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Quark-Hadron Duality

Quark-Hadron Duality. Cynthia Keppel Hampton University / Jefferson Lab. CIPANP 2003. Quark-Hadron Duality complementarity between quark and hadron descriptions of observables. At high energies: interactions between quarks and gluons become weak (“asymptotic freedom”)

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Quark-Hadron Duality

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  1. Quark-Hadron Duality Cynthia Keppel Hampton University / Jefferson Lab CIPANP 2003

  2. Quark-Hadron Dualitycomplementarity between quark and hadron descriptions of observables • At high energies: interactions between quarks and gluons become weak (“asymptotic freedom”) • efficient description of phenomena afforded in terms of quarks • At low energies: effects of confinement make strongly-coupled QCD highly non-perturbative • collective degrees of freedom (mesons and baryons) more efficient • Duality between quark and hadron descriptions • reflects relationship between confinement and asymptotic freedom • intimately related to nature and transition from non-perturbative to perturbative QCD

  3. Example: e+e- hadrons / m+m-lim s(e+e- X) = NC S eq2E  s(e+e- m+m-) q

  4. Duality in Inclusive electron scattering Single Photon Exchange Deep Inelastic Resonance Elastic ds= G[s T(x,Q2) + e sL(x,Q2)} In terms of gcoupling: dWdE' Where G: flux of transversely polarized virtual photons e: relative longitudinal polarization ds∝G[2xF1(x,Q2) + eFL(x,Q2)] Alternatively: dW dE' F2 prop sL + s T FL = F2 – 2xF1 + 2MpF2 R =sL / s T = FL /2xF1

  5. Duality in the F2 Structure Function First observed ~1970 by Bloom and Gilman at SLAC • Bjorken Limit: Q2, n  • Empirically, DIS region is where logarithmic scaling is observed: Q2 > 5 GeV2, W2 > 4 GeV2 • Duality: Averaged over W, logarithmic scaling observed to work also for Q2 > 0.5 GeV2, W2 < 4 GeV2, resonance regime

  6. What about the other structure functions FL, F1, g1,….? World's L/T Separated Resonance Data (before 2002): R = sL/sT • Not able to study the Q2 dependence of individual resonance regions! • No resonant behaviour can be observed! (All data for Q2 < 9 (GeV/c)2) JLab E94-110: a global survey of longitudinal strength in the resonance region…...

  7. JLab Hall C E94-110: Global Survey of Longitudinal Strength in Nucleon Resonance Region R = sL/sT < • Covers 0.4 < Q2 < 5.0 (GeV/c)2, Mp < W2 < 4.0 GeV2 • Clear resonant behaviour can be observed! • Now able to study the Q2 dependence of individual resonance regions! (All data for Q2 < 9 (GeV/c)2) Now able to extract F2, F1, FL and study duality!...

  8. Rosenbluth Separations • 180 L/T separations total (most with 4-5 e points) • Spread of points about the linear fits is fairly Gaussian with s ~ 1.6 %- consistent with the estimated pt-pt experimental uncertainty • a systematic “tour de force”

  9. Duality now observed in all unpolarized structure functions

  10. …and in Nuclei (F2) x = 2x[1 + (1 + 4M2x2/Q2)1/2] GRV curve p d Fe

  11. Scaling (F2) in Nuclei

  12. Duality and the EMC Effect Medium modifications to the pdfs are the same in the resonance region Rather surprising (deltas in nuclei, etc.) J. Arrington, et al., in preparation

  13. …and in Spin Structure Functions HERMES JLab Hall B A1p A1p g1

  14. Qualitatively, duality is observed to hold in all unpolarized structure functions, in nuclei, and in tested spin structure functions down to surprisingly low Q2 Apparently a non-trivial property of nucleon structure If we had used only scintillators, scaling would be thought to hold down to low Q2!

  15. Quantification Integral Ratio Res / Scaling

  16. The available pdf-based parameterizations significantly undercut the data at large x Quantification SLAC data above W2 = 4 GeV2

  17. Duality in QCD 1 0 • Moments of the Structure Function Mn(Q2) = S dxxn-2F(x,Q2) If n = 2, this is the Bloom-Gilman duality integral! • Operator Product Expansion Mn(Q2) = (nM02/Q2)k-1Bnk(Q2) higher twistlogarithmic dependence (pQCD) • Duality is described in the Operator Product Expansion as higher twist effects being small or cancelling DeRujula, Georgi, Politzer (1977)  k=1

  18. 1 Mn(Q2) = Sdxxn-2F(x,Q2) 0 F2 + elastics……

  19. 1 n = 2 Moments of F2, F1 and FL: Mn(Q2) = Sdxx2-2F(x,Q2) 0 DIS: SLAC fit to F2 and R RES: E94-110 resonance fit Elastic Contributions F1EL = GM2 d(x-1) Preliminary F2 F2EL = (GE2 +tGM2 )d(x-1) Elastic contribution excluded 1 +t F1 t = q2/4Mp2 FLEL = GE2 d(x-1) Flat Q2 dependence  small higher twist! - not true for contributions from the elastic peak (bound quarks) FL

  20. n = 4 Moments of F2, F1 and FL Preliminary Neglecting elastics, n = 4 moments have only a small Q2 dependence as well. Momentum sum rule ML(n) = as(Q2){ 4M2(n) + 2c∫dx xG(x,Q2)} (n+1)(n+2) 3(n+1) Gluon distributions! This is only at leading twist and neglecting TM effects. ⇒ Must remove TM effects from data to extract moment of xG…we’re working on it…..

  21. For the future….

  22. Measuring Neutron Structure Functions: BONUS Electron detected in JLab Hall B CLAS spectrometer Spectator proton detected in RTPC p • Hall B CLAS spectrometer for electron detection • Thin deuterium target (7.5 atm) • Radial Time Projection Chamber (RTPC) for low momentum spectator proton detection • DVCS solenoid to contain Moller background e- n

  23. “Very Important Protons” • Deuteron ~ free proton + free neutron at small nucleon momenta • Will target Tp ~ 2 – 5 MeV spectator protons • 30% of momentum distribution is in chosen ps range • Tp > 5 MeV spectators will also be detected

  24. Duality in Meson ElectroproductionDuality and factorization possible for Q2,W2  3 GeV2 (Close and Isgur, Phys. Lett. B509, 81 (2001)) hadronic description quark-gluon description Requires non-trivial cancellations of decay angular distributions If duality is not observed, factorization is questionable ds/dz  iei2qi(x,Q2)Dqim(z,Q2) + qi(x,Q2)Dqim(z,Q2)

  25. (Semi-)Exclusive Meson Electroproduction • Large z = Eh/n to emphasize duality and factorization (Berger criterion) • Meson electroproduced along q, i.e. emphasize forward angles • Proposed SHMS in Hall C well suited to detect these mesons (cf. pion form factor) • If Berger criterion and duality  factorization

  26. MINERn-A • FermiLab proposal en route….. • Can test duality in neutrino scattering! (Melnitchouk and Close (2003), Beane (2001),….) • Can also help with large x pdfs

  27. Summary • Quark-hadron duality is a non-trivial property of nucleon structure • Duality has been shown to hold in all experimental tests thus far • All unpolarized structure functions • Polarized structure functions • Nuclei • More experiments are planned • Neutron • Semi-inclusive • Neutrino scattering • Duality may provide a valuable tool to access high x regime • Duality violations obscure comparison with lattice QCD through the structure function moments

  28. “It is fair to say that (short of the full solution of QCD) understanding and controlling the accuracy of quark-hadron duality is one of the most important and challenging problems for QCD practitioners today.”M. Shifman, Handbook of QCD, Volume 3, 1451 (2001)

  29. RTPC Design

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