1. FINAL STATE SPIN PHYSICS AT NICA SPIN-Praha-2013 and NICA-SPIN-2013 Praha, July 8, 2013 Oleg Teryaev BLTP, JINR

2. MOTIVATION: SEARCH for COMMON/RELATED SPIN PHYSICS PROBLEMS for MPD/SPD/BM@N Talks of D. Peshechonov, A. Nagaytsev,A.V.Efremov, A. Guskov, O.Shevchenko…: Developing program for SPD HIC@MPD Suggestion: explore polarisation of Lambda hyperons and tensor polrisation of vector mesons at MPD&BM@N

3. Outline Initial and final state spin effects: SPD/MPD/BM@N T-odd and T-even effects - vector and tensor polarization Spin effects - search for signs of global rotation of QCD matter Chiral Vortical Effect & neutron asymmetries @ NICA Hyperon polarizations Dilepton angular distributions

4. Initial and final state effects Polarisations of final state particles -> angular distributions SSA (T-odd) and DSA (T-even) May be studied in NN,NA,AA collsions May be correlated to initial state polarisations FS Spin effects - open possibility of spin physics at all NICA detectors (SPD,MPD,BM@N)

5. Single Spin Asymmetries (vector polarisation)

6. (Lambda) hyperon polarisation Self-analyzing in weak decay Directly related to s-quarks polarisation Probe of QCD matter formation (Jacob, Rafelsky, 80’s) Randomization – smearing – no direction normal to the scattering plane Systematic study of in pp,pA,AA collisions at the same detector (BM@N,MPD)

7. Perturbative PHASES IN QCD

8. Short+ large overlap– twist 3 Quarks – only from hadrons Various options for factorization – shift of SH separation (prototype of duality) New option for SSA: Instead of 1-loop twist 2 – Born twist 3: Efremov, OT (85, Ferminonc poles); Qiu, Sterman (91, GLUONIC poles)

9. Double spin asymmetries Tensor polarisation of vector mesons -> angular distribution of decay products (dileptons, pions,…) Quadratic effects – no P(T)-violation Correlation with initial state (vector) polarization – Sivers function in DY Modifications in QGP matter – randomization Dileptons@(BM@N)/MPD?! (H)IC@SPD?!

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

11. Positivity bound for Sivers asymmetry Not allowed for pure thansverse photons! Consistency tests for Sivers vs unpolarized asymmetries For partially polarized nucleons : |µ| -> |µ|/|s| Stronger bound for λ deviation from 1!

12. Positivity bounds vs unpolarized data: Peng, Roloff,OT’11 (plot by diploma student S. Khlebtsov)

13. BG/DYW type duality for DY SSA in exclusive limit Proton-antiproton DY – valence annihilation - cross section is described by Dirac FF squared The same SSA due to interference of Dirac and Pauli FF’s with a phase shift (Rekalo,Brodsky) Exclusive large energy limit; x -> 1 : T(x,x)/q(x) -> Im F2/F1 Both directions – estimate of Sivers at large x and explanation of phases in FF’s NN -> BG type duality with transition FF’s NN->NNπ

14. 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?!

15. Model calculations (Baznat,Gudima,Sorin,OT) arXiv:1301.7003v1 [nucl-th]

16. Structure of velocity and vorticity fields (5 GeV/c)

17. Hydrodynamical Helicity (=v rot v) separation

18. Energy dependence NICA range preferable

19. 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

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

21. 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

22. 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!

23. 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 PP?!

24. 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

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

26. 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 Positivity tests!

27. Magnetic field conductivity and asymmetries zz-component of conductivity (~hadronic) tensor dominates λ =-1 Longitudinal polarization with respect to magnetic field axis Excludes “Collins-type” angular distributions

28. 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

29. 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) – OT,Usubov, work in progress

30. New sources of Λ polarization coupling to rotation Bilinear effect of vorticity – generates quark axial current Strange quarks - should lead to Λ polarization Scale – of % order (due to relatively small volume occupied by vorticity) Proportional to (square of) chemical potential – small at RHIC – may be probed at FAIR & NICA Newly found T 2 term –compensated by (exponential) polarisation dilution

31. CONCLUSIONS FS spin effects – possibility for coherent physical program of SPD, MPD, BM@N Special role of hyperons (Λ) and VM polarisation Possible probe of vorticity Pion handedness under investigation

32. 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

33. 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 ?)

34. 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 (m s /m c ) 4 ~ 0.0001 Charm production is also suppressed – relative effects may be comparable at moderate energies (NICA?) – but low statistics

35. 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

36. 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

37. 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!)

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

39. Two-stage forbidden decays - II

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

41. Conclusions Chiral Vortical Effect – to be probed in the neutron asymmetries (at NICA?) Bilinear current correlator may be probed in dilepton asymmetries Various medium-induced decays may be related to each other