. Magnetic vortices in QCD superfluid and CP violation The Fermi momentum has to be smaller than the mass of the quark in the fluid: otherwise, energetically unfavorable - quark can escape into the fluid (no CP violation for massless quarks!) What is M in a strongly coupled fluid?

20. Magnetic vortices in QCD superfluid and CP violation Analogs: Magnetic monopole - induced baryon decay Cosmic strings Chirality generation in superfluid 3 He …………

21. Charge asymmetry w.r.t. reaction plane as a signature of strong CP violation + - excess of positive charge excess of negative charge Electric dipole moment of QCD matter!

22. Charge asymmetry w. r.t. reaction plane violates T, P, and (by CPT theorem) CP:

23. Analogy to P violation in weak interactions

24. Charge asymmetry w.r.t. reaction plane: how to detect it? + - m k S.Voloshin, hep-ph/0406311 Expect

25. Do we see strong CP violation? I. Selyuzhenkov et al., STAR Coll., nucl-ex/0510069; October 25, 2005 Need to analyze the systematics and to understand if the effect is real

26. Other signatures? I. Separation of baryon number with respect to reaction plane? Protons and anti-protons II. Other observables composed of pion momenta? Chern-Simons number of chiral fields III. Lambda helicity correlations? J. Sandweiss …

27. What are the implications for the Early Universe?

28. What is the origin of cosmic magnetic fields? Magnetic field in M51: Polarization of emission Beck 2000 Magnetic fields are abundant in the Universe at large scales: 3  G field in Milky Way; 1-40  G fields in clusters of galaxies

29. What is the origin of magnetic fields in the Universe? Primordial magnetic field (E.Fermi, 1949)? Dynamo in proto-galaxy? Stars? Galaxy? Domain walls and vortices associated with the  vacua carry magnetic field; (“magnetic helicity”,…) Primordial magnetic field generation at the QCD phase transition?

30. Baryons in the Universe Baryons in the Universe are rare: 1 baryon per ~ 2 billions photons in the Cosmic Microwave Background Radiation ~ 400 photons/cm 3 ~ 1 proton/m 3 (Almost) no visible antimatter - why the asymmetry?

31. What is the origin of the matter-antimatter asymmetry in the Universe? 1.B violation 2.CP violation 3.Non-equilibrium dynamics A.D. Sakharov, JETP Lett. 5 (1967) 24

32. Baryon asymmetry in the Universe and strong CP violation 1. Generation of Chern-Simons number at the QCD phase transition is analogous to baryon number generation in the electroweak phase transition 2. Strong CP violation separation of matter and antimatter in the Universe at the QCD phase transition ? e.g. V.Kuzmin, V.Rubakov and M.Shaposhnikov, Phys.Lett.B155(1985)36

33. Summary 1.P and CP violation in hot QCD is not forbidden 2. “All what is not forbidden is allowed” and may exist; a specific dynamical mechanism - magnetic vortices 3. Rejecting or confirming the signal of P and CP violation at RHIC is an urgent problem of fundamental importance