FINAL STATE SPIN PHYSICS AT NICA SPIN-Praha-2013 and NICA-SPIN-2013 Praha, July 8, 2013

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

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 M0> 0 1st 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 T2 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/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

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