Многомасштабный нуклон и тяжелая странность Multiscale Nucleon and Heavy Strangeness Сессия-конференция Секции Ядерной физики Отделения Физических наук РАН Протвино, ИФВЭ, 24 декабря 2008 г. О.В. Теряев ЛТФ ОИЯИ

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

Outline Axial (and trace) anomaly for massless and massive fermions: decoupling Axial anomaly and heavy quarks polarization in nucleon When strange quarks can be heavy: multiscale hadrons Support: small higher twist with IR safe QCD coupling Strangeness sign and transversity (Heavy) unpolarized strangeness momentum Charm/strange universality? Conclusions

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 Enter in pairs (triples?…) Vector current conservation chiral invariance Translational invariance dilatational invariance

Calculation of anomalies Many various ways All lead to the same operator equation UV vs IR languages- understood in physical picture (Gribov, Feynman, Nielsen and Ninomiya) of Landau levels flow (E||H)

Counting the Chirality Degeneracy rate of Landau levels “Transverse” HS/(1/e) (Flux/flux quantum) “Longitudinal” Ldp= eE dt L (dp=eEdt) Anomaly – coefficient in front of 4-dimensional volume - e 2 EH

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

Dilatational anomaly Classical and anomalous terms Beta function – describes the appearance of scale dependence due to renormalization For heavy quarks – cancellation of classical and quantum violation -> decoupling

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) For “non-standard” choice of anomalous breakings (translational anomaly) there is no decoupling Defines the Higgs coupling, neutralino scattering…

Heavy quarks matrix elements QCD at LO From anomaly cancellations (27=33-6) “Light” terms Dominated by s-of the order of cancellation

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! – CURRENT strange mass squared is ~100 times smaller – -5% - reasonable compatibility to the data! (But problem with DIS and SIDIS) Current data on f2 – appr 50% larger

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). BUT - common belief that strange quark cannot be considered heavy, In nucleon (no valence “heavy” quarks) rather than in vacuum - may be considered heavy in comparison to small genuine higher twist – multiscale nucleon picture

Are higher twists small? More theoretically clear – non singlet case – pQCd part well known (Bjorken sum rule) Low Q region – Landau pole – IR stable coupling required (Analytic,freezing…) Allows to use very accurate JLAB data to extract HT

Advantage of “denominator” form of QCD coupling “PDG” expansion “Denominator” form – no artificial singularities

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

Down to Lambda pQCD+ HT

Comparison : Gluon Anomaly for massless and massive quarks Mass independent Massless – 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 kind of circular polarization of OFF-SHELL (CS projection -> GI) gluons Very small numerically Small strange mass – partially compensates this smallness and leads to % effect

Sign of polarisation Anomaly – constant and OPPOSITE to mass term Partial cancellation – OPPOSITE to mass term Naturally requires all “heavy” quarks average polarisation to be negative IF heavy quark in (perturbative) heavy hadron is polarised positively

Heavy Strangeness transversity Heavy strange quarks – neglect higher twist: 0 = Strange transversity - of the same sign as helicity and enhanced by M/m But: only genuine HT may be be small – relation to twist 3 part of g2

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? Charm momentum of order 0.01% Strangeness momentum of order of 1%

Charm/Strangeness universality Universal behaviour of\heavy quarks distributions 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)/Delta s(x)= c(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

Conclusions Heavy quarks – cancellation of anomalous and explicit symmetry breaking Allows to determine some useful hadronic matrix elements Multiscale picture of nucleon - Strange quarks may be considered are heavy sometimes Possible universality of strange and charmed quarks distributions – similarity of spin asymetries of strange and charmed hadrons

Other case of LT-HT relations – naively leading twists TMD functions –>infinite sums of twists. Case study: Sivers function - Single Spin Asymmetries Main properties: – Parity: transverse polarization – Imaginary phase – can be seen T-invariance or technically - from the imaginary i in the (quark) density matrix Various mechanisms – various sources of phases

Phases in QCD QCD factorization – soft and hard parts- Phases form soft, hard and overlap Assume (generalized) optical theorem – phase due to on-shell intermediate states – positive kinematic variable (= their invariant mass) Hard: Perturbative (a la QED: Barut, Fronsdal (1960): Kane, Pumplin, Repko (78) Efremov (78)

Perturbative PHASES IN QCD

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

Twist 3 correlators

Twist 3 vs Sivers function(correlation of quark pT and hadron spin) Twist 3 – Final State Interaction -qualitatively similar to Brodsky-Hwang-Schmidt model Path order exponentials (talk of N. Stefanis) – Sivers function (Collins; Belitsky, Ji, Yuan) Non-suppressed by 1/Q-leading twist? How it can be related to twist 3? Really – infinite sum of twists – twist 3 selected by the lowest transverse moment Non-suppression by 1/Q – due to gluonic pole = quarks correlations with SOFT gluons

Sivers and gluonic poles at large PT Sivers factorized (general!) expression M – in denominator formally leading twist (but all twists in reality) Expand in kT = twist 3 part of Sivers

From Sivers to twist 3 - II Angular average : As a result M in numerator - sign of twist 3. Higher moments – higher twists. KT dependent function – resummation of higher twist. Difference with BFKL IF – subtracted UV; Taylor expansion in coordinate soace – similar to vacuum non-local condensates

From Sivers to gluonic poles - III Final step – kinematical identity Two terms are combined to one Key observation – exactly the form of Master Formula for gluonic poles (Koike et al, 2007)

Effective Sivers function Expressed in terms of twist 3 Up to Colour Factors ! Defined by colour correlation between partons in hadron participating in (I)FSI SIDIS = +1; DY= -1: Collins sign rule Generally more complicated Factorization in terms of twist 3 but NOT SF

Colour correlations SIDIS at large pT : -1/6 for mesons from quark, 3/2 from gluon fragmentation (kaons?) DY at large pT: 1/6 in quark antiquark annihilation, - 3/2 in gluon Compton subprocess – Collins sign rule more elaborate – involve crossing of distributions and fragmentations - special role of PION DY (COMPASS). Direct inclusive photons in pp = – 3/2 Hadronic pion production – more complicated – studied for P- exponentials by Amsterdam group + VW IF cancellation – small EFFECTIVE SF (cf talk of F. Murgia) Vary for different diagrams – modification of hard part FSI for pions from quark fragmentation -1/6 x (non-Abelian Compton) +1/8 x (Abelian Compton)

Colour flow Quark at large PT:-1/6 Gluon at large PT : 3/2 Low PT – combination of quark and gluon: 4/3 (absorbed to definition of Sivers function) Similarity to colour transparency phenomenon

Twist 3 factorization (Bukhvostov, Kuraev, Lipatov;Efremov, OT; Ratcliffe;Qiu,Sterman;Balitsky,Braun) Convolution of soft (S) and hard (T) parts Vector and axial correlators: define hard process for both double ( ) and single asymmetries

Twist 3 factorization -II Non-local operators for quark-gluon correlators Symmetry properties (from T- invariance)

Twist-3 factorization -III Singularities Very different: for axial – Wandzura-Wilczek term due to intrinsic transverse momentum For vector-GLUONIC POLE (Qiu, Sterman ’91) – large distance background

Sum rules EOM + n-independence (GI+rotational invariance) –relation to (genuine twist 3) DIS structure functions

Sum rules -II To simplify – low moments Especially simple – if only gluonic pole kept:

Gluonic poles and Sivers function Gluonic poles – effective Sivers functions-Hard and Soft parts talk, but SOFTLY Implies the sum rule for effective Sivers function (soft=gluonic pole dominance assumed in the whole allowed x’s region of quark-gluon correlator)

Compatibility of SSA and DIS Extractions of and modeling of Sivers function: – “mirror” u and d Second moment at % level Twist -3 - similar for neutron and proton and of the same sign – no mirror picture seen –but supported by colour ordering! Scale of Sivers function reasonable, but flavor dependence differs qualitatively. Inclusion of pp data, global analysis including gluonic (=Sivers) and fermionic poles HERMES, RHIC, E704 –like phonons and rotons in liquid helium; small moment and large E704 SSA imply oscillations JLAB –measure SF and g2 in the same run

CONCLUSIONS (At least) 2 reasons for relations between various twists: exact operator equations naively leading twist object contains in reality an infinite tower Strange quark (treated as heavy) polarization – due to (twist 4, anomaly mediated) gluon polarization Sivers function is related to twist 4 gluonic poles – relations of SSA’s to DIS

2 nd Spin structure - TOTAL Angular Momenta - Gravitational Formfactors Conservation laws - zero Anomalous Gravitomagnetic Moment : (g=2) May be extracted from high-energy experiments/NPQCD calculations Describe the partition of angular momentum between quarks and gluons Describe interaction with both classical and TeV gravity

Electromagnetism vs Gravity Interaction – field vs metric deviation Static limit Mass as charge – equivalence principle

Equivalence principle Newtonian – “Falling elevator” – well known and checked Post-Newtonian – gravity action on SPIN – known since 1962 (Kobzarev and Okun’) – not checked on purpose but in fact checked in atomic spins experiments at % level Anomalous gravitomagnetic moment iz ZERO or Classical and QUANTUM rotators behave in the SAME way

Gravitomagnetism Gravitomagnetic field – action on spin – ½ from spin dragging twice smaller than EM Lorentz force – similar to EM case: factor ½ cancelled with 2 from Larmor frequency same as EM Orbital and Spin momenta dragging – the same - Equivalence principle

Equivalence principle for moving particles Compare gravity and acceleration: gravity provides EXTRA space components of metrics Matrix elements DIFFER Ratio of accelerations: - confirmed by explicit solution of Dirac equation (Silenko,OT)

Generalization of Equivalence principle Various arguments: AGM 0 separately for quarks and gluons – most clear from the lattice (LHPC/SESAM)

Extended Equivalence Principle=Exact EquiPartition In pQCD – violated Reason – in the case of EEP - no smooth transition for zero fermion mass limit (Milton, 73) Conjecture (O.T., 2001 – prior to lattice data) – valid in NP QCD – zero quark mass limit is safe due to chiral symmetry breaking Supported by smallness of E (isoscalar AMM) Polyakov Vanderhaeghen: dual model with E=0

Vector mesons and EEP J=1/2 -> J=1. QCD SR calculation of Rho’s AMM gives g close to 2. Maybe because of similarity of moments g-2= ; B= Directly for charged Rho (combinations like p+n for nucleons unnecessary!). Not reduced to non-extended EP: Gluons momentum fraction sizable. Direct calculation of AGM are in progress.

EEP and AdS/QCD Recent development – calculation of Rho formfactors in Holographic QCD (Grigoryan, Radyushkin) Provides g=2 identically! Experimental test at time –like region possible

Another relation of Gravitational FF and NP QCD (first reported at 1992: hep-ph/ ) BELINFANTE (relocalization) invariance : decreasing in coordinate – smoothness in momentum space Leads to absence of massless pole in singlet channel – U_A(1) Delicate effect of NP QCD Equipartition – deeply related to relocalization invariance by QCD evolution

Conclusions 2 spin structures of nucleon – related to fundamental properties of NPQCD Axial anomaly – may reside not only in gluon, but in strangeness polarization (connection of laeding and higher twists) Multiscale (“fluctonic”) nucleon: M>>m(strange)>>HT Total angular momenta – connection to (extended) equivalence principle and AdS/QCD Relation of 2 spin structures?!

Sum rules -II To simplify – low moments Especially simple – if only gluonic pole kept:

Compatibility of SSA and DIS Extractions of Sivers function: – “mirror” u and d First moment of EGMMS = ( – 0.014) Twist -3 - similar for neutron and proton (0.005) and of the same sign – nothing like mirror picture seen –but supported by colour ordering! Current status: Scale of Sivers function – seems to be reasonable, but flavor dependence differs qualitatively. Inclusion of pp data, global analysis including gluonic (=Sivers) and fermionic poles

Relation of Sivers function to GPDs Qualitatively similar to Anomalous Magnetic Moment (Brodsky et al) Quantification : weighted TM moment of Sivers PROPORTIONAL to GPD E (hep-ph/ ): Burkardt SR for Sivers functions is now related to Ji SR for E and, in turn, to Equivalence Principle

Sivers function and Extended Equivalence principle Second moment of E – zero SEPARATELY for quarks and gluons –only in QCD beyond PT (OT, 2001) - supported by lattice simulations etc.. -> Gluon Sivers function is small! (COMPASS, STAR, Brodsky&Gardner) BUT: gluon orbital momentum is NOT small: total – about 1/2, if small spin – large (longitudinal) orbital momentum Gluon Sivers function should result from twist 3 correlator of 3 gluons: remains to be proved!