What is the QuarkHadron Duality

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Quark-Hadron Duality in the Rein-Sehgal Model
?? ?? KEK????????????????? 22 Dec. 2007
K. Graczyk, C. Juszczak, J. Sobczyk Nucl. Phys.
A781, 227 (2007), hep-ph/0512015

• Introduction
• What is the Quark-Hadron Duality?
• Single Pion Production in nN Scattering
• Numerical Results
• Summary

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Motivation

• Complementarity between quark (gluon) and hadron
  description of observables
• In principle, QCD describes all of hadron physics
  at all distance scales. but how does it work?
• We want to understand it in language of QCD.

low energy Hadronic cross section
high energy Perturbative quark-gluon theory
How connected??
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Bloom-Gilman Duality

• Average over (strongly Q2 dependent) resonance
  Q2 independent scaling function!!
• Finite energy sum rule for eN scattering

Bloom and Gilman, PRL85,1185(1970)
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Recent Data

• Resonance region data oscillate around the
  scaling curve.
• Resonance data are on average equivalent to the
  scaling curve.
• The data slide along the DIS curve with
  increasing Q2.

Data from SLAC and J-Lab 0.06 lt Q2 lt 3.30 GeV2
Solid curve is DIS fit at Q25 GeV2 at the same ?
F2p
Nachtman variable
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Duality in QCD

• Operator Product Expansion
• Expand moments of structure functions in powers
  of 1/Q2
• If moments are independent of Q2
• Duality suppression of higher twist
• If higher twists are small (duality works)
• can use single parton approximation to describe
  structure function
• extract leading twist parton distributions
• If duality is violated, and if violations are
  small
• can use to extract higher twist matrix elements
• learn about nonperturbative qq or qg corrections

• nonperturbative interactions not dominate?
• strong cancellations between resonances?

? higher twist terms are small.
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Aim of This Paper

• Single Pion Production (SPP) in nN scattering
• Two different scheme Resonance DIS
• Rein-Sehgal model Resonance region
• pQCDPDFs DIS region

discuss that the duality holds in this calculation
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Rein-Sehgal Structure Function

• Single Pion Production in CC and NC reactions

Decomposition into 3 Component sL, sR, sS cross
section of gauge boson in polarization state
scattered off nucleon
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• Cross Section in RS Model
• In language of structure functions

calculated within quark model, given for each SPP
channel
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• Rein-Sehgal Structure Functions
• Energy Range
• ss are calculated in the quark model.
• In each processes, ?, S11, P11, D13,,,,,, using
  Breit-Wigner function and transition matrix
  elements
• Both resonant and non-resonant contributions are
  shown.

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DIS Structure Function

• DIS structure functions are represented by linear
  combination of the parton distribution functions
  (PDFs).
• CC nN interaction
• NC nN interaction
• F1 is obtained from Callan-Gross relation

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Single Pion Production and DIS

• They evaluate SPP in the QCD framework
  extrapolated to resonance region.
• Introduce 1-pion function f1p(W)
• f1p(W) is obtained from Monte Carlo simulation by
  LUND algorithm.
• It is defined by fragmentation and hadronization
  routines.
• Assume that scaling structure function is
  expressed as
• Artificial, how about the effects beyond the
  leading order?.

defined as the probabilities that the final state
is that of the SPP
strongly model dependent analysis
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Quark-Hadron Duality

• The quark-hadron duality holds the relation
• should hold for different values of Q2RES, also
  at Q2RES lt 1 GeV2.
• In this paper, Q2DIS is set as Q2DIS 10 GeV2.
• The ratio of these structure functions

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RS vs DIS Structure Function

• CC nN scattering

GRV94 (LO) PDFs are used Q2 gt 0.23 GeV2, x gt 10-5
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RS vs DIS Structure Function (cont.)

• NC nN scattering

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RS vs DIS Structure Function (cont.)

• CC and NC neutrino-isoscalar target scattering

Duality hold well for xF1 and xF3, while DIS
dominates for F2.
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F2 Ratio RES to DIS

• How does 1-pion function affect the duality?

1-pion function restore the duality picture,
except Rci,1p(p) in CC. The quark-hadron duality
holds very well in NC.
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F3 Ratio RES to DIS

• Discussion is almost same as for F2.

It seems that 1-pion function improve the duality.
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Two-Component Duality

• Decomposition of structure functions
• Hypothesis of two-component duality

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Summary

• The quark-hadron duality gives a relation between
  the structure function of resonance region and
  that of DIS region.
• Powerful tool to constrain the PDFs
• Useful to learn about nonperturbative corrections
• The quark-hadron duality for single pion
  production in nN scattering.
• Qualitative compare the RS and DIS structure
  functions
• Quantitative evaluate the ration of (integrated)
  structure functions
• 1-pion function is introduced to describe the
  SPP.
• This function improve the duality. ?all of
  neutron and isoscalar targets
• Proton Fi in CC is not the case.