Многомасштабный нуклон Многомасштабный нуклон ИТЭФ O.В. Теряев БЛТФ, ОИЯИ

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

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)

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

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 )

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

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

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)

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

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)

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

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

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

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

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

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

(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?

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 (2 nd partt of talk) Very small numerically Small strange mass – partially compensates this smallness and leads to % effect

Unpolarized strangeness – can it be considered as heavy? Heavy quark momentum – defined by 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%

Heavy unpolarized Strangeness: possible escape Conjecture: 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%

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

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

Heavy unpolarized Strangeness: vector current Follows from Heisenberg-Euler effective lagrangian Published in Z.Phys.98: ,1936. e-Print: physics/ 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)

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 ?)

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

CME on the lattice

CME on the lattice-II

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 ~ Charm production is also suppressed – relative effects may be comparable at moderate energies (NICA?) – but low statistics

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

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

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

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 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 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