Oleg Teryaev JINR

1. Oleg Teryaev JINR Vorticity in Heavy-Ion Collisions and its manifestations ECT*,Trento QCD in Strong Magnetic fields November 13 2012

2. Outline Rotating QCD matter: comparing magnetic field and vorticity • Chiral Vortical Effect & neutron asymmetries (@ NICA) • Vorticity in model calculations • Background: Dilepton angular distributions in heavy ion collisions • Hyperon polarizations

3. How fast is the rotation in HIC? • Magnetic field – highest possible ever = CME • Rotation – another pseudovector – angular velocity • Also highest possible! - velocities ~ c at the distances ~ Compton length • But! No charge conservation constraining electric current and magnetic field • Is it observable?!

4. Anomaly in medium – new external lines in VVA graph • Gauge field -> velocity • CME -> CVE • Kharzeev, Zhitnitsky (07) – EM current • Straightforward generalization: any (e.g. baryonic) current – neutron asymmeries@NICA - Rogachevsky, Sorin, OT – PRC10’

5. Baryon charge with neutrons – (Generalized) Chiral Vortical Effect • Coupling: • V2=1: Specific (non-linear) gauge • Current: • - Uniform chemical potentials: • - Rapidly (and similarly) changing chemical potentials:

6. What part of VVA is (non-renormalized anomaly?) • Massless VVA with real photons –entirely anomaly • Experience from virtual photons: anomaly – integral relation for spectral denisty (“Anomaly sum rule”) even in the massless limit • Can temperature and/or chemical potentia play the same role as photon virtuality?

7. Anomaly and virtual photons Often assumed that only manifested in real photon amplitudes Not true – appears at any Q2 Natural way – dispersive approach to anomaly (Dolgov, Zakharov’70) - anomaly sum rules One real and one virtual photon – Horejsi,OT’95 where

8. Anomaly – collective effect(Klopot, Oganesian, OT ‘10)

9. Comparing CME and CVE • Orbital Angular Momentum and magnetic moment are proportional – Larmor theorem • Vorticity for uniform rotation – proportional to OAM • Same scale as magnetic field • Tests are required

10. Model calculations (Baznat,Gudima,Sorin,OT)

11. Distribution of vorticity and HELICITY (v curlv)

12. Hydrodynamical Helicity separation

13. Hydrodynamical Helicity separation in a hybrid model (hydro stage) - Steinheimer,Bleicher,Stoecker

14. Qualitative picture of separation • yy (same vorticity, mirror velocity) ~ zz

15. Dimensionless scale of helicity

16. Collective effects for rotation- L =[rp] - sensitivity to transverse spatial separation sign

17. Observation of GCVE • Sign of topological field fluctuations unknown – need quadratic (in induced current) effects • CME – like-sign and opposite-sign correlations – S. Voloshin • No antineutrons, but like-sign baryonic charge correlations possible • Look for neutron pairs correlations! • MPD may be well suited for neutrons!

18. Estimates of statistical accuracy at NICA MPD (months of running) • UrQMD model : • 2-particles -> 3-particles correlations no necessity to fix the event plane • 2 neutrons from mid-rapidity • +1 from ZDC

19. Other sources of quadratic effects • Quadratic effect of induced currents – not necessary involve (C)P-violation • May emerge also as C&P even quantity • Complementary probes of two-current correlators desirable • Natural probe – dilepton angular distributions

20. Observational effects of current correlators in medium • McLerran Toimela’85 • Dileptons production rate • Structures –similar to DIS F1, F2 (p ->v)

21. Tensor polarization of in-medium vector mesons (Bratkovskaya, Toneev, OT’95) • Hadronic in-medium tensor – analogs of spin-averaged structure functions: p -> v • Only polar angle dependence • Tests for production mechanisms

22. General hadronic tensor and dilepton angular distribution • Angular distribution • Positivity of the matrix (= hadronic tensor in dilepton rest frame) • + cubic – det M> 0 • 1st line – Lam&Tung by SF method

23. Magnetic field induced conductivity (Buividovich, Polikarpov et al) and asymmetries • zz-component of conductivity (~hadronic) tensor dominates • λ =-1 • Longitudinal polarization with respect to magnetic field axis • Extra dileptons fly predominantly in reaction plane • No azimuthal asymmetry due to positivity

24. Other signals of rotation • Hyperons (in particular, Λ) polarization (self-analyzing in weak decay) • HIC – smearing of production plane asymmetry -> reaction plane (M. Jacob) • Searched at RHIC (S. Voloshin et al.) – oriented plane (slow neutrons) - no signal observed • No tensor polarizations as well

25. Why rotation is not seen? • Possible origin – distributed orbital angular momentum and local spin-orbit coupling • Only small amount of collective OAM is coupled to polarization • The same should affect lepton polarization • Global (pions) momenta correlations (handedness)

26. New sources of Λ polarization coupling to rotation • Bilinear effect of vorticity – generates quark axial current (Son, Surowka) • Strange quarks - should lead to Λ polarization • Proportional to strange chemical potential squared – small at RHIC – may be probed at FAIR & NICA

27. Another description of spin-rotation coupling – gravitomagnetic effects • Rotation +Equivalence Principle = gravitomagnetic field • Coupled to Gravitational Formfactors • Analogous to EM ones – related to Generalized Parton Distributions and angular momenta of quarks and gluons • Dirac equation in (strong) gravitational fields – Obukhov, Silenko, OT 05-10’ • HIC applications in progress

28. Induced current for (heavy - with respect to magnetic field strength) strange quarks • Effective Lagrangian • Current and charge density from c (~7/45) –term • (multiscale medium!) • Light quarks -> matching with D. Kharzeev et al’ -> correlation of density of electric charge with a gradient of topological one (Lattice ?)

29. Properties of perturbative charge separation • Current carriers are obvious - strange quarks -> matching -> light quarks? • NO obvious relation to chirality – contribution to axial current starts from pentagon (!) diagram • No relation to topology (also pure QED effect exists) • Effect for strange quarks is of the same order as for the light ones if topological charge is localized on the distances ~ 1/ms , strongly (4th power!) depends on the numerical factor : Ratio of strange/light – sensitive probe of correlation length • Universality of strange and charm quarks separation - charm separation suppressed as (ms /mc)4 ~ 0.0001 • Charm production is also suppressed – relative effects may be comparable at moderate energies (NICA?) – but low statistics

30. Comparing CME to strangeness polarization • Strangeness polarization – correlation of • (singlet) quark current • (chromo)magnetic field • (nucleon) helicity • Chiral Magnetic Effect - correlation of • (electromagnetic) quark current • (electro)magnetic field • (Chirality flipping) Topological charge gradient

31. Local symmetry violation • CME – assumed to be the sign of local P(C) violation • BUT Matrix elements of topological charge, its density and gradient are zero • Signs of real C(P) violation – forbidden processes

32. Forbidden decays in vacuum – allowed in medium • C-violation by chemical potential -> (Weldon ’92) • (OT’96; Radzhabov, Volkov, Yudichev ’05,06 - NJL) • New (?) option: in magnetic field • Polarization (angular distribution in c.m. frame ) of dilepton (with respect to field direction!)

33. Approximation: EM part – vacuum value Two-stage forbidden decays - I

34. Two-stage forbidden decays -II

35. Relating forbidden and allowed decays • In the case of complete mass degeneracy:

36. Conclusions • Chiral Vortical Effect may be probed in the neutron asymmetries (at NICA?) • Model calculation manifest hydrodynamical helicity separation effect • Collective in-plane correlation <pz px> as a probe of rotation • Bilinear current correlator may be probed in dilepton asymmetries • Vorticity – new source of hyperon polarization