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Quark-Hadron Duality

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

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Quark-Hadron Duality

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

  2. “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)

  3. 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 Duality defines the transition from soft to hard QCD.

  4. Example: e+e- hadrons / m+m-lim s(e+e- X) = NC S eq2 E  s(e+e- m+m-) q

  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? World's L/T Separated Resonance Data (until 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. What about the other structure functions FL, F1? R =  / T R = sL/sT < • Now able to study the Q2 dependence of individual resonance regions! • Clear resonant behaviour can be observed! (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] p d Fe

  11. Quark-Hadron Duality (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 g1

  14. Experimentally, duality holds in all unpolarized structure functions, in tested spin structure functions, even better in nuclei, all 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. For tomorrow Quantification Integral Ratio Res / Scaling

  16. Quantification Large x Structure Functions

  17. Close and Isgur Approach How many states does it take to approximate closure? Proton W~1.5 Neutron W ~ 1.7 Phys. Lett. B509, 81 (2001): Sq = Sh Relative photo/electroproduction strengths in SU(6) “The proton – neutron difference is the acid test for quark-hadron duality.” To spectrometer The BONUS experiment will measure neutron structure functions……. p n e- To recoil detector

  18. Experimental Setup • Hall B CLAS spectrometer for electron detection • Thin deuterium target (7.5 atm) • Radial Time Projection Chamber (RTPC) for spectator proton detection • DVCS solenoid to contain Moller background

  19. “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

  20. RTPC Design

  21. F2n / F2p Ratio at Large x – Projected Results • Yellow shaded area represents current theoretical uncertainty • RR data begin the Resonance Region (W2 > 3 GeV2, Q2 ~ 5) • Gray shaded areas represent systematic uncertainty • Light = total • Dark = normalized, point-to-point

  22. 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

  23. 1 Mn(Q2) = Sdxxn-2F(x,Q2) For moments add elastics…… 0 F2 Duality Above Q2=1 Below Q2=1, duality breaks Down (empirical fits shown)

  24. 1 0 n = 2 Moments of F2, F1 and FL: Mn(Q2) = ∫ dxx2-2F(x,Q2) 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

  25. 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…..

  26. Moments are Calculated on the Lattice: F2n – F2p • D. Dolgov et al., Phys. Rev. D 66:034506, 2002 • Data from JLab Hall C • Current (data) uncertainties are in nuclear extraction of F2n

  27. Another approach And some new experiments

  28. Close and Isgur Approach How many states does it take to approximate closure? Proton W~1.5 Neutron W ~ 1.7 Phys. Lett. B509, 81 (2001): Sq = Sh Relative photo/electroproduction strengths in SU(6) “The proton – neutron difference is the acid test for quark-hadron duality.”

  29. 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)

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

  31. More of the experimental future

  32. Separated Unpolarized Structure Functions at 11 GeV Hall C x = 0.8 De > 0.3 SHMS HMS Also necessary for polarized structure function measurements...

  33. Polarized Structure Functions at 11 GeV Hall C

  34.  JLab Hall A A1n from 3He(e,e’) 2

  35. Summary • Quark-hadron duality is a non-trivial property of QCD Soft-Hard Transition! • 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 • Polarized structure functions • 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

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