Study of quark-hadron duality of nucleon spin structure functions by Dong Yu-Bing (???)

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Study of quark-hadron duality of nucleon spin
structure functions by Dong
Yu-Bing (???)

• Institute of High Energy Physics (IHEP)
• Beijing

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Outline

• 1), Quark-hadron Duality
• 2), Constituent quark model
• 3), Target mass corrections
• to structure functions
• to duality
• to high-twist effects
• 4), Summary

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1,Quark-hadron duality

• Transitions properties
• Resonance structures, Structure functions,
• GDH sum rule, quark structure
• Strong interaction Two end points
• 1), nQCD, Confinements Resonance bumps
• 2), pQCD, Asymptotic freedom
• 3), Connection of pQCD and nQCD.

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• Duality(BG) for the structure functions
• Observable can be explained by two different
  kinds of Languages (Resonance, Scaling)
• Bloom-Gilman Duality( ,1970)
• Resonance region data oscillate around
  the scaling curve.
• Smooth scaling curve seen at high Q2
  was an accurate average over the resonance bumps
  at a low Q2(4GeV2)

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Duality and OPE(operator production expansion)

• The resonance strengths average to a global
  scaling curve resembling the curve of DIS, as the
  higher-twist effect is not large, if averaged
  over a large kinematics region.

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Other experiment(II)

• Hermes, by Fantoni, Bianchi, Liuti(EJPA05) for g1
• Onset 1.7GeV2

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Studies of quark-hadron duality

• Rujula,Georgi and Politzer (PLB76) OPE
• Carlson, Mukhopadhyay(PRD93), Stoler, Sterman
• resonance transition
  properties
• Simula (Italy group), (parameterizations of SFs)
• Melnitchouk (Jefferson Lab., Phys. Report 05)
• Isgur,Jechonnek, Melnitchouk and Van Orden
  (PRD01)
• confinement plus Dirac
  equation
• Close and Isgur (PLB01)
• evolution from a coherent
  resonance region
• to incoherent inelastic one
• Matsui, Sato and Lee(PRC05) (Isobar model)
• Paris et al.,(PRC02)
• Fiore et al.,(PRD04) (Regge-dual model)

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2), Constituent quark model
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Simple interpretation
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CQM calculations
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Quark model calculation for the structure
function
Donnnachie and Landshoff(84) F2 structure
function NMC(95) ,Gluek,Reya,Vogt(98)
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Donnnachie and Landshoff(84)
F2 structure function NMC(95)
,Gluek,Reya,Vogt(98)
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• The onset of the duality for F2 is about 1 GeV2
• Duality for g1
• The onset of the quark-hadron duality for g1 is
  expected to be at a large Q2 than that of F2 due
  to the DHG sum rule.

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For g1 spin structure function
HEARMS SLAC-E143(95),GOTO(AAC, 00),

Gluek, Reya et al(98)
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Further study of g1 duality precisely

• by
  Simula et al PRD (parameterizations)

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Further study of duality for g1

• Parametrization form of by Simula (PRD64)

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3), Target mass corrections

• Resonance language
• Scaling range (large Q02)
• Same definite Q2
• Simultaneously explained by the two
• Languages
• GRSV Glueck, Reya, Stratmann Vogelsang
• AAC Asymmetry analysis collaboration
  No TMCs
• LSS Leader,Sidorov Stamenov

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Target mass corrections(TMCs)

• Literature Georgi and Polizter(PRD76)
• Nachtmann (NPB75) Wandzura and Uematsu(NPB77)
  Matsuda(NPB80), Kawamura(PLB95).
• Piccone and Ridolfi(NPB98) Blumlein Tkabladze
  (NPB99), Sidorov Stamenov(MPLA06) Steffens
  Melnitchouk(PRC06)

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The target mass corrections to SSFby Piccione
Ridolfi

• Twist-2(Georgi-Politzer (GP) implementation)
• The Cornwall-Norton moment

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The target mass corrections to SSFby Piccione
Ridolfi (twist-2)

• Results

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TMCs to nucleon SSFs

• define

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TMCs to the Cornwall-Norton moments

• CN-moment
• Expansion in order

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TMCs to the Nachtmann moments
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• Cornwall-Norton moments contain TMCs (one SF,
  mix)
• Nachtmann Moments contains no TMCs (two SSFs,
  pure)

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TMCs to duality

• To study quark-hadron duality and TMCs
• Without TMCs

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Global duality in the resonance region

• Results

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Duality in the elastic local region

• Form factors and duality (elastic region)

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Discussions of x 1

• GP implementation for TMCs
• Xgt1(TMCs) SF dose not vanishing ? Dynamical
  reasons at x1
• Threshold problem
• (?-dependent) ?_0 ?(x1)lt1, the parton
  distribution isnt well
• defined in the unphysical region between elastic
  limit ?_0 and ? 1
• Higher-twist operators
• There is a non-uniformity in the limits as n?8
  Q2 ?8, and the
• appearance of the higher-twist effects
  proportional to nM2/Q2 for
• the n-th moment signals the breakdown of the
  entire approach at
• low W. Higher-twist is no longer suppressed by
  1/Q2
• Steffens and Melnitchouk proposed a new
  implementation of the TMCs which has a correct
  kinematics threshold behavior at finite Q2 in
  the limit of x?1

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TMCs to higher-twist (CN)

• Without TMCs (CN moment)

With TMCs (CN moments)
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Scaling SSFs with pQCD

• Target mass corrections is of purely kinematics
  origin

Before one can reliably extract the information
of the higher-twist contributions, it is
important to remove from the data the corrections
arising from purely kinematics effects (TMCs).
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The other higher-twist terms result from the
reduced matrix elements. They are of dynamical
origin, since they show the correlation among the
partons
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TMCs to twist-3

• The Nachtmann moments do not contain TMCs
• The Nachtmann moment is a right one for d2

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TMCs to g2 Wandzura-Wilczek relation

• WW relation for twist-2
• With twist-3

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E155(2003,1999) g2 and A2

• Experimental data

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TMCs to twist-3

• Consider the Nachtmann moment

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5), Summary

• 1), Duality is seen from CQM calculation
• 2), Duality of g1 or g2 is about
• 3), Target mass corrections are important
• to structure functions at large x,
• to the quark-hadron duality
• to the higher-twist d2
• 4), More precise data are required to get d2
• ------------------------------- The
  End----------------------------------

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The Nachtmann variable

• In general case
• When the target mass corrections are considered,
  one should consider the Nachtmann variable

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TMCs to SSFs