1. Nuclear Duality, electron scattering, and neutrino scattering: Nucleon Resonance Region P. Bosted August 1 2006  Quark-Hadron duality in F1, F2, g1, and semi-inclusive DIS  Nuclear dependence: what’s new  PV electron scattering in the resonance region

2. Why I got interested  Needed for radiative correction calculations.  Needed to get “dilution factor” in experiments using NH 3 or ND 3 targets to measure g 1 (inclusive exclusive, SIDIS)  Needed to predict PV asymmetry in ep inelastic scattering (background to Moller scattering and DIS tests of Standard Model

3. 3 Duality and the Transition to Perturbative QCD Asymptotically Free Quarks: regime of pQCD Long Distance Physics: hadronic observables

4. 4 Textbook Example: e + e - hadrons Only evidence of hadrons produced is narrow states oscillating around step function determined by quark color, charge. R =

5. 5. First observed ~1970 by Bloom and Gilman at SLAC by comparing resonance production data with deep inelastic scattering data using ad hoc variable. Integrated F 2 strength in nucleon resonance region equals strength under scaling curve.. Resonances oscillate around curve - for Q 2 >1 or so Shortcomings: Only a single scaling curve and no Q 2 evolution (theory inadequate in pre-QCD era)  ’ = 1+W 2 /Q 2 Q 2 = 0.5 Q 2 = 0.9 Q 2 = 1.7Q 2 = 2.4 F2F2 F2F2 Bloom-Gilman Duality

6. 6 Bloom-Gilman Duality in F 2 proton Today F 2 DIS well-measured over several orders of magnitude in x, Q 2 QCD established theory Perturbative predictions (based on extracted PDF’s, evolution) available Target mass prescription Quark-Hadron Duality quantifiable (more later….) Show to hold to better than 5% above Q 2 ~ 0.5 GeV 2 F 2 average Q 2 dependence

7. 7 Bloom-Gilman Duality in F 2 Today Difference between Alekhin NNLO curve (formed from lepton-nucleon scattering only) and resonance data, integrated for many spectra

8. 8 Experimental Status of L/T Separated Structure Functions: 2xF 1 Experimental Status of L/T Separated Structure Functions: 2xF 1 Smooth transition from DIS (solid squares) to resonance region Resonances oscillate about perturbative curves Target mass corrections large and important (subject of much recent theory work - Steffens, Melnitchouk, Qiu, Reno, Kretzer,…) Alekhin NNLO MRST NNLO MRST NNLO with Barbieri Target Mass Corrections Data from JLab E94-110 (nucl-ex/0410027)

9. 9 Experimental Status of L/T Separated Structure Functions: F L Experimental Status of L/T Separated Structure Functions: F L Smooth transition from DIS (solid squares) to resonance region Resonances oscillate about perturbative curves for Q 2 >1 GeV 2 Target mass corrections large and important Alekhin NNLO MRST NNLO MRST NNLO with Barbieri Target Mass Corrections

10. 10 Duality in QCD Moments of the Structure Function M n (Q 2 ) = ∫ dx x n-2 F(x,Q 2 ) If n = 2, this is the Bloom-Gilman duality integral! Operator Product Expansion M n (Q 2 ) =  (nM 0 2 / Q 2 ) k-1 B nk (Q 2 ) higher twist logarithmic dependence (pQCD) Duality is described in the Operator Product Expansion as higher twist effects being small or cancelling DeRujula, Georgi, Politzer (1977) 0 1 k=1 

11. 11 0 1 M n (Q 2 ) = dx x n-2 F(x,Q 2 ) Need data covering wide range in x, at fixed Q2 Large x increasingly important at large n + elastics…… F2F2

12. 12 Preliminary n = 2 Cornwall-Norton Moments F2F2 FLFL FTFT F 2, F 1 in excellent agreement with NNLO + TM above Q 2 = 2 GeV 2 No (or canceling) higher twists Yet, dominated by large x and resonance region Remove known HT ( elastic), and there are no more down to Q 2 = 0.5 GeV 2 The case looks different for F L (target mass larger issue - still under study)

13. 13 Duality Works even better in Nuclei, (F 2 ) p Fe d  = 2x [ 1 + (1 + 4M 2 x 2 /Q 2 ) 1/2 ] Data in resonance region, spanning Q 2 range 0.7 - 5 GeV 2 GRV curve The nucleus does the averaging For larger A, resonance region indistinguishable from DIS

14. 14 Duality (F 2 ) in Deuterium Resonant structure mostly gone for W>1.4 GeV

15. 15 Duality and the EMC Effect J. Arrington, et al., submitted Medium modifications to the structure functions are the same in the resonance region as in the DIS for Q 2 >2 GeV 2 or so. Note use of xi, not x! (approximates TM) C/D Fe/D Au/D

16. 16 And these results just in… C/D4He/D

17. 17 Duality in g 1 Data both p and d oscillate round NLO PDF curves with TM corrections.

18. 18 Average g 1 (over M<W<2 GeV) agrees very well with PDF fits with TM corrections down to about 1.5 GeV 2. Power law (HT) deviations clear at lower Q 2. Adding elastic peak seems to help in this case.

19. 19 Locally, Delta(1232) region systematically low, 1.5 GeV region high

20. 20 Duality in Meson Electroproduction hadronic descriptionquark-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 Q 2,W 2  3 GeV 2 (Close and Isgur, Phys. Lett. B509, 81 (2001))

21. 21 The Origins of Quark-Hadron Duality – Semi-Inclusive Hadroproduction Destructive interference leads to factorization and duality Predictions: Duality obtained by end of second resonance region Factorization and approximate duality for Q 2,W 2 < 3 GeV 2 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

22. 22 Missing mass of pions in ep->e’  X Duality question: will factorization work if M x <2 GeV, even though Delta(1232) reonance Visible? For pi-, guess need M x >1.4 GeV. -- 00 ++ n 00  ++

23. 23 Z-Dependence of cross sections Good agreement with prediction using CTEQ5M PDFs and Binnewies fragmentation functions, except for z>0.7, or Mx>1.4 GeV. X=0.3, Q 2 =2.5 GeV 2, W=2.5 GeV

24. 24 R pd+ R pd- Both ratios agree PDF models for z 1.4 GeV)

25. 25 Summary so far Duality useful at O(10%) for Q 2 >1 to 2 GeV 2 –Spin-averaged structure functions –Tested spin structure functions Duality observed in Nuclei –Even displays EMC effect Duality in semi-inclusive meson production

26. 26 Questions raised How to extend to low Q 2 –M. Eric Christy et al have excellent empirical fit to all F 1, F 2 data covering M<W<5 GeV, 0<Q 2 <10 GeV 2. Duality used in determining functional form –No good fit to deuteron at low Q 2 (in progress though). –Nuclear dependance. New data 15 N/C What is nuclear depeance of specific final statesin resonance region (good direction for future work: data exist but not analyzed.

27. 27 Hall C VERY PRELIMINARY DATA TYPICAL MODEL Inelastic scattering on deuteron

28.  To study problem further, used large sample (about 10 billion scattered electrons) of data from CLAS Eg1b experiment using CLAS in Hall B at Jlab.  Targets filled with ND 3 or NH 3 (plus some liquid helium) were alternated frequently (so acceptance cancels) and electrons were detected 10<  <40 degrees for beam energies 1.7, 2.5, 4.2, 5.7 GeV. Inelastic scattering on deuteron

29. 29 Curves using Eric Christy for p and Steve Rock fit d Data: CLAS Eg1b VERY PRELIMINARY from NH3/ND3 Inelastic proton/deuteron ratio in Resonance Region Q 2 =0.12 Q 2 =0.6 Q 2 =1.0Q 2 =1.8 Q 2 =0.2Q 2 =0.4

30. 30 Curves using Eric Christy for p and D2MODEL_IOANA fit d Data: CLAS Eg1b VERY PRELIMINARY from NH3/ND3 Inelastic proton/deuteron ratio in Resonance Region Q 2 =0.12 Q 2 =0.6 Q 2 =1.0Q 2 =1.8 Q 2 =0.2Q 2 =0.4

31. 31 Curves using Eric Christy for p and E665 fit for d Data: CLAS Eg1b VERY PRELIMINARY from NH3/ND3 Inelastic proton/deuteron ratio in Resonance Region Q 2 =0.12 Q 2 =0.6 Q 2 =1.0Q 2 =1.8 Q 2 =0.2Q 2 =0.4

32. 32 Curves using E665 fit for both p and d Data: CLAS Eg1b VERY PRELIMINARY from NH3/ND3 Inelastic proton/deuteron ratio in Resonance Region Q 2 =0.12 Q 2 =0.6 Q 2 =1.0Q 2 =1.8 Q 2 =0.2Q 2 =0.4

33. 33  Looks like what works best among available models is E665 fit (A. V. Kotwal, January 1994), hich makes assumption n=0.76p in the resonance region.  Next step: add Fermi smearing for deuteron.  Next step: study best transition to DIS region (W>2 GeV): clearly n/p=(1-0.8x) inadequate: need to consider using (1- 0.8xi) and also make shadowing corrections. Inelastic scattering on deuteron

34. 34  Presently, apply simple y-scaling-based Fermi smearing model to free neutron and proton fits, plus a Steve Rock fit to “EMC” ratio for x<0.8 to take into account binding and shadowing.  This prescription predicts ratio of 15 N to C essentially independent of W in the resonance region.  This seems to be born out by very preliminary ratios measured in CLAS. Inelastic scattering on nuclei

35. 35  Presently, apply simple y-scaling-based Fermi smearing model to free neutron and proton fits, plus a Steve Rock fit to “EMC” ratio for x<0.8 to take into account binding and shadowing.  This prescription predicts ratio of 15 N to C essentially independent of W in the resonance region (BUT, not quasielastic!).  This seems to be born out by very preliminary ratios measured in CLAS. Inelastic scattering on nuclei

36. 36 Very preliminary ratios 15N/C (per gm) from CLAS Eg1b W (GeV) Curve use DIS limit n/p=(1-0.8x)

37. 37 To obtain fraction of events from polarized protons (deuterons) in NH3 (ND3), used recent data for deuteron to carbon ratio in SIDIS from E02-104 (Will Brooks). Few representative points shown. MUCH MORE DATA coming soon over wide kinematic range. Studies quark propogation in cold QCD matter. CLAS 5.7 GeV PRELIMINARY

38. 38  The cross section in terms of electromagnetic, weak and interference contribution  Asymmetry due to interference between Z 0 and  Electron can scatter off of proton by exchanging either a virtual photon or a Z 0 e’ e P e’ e P Z0Z0  + Parity Violating Asymmetry

39. For inelastic scattering, A RL can be written in terms of response functions Isospin symmetry relates weak and EM vector current Sensitive to axial hadronic current also Details have so far been worked out only for N → ∆(1232) weakly sensitive to axial vector transition form factor Resonance Region asymmetry

40. For an isolated resonance, A RL can be written in terms of response functions Isospin symmetry relates weak and EM vector current Sensitive to axial hadronic current also Details have so far been worked out only for N → ∆(1232) weakly sensitive to axial vector transition form factor Resonance Region Asymmetry

41. Leading order criteria DATA NEEDED! Duality is satisfied if on average  n /  p = 2/3 PROTON Simple Model  No reliable model for n/p ratio in res. region: use simple toy model  Will data look anything like this?  Duality good to ~5% in F 2, our goal is to measure A LR to ~5% locally and <3% globally DIS model Resonance model DUALITY for  -Z interference tensor?

42. Leading order criteria Duality is satisfied if on average  n /  p = 2/3 PROTON Simple Model  No reliable model for n/p ratio in res. region: use simple toy model  Will data look anything like this?  Duality good to ~5% in F 2, our goal is to measure A LR to ~5% locally and <3% globally DIS model Resonance model DUALITY for  -Z interference tensor?

43. 43  Study A-dependence of axial contribution  Will duality averaging work similarly to vector hadronic current? Physics Goals – Nuclear targets

44. 44  Neutron / Proton ratio almost constant in the nucleon resonance region.  New data from CLAS and Hall C will soon pin down vector current for proton, neutron, carbon, 15 N, and heavier targets from quasi-elastic region up to W-3 GeV and for 0.05<Q 2 <5 GeV 2  Better emipirical fits needed for modeling radiative corrections, neutrino interactions, and many other applications. Duality useful here. Study of specific final states needed for A>1!  Potential for PV electron scattering to constrain axial-vector piece. CONCLUSIONS