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Axial Anomaly and Strange Strange Quarks
FOURTEENTH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

Moscow, MSU, August 21 2009
Oleg Teryaev JINR, Dubna


Outline
Axial 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 QCD coupling Charm/strange universality? Chiral magnetic effect for strangeness in Heavy Ions collisions Conclusions


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


Symmetries and conserved operators
(Global) Symmetry -> conserved J = 0 ) current ( Exact: U(1) symmetry ­ charge conservation electromagnetic (vector) current Translational symmetry ­ energy momentum tensor T = 0


Massless fermions (quarks) ­ approximate symmetries
Chiral symmetry (mass flips the helicity)

J

5



=0

Dilatational invariance (mass introduce dimensional scale ­ c.f. energymomentum tensor of electromagnetic radiation )

T = 0


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

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


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 ­ talk of D. Peshekhonov) Current data on f2 ­ somewhat 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

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

HT ­ small indeed


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


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 naОve estimate Tests in models/lattice QCD (Done) Charm momentum of order 0.01% Strangeness momentum of order of 1%


Heavy unpolarized Strangeness: vector current
Follows from Heisenberg-Euler effective lagrangian (confirmed: A. Moiseeva, M. Polyakov) FFFF -> FGGG -> Describes strangeness contribution to nucleon magnetic moment and pion mean square radius FFFF->FFGG -> perturbative description of chiral magnetic effect for haeavy (strange) quarks in Heavy Ion collisions


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


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 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 Chiral magnetic effect for stange quarks ­ straightforward modification of HeisenbergEuler lagrangian