Rolf Ent, DIS2004

1. Measurements of R and the Longitudinal and Transverse Structure Functions in the Nucleon Resonance Region and Quark-Hadron Duality Rolf Ent, DIS2004 • Formalism: R, 2xF1, F2, FL • E94-110: L/T Separation at JLab • Quark-Hadron Duality • Or: Why does DIS care about the Resonance Region? • If time left: Duality in nuclei/g1 • Summary

2. Inclusive e + p  e’ + X scattering Single Photon Exchange Resonance Elastic DIS Where Alternatively:

3. Resonance Region L-Ts Needed For Extracting spin structure functions from spin asymmetries s/2 –s3/2 s1/2 –s3/2 A1 = = s1/2 + s3/2 2sT DA1 edR (for R small) _ ~ A1 F1(A1 – gA2) From measurements of F1 and A1 extract s1/2 and s3/2! (Get complete set of transverse helicity amplitudes) g1 = 1 + g2 F2(1 + eR) _ ~ 1 + R (Only insensitive to R if F2 in relevant (x,Q2) region was truly measured at e = 1)

4. E94-110 Experiment performed at JLab-Hall C HMS SOS G0

5. JLab-HALL C Shielded Detector Hut Superconducting Dipole Target Scattering Chamber HMS SOS Superconducting Quadrupoles Electron Beam

6. Rosenbluth Separations Hall C E94-110: a global survey of longitudinal strength in the resonance region…... sL +sT sT = sLsT / (polarization of virtual photon)

7. Rosenbluth Separations Hall C E94-110: a global survey of longitudinal strength in the resonance region…... • Spread of points about the linear fits is Gaussian with s ~ 1.6 % consistent with the estimated point-point experimental uncertainty (1.1-1.5%) • a systematic “tour de force”

8. World's L/T Separated Resonance Data R = sL/sT < < R = sL/sT (All data for Q2 < 9 (GeV/c)2)

9. World's L/T Separated Resonance Data R = sL/sT < Now able to study the Q2 dependence of individual resonance regions! Clear resonant behaviour can be observed! Use R to extract F2, F1, FL R = sL/sT (All data for Q2 < 9 (GeV/c)2)

10. E94-110 Rosenbluth Extractions of R • Clear resonant behaviour is observed in R for the first time! → Resonance longitudinal component NON-ZERO. → Transition form factor extractions should be revisited. • Longitudinal peak in second resonance region at lower mass than S11(1535 MeV) → D13(1520 MeV) ? P11(1440 MeV)? • R is large at low Q high W (low x) → Was expected R → 0 as Q2 → 0 → R → 0 also not seen in recent SLAC DIS analysis (R1998)

11. Kinematic Coverage of Experiment sR = (ds/G) = sT(W2,Q2) + esL(W2,Q2) 2 Methods employed for separating Structure Functions: • Rosenbluth-type separations where possible (some small kinematic evolution is needed) • Iteratively fit F2 and R over the entire kinematic range. Also perform cross checks with elastic and DIS (comparing with SLAC data)

12. L-T Separated Structure Functions Good agreement between methods ( model available for use!) Very strong resonant behaviour in FL! Evidence of different resonances contributing in different channels?

13. DualityintheF2StructureFunction First observed ~1970 by Bloom and Gilman at SLAC by comparing resonance production data with deep inelastic scattering data • Integrated F2 strength in Nucleon Resonance region equals strength under scaling curve. Integrated strength (over all w’) is called Bloom-Gilman integral Shortcomings: • Only a single scaling curve and no Q2 evolution (Theory inadequate in pre-QCD era) • No sL/sT separation  F2 data depend on assumption of R = sL/sT • Only moderate statistics F2 Q2 = 0.5 Q2 = 0.9 F2 Q2 = 1.7 Q2 = 2.4 w’ = 1+W2/Q2

14. DualityintheF2StructureFunction First observed ~1970 by Bloom and Gilman at SLAC Now can truly obtain F2 structure function data, and compare with DIS fits or QCD calculations/fits (CTEQ/MRST) Use Bjorken x instead of Bloom-Gilman’s w’ • Bjorken Limit: Q2, n • Empirically, DIS region is where logarithmic scaling is observed: Q2 > 5 GeV2, W2 > 4 GeV2 • Duality: Averaged over W, logarithmic scalingobserved to work also for Q2 > 0.5 GeV2, W2 < 4 GeV2, resonance regime (note: x = Q2/(W2-M2+Q2) • JLab results: Works quantitatively to better than 10% at such low Q2

15. Numerical Example: Resonance Region F2 w.r.t. Alekhin Scaling Curve (Q2 ~ 1.5 GeV2)

16. Duality in FT and FL Structure Functions Duality works well for both FT and FL above Q2 ~ 1.5 (GeV/c)2

17. Also good agreement with SLAC L/T Data Alekhin SLAC MRST (NNLO) + TM E94-110 MRST (NNLO)

18. 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 useeitherset of complete basis states to describe physical phenomena But why also in limited local energy ranges?

19. If one integrates over all resonant and non-resonant states, quark-hadron duality should be shown by any model. This is simply unitarity. However, quark-hadron duality works also, for Q2 > 0.5 (1.0) GeV2, to better than 10 (5) % for the F2 structure function in both the N-D region and the N-S11 region! (Obviously, duality does not hold on top of a peak! -- One needs an appropriate energy range) One resonance + non-resonant background Few resonances + non-resonant background Why does local quark-hadron duality work so well, at such low energies? ~ quark-hadron transition Confinement is local ….

20. Quark-Hadron Duality – Theoretical Efforts One heavy quark, Relativistic HO N. Isgur et al : Nc ∞ qq infinitely narrow resonances qqq only resonances Q2 = 1 Q2 = 5 u Scaling occurs rapidly! • 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 • Similar arguments for e.g. DVCS and semi-inclusive reactions • Distinction between Resonance and Scaling regions is spurious • Bloom-Gilman Duality must be invoked even in the Bjorken Scaling region  Bjorken Duality

21. Duality ‘’easier” established in Nuclei EMC Effect Fe/D Resonance Region Only The nucleus does the averaging for you! (s Fe/s D) IS x (= x corrected for M  0) Nucleons have Fermi motion in a nucleus

22. … but tougher in Spin Structure Functions Pick up effects of both N and D (the D is not negative enough….) CLAS EG1 CLAS: N-D transition region turns positive at Q2 = 1.5 (GeV/c)2 Elastic and N-D transition cause most of the higher twist effects g1p D

23. … but tougher in Spin Structure Functions (cont.) SLAC E143: g1p and g1d data combined Hint of overall negative g1n even in resonance region at Q2 = 1.2 (GeV/c)2 Duality works better for neutron than proton? – Under investigation g1n

24. Summary • Performed precision inclusive cross section measurements in the nucleon resonance region (~ 1.6% pt-pt uncertainties) • R exhibits resonance structure (first observation) • Significant longitudinal resonant component observed. • Prominent resonance enhancements in R and FL different from those in transverse and F2 • Quark-hadron duality is observed for ALL unpolarized structure functions. • Quarks and the associated Gluons (the Partons) are tightly bound in Hadrons due to Confinement. Still, they rely on camouflage as their best defense: • a limited number of confined states acts as if consisting of free quarks  • Quark-Hadron Duality, which is a non-trivial property of QCD, telling us • that contrary to naïve expectation quark-quark correlations tend to cancel • on average • Observation of surprising strength in the longitudinal channel at Low Q2 and x ~ 0.1

25. QCD and the Operator-Product Expansion 1 0 • Moments of the Structure Function Mn(Q2) = 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 • Duality is described in the Operator Product Expansion as higher twist effects being small or cancelingDeRujula, Georgi, Politzer (1977)  k=1

26. Example: e+e- hadrons Textbook Example R = Only evidence of hadrons produced is narrow states oscillating around step function

27. Preliminary: Still DR = 0.1 point-to-point (mainly due to bin centering assumptions to x = 0.1) E99118

28. Model Iteration Procedure Starting model is used for input for radiative corrections and in bin-centering the data in θ σexpis extracted from the data Model is used to decompose σexp into F2exp and Rexp Q2 dependence of both F2 and R is fit for each W2 bin to get new model

29. Example SF Iteration Measurements at different ε are inconsistent ⇒ started with wrong splitting of strength! Q2 Iteration results in shuffling of strength Consistent values of the separated structure functions for all ε ! Q2

30. Point-to-Point Systematic Uncertainties for E94-110 Total point-to-point systematic uncertainty for E94-110 is 1.6%.

31. Experimental Procedure and CS Extraction Cross Section Extraction • Acceptance correct e- yield bin-by-bin (δ, θ). • Correct yield for detector efficiency. • Subtract scaled dummy yield bin-by-bin, to remove e- background from cryogenic target aluminum walls. • Subtract charge-symmetric background from π0 decay via measuring e+ yields. • bin-centering correction. • radiative correction. Elastic peak not shown W2 (GeV2) At fixed Ebeam, θc, scan E’ from elastic to DIS. (dp/p =+/-8%, dθ =+/-32 mrad) Repeat for each Ebeam, θcto reach a range in ε for each W2, Q2.

32. QCD and the Parton-Hadron Transition One parameter, LQCD, ~ Mass Scale or Inverse Distance Scale where as(Q) = infinity “Separates” Confinement and Perturbative Regions Mass and Radius of the Proton are (almost) completely governed by Constituent Quarks Q > L as(Q) large Hadrons Q < L as(Q) > 1 QCD213 MeV Asymptotically Free Quarks Q >> L as(Q) small L

33. QCD and the Parton-Hadron Transition One parameter, LQCD, ~ Mass Scale or Inverse Distance Scale where as(Q) = infinity “Separates” Confinement and Perturbative Regions Mass and Radius of the Proton are (almost) completely governed by QCD213 MeV