Vorticity in Heavy Ion Collisions and its manifestations

Vorticity in Heavy Ion Collisions and its manifestations NICA/JINR-FAIR Bilateral Workshop, FIAS, April 4 2012 Oleg Teryaev JINR

Outline Rotating QCD matter Spin@NICA/MPD - search for signs of global rotation Chiral Vortical Effect & neutron asymmetries @ NICA Background: Dilepton angular distributions in heavy ion collisions Hyperon polarizations

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 Is it observable? !

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 - PRC 82: 054910, 2010.

Сomments on anomaly in medium Quarks or hadrons? The same – t’Hooft principle Real photons-massless modes (like pion) Used also for media Virtual – collective effect (Klopot, Oganesian, OT) T or chemical potential – like virtuality? Anomaly = averaged quark diagram Quark diagram – only an estimate

Baryon charge with neutrons – (Generalized) Chiral Vortical Effect Coupling: Current: - Uniform chemical potentials: - Rapidly (and similarly) changing chemical potentials:

Comparing CME and CVE Orbital Angular Momentum and magnetic moment are proportional – Larmor theorem No antibaryons – no mirror correlations CME for 3 flavours – no baryon charge separation (2/3 -1/3=0!) (Kharzeev, Son) - but strange mass! Same scale as magnetic field

Studying vorticity Vorticity for uniform rotation – proportional to OAM Tests are required Natural object – hydrodynamical helicity (= v rot v)-related to chaos Model calculations: JINR(DSM: Baznat, Gudima, Sorin, OT)+FIAS(Ur. QMD: Bleicher, Steinheimer, Stoecker)

Relativistic Vorticity and Lagrangian Chaos (A. S. Sorin, OT, in progress) “Maximal” vorticity/helicity Beltrami flows For ideal fluid – Bernoulli condition in the 3 D region ~ chaos (normally only along streamlines ~ integrability) Relativistic generalization for isentropic “steady”( )flows Relativistic Bernoulli condition in 4 D region Causality: account for compressiibility required (in progress)

Hydrodynamical Helicity separation (DCM)

Hydrodynamical Helicity separation (Ur. QMD)

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!

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

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

Observational effects of current correlators in medium Mc. Lerran Toimela’ 85 Dileptons production rate Structures –similar to DIS F 1, F 2 ->v) (p

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

Dilepton anisotropies vs (CME)2 correlations Small correlations -> small anisotropies? Dileptons -> EM currents Vector currents correlator for hadrons production – quark hadron duality How it works in medium? ! Hagedorn spectrum – small coupling of currents to higher states – suppression of anisotropies present in correlator

P-odd effects from W 3 type function For dilepton productions – due to interference with Z 0 exchange Suppressed as Q 2/MZ 2 ~10 -6 Leads to energy disbalance between positively and negatively charges leptons Also for hadrons? !

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

Magnetic field conductivity and asymmetries zz-component of conductivity (~hadronic) tensor dominates λ =-1 Longitudinal polarization with respect to magnetic field axis Extra dileptons hidden in the reaction plane Azimuthal asymmetries suppressed by positivity

Other signals of rotation Hyperons (in particular, Λ) polarization (self-analyzing in weak decay) Searched at RHIC (S. Voloshin et al. ) – oriented plane (slow neutrons) - no signal observed No tensor polarizations as well

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)

New source of Λ polarization coupling to vorticity Bilinear effect of vorticity – generates quark axial current (Son, Surowka) Strange quarks - should lead to Λ polarization Simulations -> ~ 1 unit of chirality (helicity) per event -> ~ % polarization Proportional to chemical potential – small at RHIC – may be probed at FAIR & NICA

Induced current (Ur. QMD)

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 HIC applications in progress

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 ? )

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 topollogy (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/m s , strongly (4 th 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

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

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

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!)

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

Two-stage forbidden decays II

Relating forbidden and allowed decays In the case of complete mass degeneracy (OT’ 05, unpublished): Tests and corrections – in progress

Conclusions Chiral Vortical Effect may be probed in the neutron asymmetries at NICA Bilinear current correlator may be probed in dilepton asymmetries CME/CVE for (heavy) strange quarks is similar to their polarization in a nucleon Various medium-induced decays may be related to each other