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Parton-Hadron Transition (duality) in Structure Functions

Parton-Hadron Transition (duality) in Structure Functions. Ioana Niculescu James Madison University April 28, 2005. Introduction Proton (unpolarized) Nuclei Proton and deuteron (polarized) Semi-inclusive electroproduction.

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Parton-Hadron Transition (duality) in Structure Functions

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  1. Parton-Hadron Transition (duality) in Structure Functions Ioana Niculescu James Madison University April 28, 2005 • Introduction • Proton (unpolarized) • Nuclei • Proton and deuteron (polarized) • Semi-inclusive electroproduction

  2. Asymptotically the photon couples to quarks, yet confinement ensures that only hadronic final states are observed. Asymptotically Free Quarks: regime of pQCD Long Distance Physics: hadronic observables Duality is intimately related to the transition from soft to hard QCD.

  3. Hadronic Cross Sections averaged over appropriate energy range Shadrons Perturbative Quark-Gluon Theory Quark-Hadron Dualitycomplementarity between quark and hadron descriptions of observables At high enough energy: = Squarks+gluons Can useeither set of complete basis states to describe physical phenomena

  4. Inclusive Electron Scattering Q2 : Four-momentum transfer x : Bjorken variable (=Q2/2Mn)  : Energy transfer M : Nucleon mass W : Final state hadronic mass

  5. Duality in the F2 Structure Function • Empirically, DIS region is where logarithmic scaling is observed: Q2 > 5 GeV2, W2 > 4 GeV2 • Duality: Averaged over W, log scalingobserved to work also for Q2 > 0.5 GeV2, W2 < 4 GeV2 • JLab results (E94110): Works quantitatively to better than 10%

  6. Cornwall-Norton moments • Duality is described in the Operator Product Expansion as higher twist effects being small or canceling • DeRujula, Georgi, Politzer (1977) Logarithmic dependence Higher twists

  7. Moments of F2p at low Q2 Proton Charge (Coulomb Sum Rule) @ Q2 = 2 (GeV/c)2 30% of M2 comes from the resonance region W2 > 4 GeV2 (“DIS”) elastic total n = 2 n = 2 n = 4 n = 6 D-region n = 8 S11-region Elastic contribution

  8. Duality in Nuclei p • Data in resonance region, spanning Q2 range 0.7 - 5 GeV2 • GRV curve • The nucleus does the averaging • For larger A, resonance region indistinguishable from DIS d Fe

  9. Duality and the EMC Effect C/D Medium modifications to the structure functions are the same in the resonance region as in the DIS. Fe/D Au/D J. Arrington, et al., submitted

  10. Moments in Nuclei

  11. Lattice QCD (D. Dolgov et al., Phys. Rev. D 66:034506, 2002)

  12. Neutron Structure Function large uncertainty in neutron extraction….. …must consider deuteron wave function, Fermi smearing, off-shell effects, neutron structure function shape,...

  13. Duality in g1(from T. Forest et al., Hall B EG1) proton Preliminary deuteron

  14. Spin Structure Functions, g1 Local duality Global duality Preliminary

  15. Duality in Meson Electroproduction (predicted by Afanasev, Carlson, and Wahlquist, Phys. Rev. D 62, 074011 (2000)) Hall C Experiment E00-108 Spokespersons: Hamlet Mkrtchyan (Yerevan) Gabriel Niculescu (JMU) Rolf Ent (JLab) (e,e’) W2 = M2 + Q2 (1/x – 1) For Mm small, pm collinear with g, and Q2/n2 << 1 (e,e’m) W’2 = M2 + Q2 (1/x – 1)(1 - z) z = Em/n

  16. Duality in Meson Electroproduction hadronic description quark-gluon description Transition Form Factor Decay Amplitude Fragmentation Function Requires non-trivial cancellations of decay angular distributions If duality is not observed, factorization is questionable Duality and factorization possible for Q2,W2  3 GeV2(Close and Isgur, Phys. Lett. B509, 81 (2001))

  17. Berger Criterion Dh > 2 Rapidity gap for factorization Factorization P.J. Mulders, hep-ph/0010199 (EPIC Workshop, MIT, 2000) Typical JLab z>0.4 Typical HERMES z>0.2 Separates Current and Target Fragmentation Region in Rapidity

  18. Experiment ran in August 2003 • Close-to-final data analysis • Small Q2 variation not corrected yet E00-108 data x = 0.32 x = 0.32 No visual “bumps and valleys” in pion ratios off deuterium

  19. From deuterium data: D-/D+ = (4 – Np+/Np-)/(4Np+/Np- - 1) z = 0.55 • D-/D+ ratio should be independent of x • but should depend on z x = 0.32 HERMES fit Feynman-Field

  20. Summary • Quark-Hadron Duality • Proton (unpolarized) • Nuclei • Proton and deuteron (polarized) • Semi-inclusive electroproduction

  21. Backup slides

  22. Duality in Meson Electroproduction hadronic description quark-gluon description Transition Form Factor Decay Amplitude Fragmentation Function A little bit more complicated…. Pt, f q, q dN/dz  iei2qi(x,Q2)Dqim(z,Q2) + qi(x,Q2)Dqim(z,Q2)

  23. E00-108 data A little bit more complicated…. Pt, f q, q dN/dz  iei2qi(x,Q2)Dqim(z,Q2) + qi(x,Q2)Dqim(z,Q2) Pt dependence for 1H(e,e’p-)X (W’ ~ 1.8 GeV)

  24. E00-108 data A little bit more complicated…. Pt, f q, q dN/dz  iei2qi(x,Q2)Dqim(z,Q2) + qi(x,Q2)Dqim(z,Q2) Pt dependence for 1H(e,e’p+/-)X, 2H(e,e’p+/-)X, 27Al(e,e’p+/-)X [Scaling in Electropion Production earlier shown with Cornell data by Calogeracos, Dombey and West, who also show that the pt distribution is, within uncertainties, independent of kinematics, with much of the data at W’ < 2 GeV: Phys. Rev. D 51, 6075 (1995).] x = 0.32 z = 0.55

  25. The Origins of Quark-Hadron Duality – Semi-Inclusive Hadroproduction F. Close et al : SU(6) Quark Model How many resonances does one need to average over to obtain a complete set of states to mimic a parton model? 56 and 70 states o.k. for closure Destructive interference leads to factorization and duality Predictions: Duality obtained by end of second resonance region Factorization and approximate duality for Q2,W2 < 3 GeV2

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