Многомасштабный нуклон ИТЭФ. 23.11.11

1. O.В. Теряев БЛТФ, ОИЯИ Многомасштабный нуклонИТЭФ. 23.11.11

2. Outline • When strange quarks can be heavy: multiscale hadrons • (Squared) Nucleon mass >> strange mass >> (intrinsic) higher twist scale • Strangeness polarization • HT from Bjorken sum rule: Duality with (4) loop corrections

3. Heavy strange quark?! • With respect to WHAT? • Light with respect to hadron mass • BUT • Heavy with respect to higher twists parameters • Multiscale nucleon • Possible origin – small correlations of gluon (and quark) fields (may be related to asymptotic nature of perturbative series • Rigorous tool – anomalies (talk of A. Oganesian)

4. Symmetries and conserved operators • (Global) Symmetry -> conserved current ( ) • Exact: • U(1) symmetry – charge conservation - electromagnetic (vector) current • Translational symmetry – energy momentum tensor

5. Massless fermions (quarks) – approximate symmetries • Chiral symmetry (mass flips the helicity) • Dilatational invariance (mass introduce dimensional scale – c.f. energy-momentum tensor of electromagnetic radiation )

6. Quantum theory • Currents -> operators • Not all the classical symmetries can be preserved -> anomalies • Intermediate between explicit and spontaneous – specifically quantum • Enter in pairs (triples?…) • Vector current conservation <-> chiral invariance

7. Massive quarks • One way of calculation – finite limit of regulator fermion contribution (to TRIANGLE diagram) in the infinite mass limit • The same (up to a sign) as contribution of REAL quarks • For HEAVY quarks – cancellation! • Anomaly – violates classical symmetry for massless quarks but restores it for heavy quarks

8. Decoupling • Happens if the symmetry is broken both explicitly and anomalously • Selects the symmetry in the pair of anomalies which should be broken (the one which is broken at the classical level)

9. Heavy quarks polarisation Non-complete cancellation of mass and anomaly terms (97) Gluons correlation with nucleon spin – twist 4 operator NOT directly related to twist 2 gluons helicity BUT related by QCD EOM to singlet twist 4 correction (colour polarisability) f2 to g1 “Anomaly mediated” polarisation of heavy quarks

10. Numerics Small (intrinsic) charm polarisation Consider STRANGE as heavy! (OT’09)– CURRENT strange mass squared is ~100 times smaller – -5% - reasonable compatibility to the data! (But problem with DIS and SIDIS)

11. Strangeness Polarization IN DIS and SIDIS • Seen in DIS (fits) and not in SIDIS) • Global fit – polarization concentrated at small x ~0.02 (but depends on fragmentation functions) • Models – typically larger • Gluons – natural candidates for low x polarization

12. Can s REALLY be heavy?! Strange quark mass close to matching scale of heavy and light quarks – relation between quark and gluon vacuum condensates (similar cancellation of classical and quantum symmetry violation – now for trace anomaly) Strange sigma term from recent lattice data l – compatible with heavy quark limit 2/29 M! In nucleon (no valence “heavy” quarks) rather than in vacuum - may be considered heavy in comparison to small genuine higher twist – multiscale nucleon picture

13. Polarizabilities from data • Current value of colour polarizability – larger than used in estimate with large errors • J.P. Chen

14. Are higher twists small? • More theoretically clear – non singlet case – pQCD part well known (Bjorken sum rule) • Low Q region – Landau pole – free coupling required (Analytic,freezing-cf talk of Yu. A. Simonov)) • Allows to use very accurate JLAB data to extract HT

15. Higher twists from Bjorken Sum Rule • Accurate data + IR stable coupling -> low Q region • HT – small indeed

16. 4-loop corrections included V.L. Khandramai, R.S. Pasechnik, D.V. Shirkov, O.P. Solovtsova, O.V. Teryaev. Jun 2011. 6 pp. e-Print: arXiv:1106.6352 [hep-ph] • HT decrease with PT order and becomes compatible to zero (V.I. Zakharov’s duality) • APT – resummation to analytic function?

17. (Intermediate) conclusions • Three scales – strange quark may be considered heavy sometimes • Smallness of HT – due to combination of duality and asymptotic nature of PT series?

18. Comparison : Gluon Anomaly for massless and massive quarks • Mass independent • Massless (Efremov, OT ’88) – naturally (but NOT uniquely) interpreted as (on-shell) gluon circular polarization • Small gluon polarization – no anomaly?! • Massive quarks – acquire “anomaly polarization” • May be interpreted as a sort of correlation of quark current to chromomagnetic field • Qualitatively similar to CME (2nd partt of talk) • Very small numerically • Small strange mass – partially compensates this smallness and leads to % effect

19. Unpolarized strangeness – can it be considered as heavy? • Heavy quark momentum – defined by <p|GGG|p> matrix element (Franz,Polyakov,Goeke) • IF no numerical suppression of this matrix element – charm momentum of order 0.1% • IF strangeness can be also treated as heavy – too large momentum of order 10%

20. Heavy unpolarized Strangeness: possible escape • Conjecture: <p|GGG|p> is suppressed by an order of magnitude with respect to naïve estimate • Tests in models/lattice QCD (Done) • Charm momentum of order 0.01% • Strangeness momentum of order of 1%

21. Charm/Strangeness universality • Universal behaviour of heavy quarks distributions - from non-local (C-even) operators • c(x)/s(x) = (ms /mc)2 ~ 0.01 • Delta c(x)/Delta s(x)= (ms /mc)2 ~ 0.01 • Delta c(x)/c(x) = Delta s(x)/s(x) • Experimental tests – comparison of strange/charmed hadrons asymmetries

22. Higher corrections • Universality may be violated by higher mass corrections • Reasonable numerical accuracy for strangeness – not large for s –> negligible for c • If so, each new correction brings numerically small mass scale like the first one • Possible origin – semiclassical gluon field • If not, and only scale of first correction is small, reasonable validity for s may be because of HT resummation

23. Heavy unpolarized Strangeness: vector current • Follows from Heisenberg-Euler effective lagrangian Published in Z.Phys.98:714-732,1936. e-Print: physics/0605038 • FFFF -> FGGG -> Describes strangeness contribution to nucleon magnetic moment and pion mean square radius • FFFF->FFGG -> perturbative description of chiral magnetic effect for heavy (strange) quarks in Heavy Ion collisions – induced current of strange quarks • Starting point – very strong magnetic fields in heavy ions coliisions (D, Kharzeev et al. – next slide)

25. 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 ?)

26. CME from CS term D. Kharzeev –this and two next slides

29. CME on the lattice

30. CME on the lattice-II

31. 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

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

33. 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

34. Effect of EM fields New structures CG type relations in the real photon limit Linear terms – zero real photon limit Effect on polar and azimuthal asymmetries – in progress

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 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 Strange quarks may be considered as heavy sometimes • Reasonable value for strangeness polarization • Strangeness separation in magnetic field – straightforward modification of Heisenberg-Euler lagrangian • Strange-light transition; strange mass against topological charge correlation length • Qualitative similarity of CME and strangness polrization • Local C-violation in medium – decays forbidden in vacuum with predictable ratios