Многомасштабный нуклон ИТЭФ. 23.11.11
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Многомасштабный Многомасштабный нуклоннуклон
ИТЭФ. 23.11.11
O.В. ТеряевБЛТФ, 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
0J
0T
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 )
5 0J
0T
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
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?
(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 (2nd 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 <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%
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%
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
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)
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 ?)
44 /))((/)~
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mGGFcj
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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/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
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
)()(
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qqqqqq
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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!)
ee
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4
2
~
m
Hee
2cos1~
Approximation: EM part – vacuum value Two-stage forbidden decays - I
Two-stage forbidden decays -II
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Relating forbidden and allowed decays
In the case of complete mass degeneracy (OT’05, unpublished):
Tests and corrections in progress
eeee
4
9
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
top related