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Nuclear Duality (and related topics…)

Nuclear Duality (and related topics…). Cynthia Keppel Hampton University / Jefferson Lab. First Workshop on Quark-Hadron Duality Frascati, Italy June 2005. A Program of Inclusive Structure Function Measurements in Hall C at Jefferson Lab. E94-110: L/T Hydrogen Resonance Region

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Nuclear Duality (and related topics…)

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  1. Nuclear Duality(and related topics…) Cynthia Keppel Hampton University / Jefferson Lab First Workshop on Quark-Hadron Duality Frascati, Italy June 2005

  2. A Program of Inclusive Structure Function Measurements in Hall C at Jefferson Lab • E94-110: L/T Hydrogen Resonance Region • E99-118: L/T Low x, Q2 A-Dependence • E00-002: L/T Low Q2 Deep Inelastic H, D • E00-116: High Q2 H,D • E04-001: L/T Nuclear Dependence, Neutrino Modeling • E02-109: L/T Deuterium Resonance Region • E02-109: x>1, A-Dependence • E03-103: EMC effect

  3. Inclusivee + p  e + X Scattering Rosenbluth: Where:  = flux of transversely polarized virtual photons  = relative longitudinal polarization Alternatively: Transverse longitudinal mIxEd

  4. High Precision Data E94-110 Example: 180+ L/T’s R = sL/sT < R = sL/sT (All data for Q2 < 9 (GeV/c)2) ds/dWdE/G (nb/sr/GeV)  ~ 1.6%

  5. Example Precision Proton Structure Function: FL Alekhin NNLO MRST NNLO MRST NNLO with Barbieri Target Mass Corrections Smooth transition from DIS (solid squares) to resonance region Resonances oscillate about leading order curves Q2 dependence same for leading order scaling, resonances Target mass corrections large and important

  6. Duality in F2…let the nucleus do the averaging x = 2x[1 + (1 + 4M2x2/Q2)1/2] • 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 p d Fe

  7. Duality and the EMC Effect C/D Red = resonance region data Blue, purple, green = deep inelastic data from SLAC, EMC Medium modifications to the structure functions are the same in the resonance region as in the DIS Cross-over can be studied with new data Fe/D Au/D J. Arrington, et al., submitted

  8. 1 Fe data = data :) Fe curve = 26p + 30n** d from e-d data (sum = 0.31) p from hydrogen **n = d-p (sum rule = 0.14) Momentum Sum Rule M2(Q2) = ∫dxF2(x,Q2) 0 ….elastic contributions I. Niculescu, et al, in preparation

  9. More quantitatively….. Momentum sum rule from iron agrees with simple sum p,n to within 5% (not very sensitive to neutron excess) EMC effect is a redistribution, not additional, momentum of quarks Where is the nuclear binding? 7 MeV / nucleon / 938 MeV ~ expect 6% difference!

  10. Extraction of Nuclear Moments 2 2 JLab Hall C E89-009 E02-109 x>1: (2004) H,D,3He,4He,C,Cu,Au E03-103 EMC effect: (2004) H,D, 3He, 4He,C, Cu, Au 2

  11. ML(n) = s(Q2){ 4M2(n) + 2c∫dx xG(x,Q2)} (n+1)(n+2) 3(n+1) Proton Momentum Sum Rule For F2, QPM gives: (1/3)2(0.17) + (2/3)2(0.34) = 0.17 ~50% of momentum carried by quarks - the rest, assumably, by the glue FL gives a direct measurement of the glue But, we get 0.70 (preliminary) - also different from pdfs Preliminary

  12. n = 2 Cornwall-Norton Proton Moments F2, F1 in excellent agreement with NNLO + TM above Q2 = 2 GeV2 Very small (or canceling) higher twists Yet, dominated by large x and resonance region Remove known HT (a bit novel), the elastic, and there is no more down to Q2 = 0.5 GeV2 The case looks different for FL (data or curve?) F2 2xF1 FL

  13. “Neutron” - Proton Moments: Compare to Lattice D. Dolgov, et al., Phys.Rev.D66:034506, 2002 n-p reduces sea, higher twist effects Need to wait for BONUS,,,,,,,

  14. Parton Distribution Functions not well known at large x largely due to uncertainties associated with neutron extraction from deuterium CTEQ u,d(x) uncertainty bands Similar for HERA, note also glue important still at large x (scaled by factor of 20!)

  15. Being bold….. F2 Need to get scaling curves for p, n at large x Duality implies nucleus averaging to scaling, small higher twist Use duality-averaged curve to get neutron Fix range in , average data, obtain curve ……………….let’s see…. D P

  16. A Prediction from Duality and Large x p,d Data: Helicity Conservation and d/u = 1/5 Naïve SU(6) quark model, d/u = 1/2 Helicity conservation, d/u = 1/5 1 gluon exchange. d/u = 0

  17. Challenges / Issues / Physics at Low Q2 higher twists • NEED L/T separations to extract inclusive structure functions F1, FL, and F2 • Low Q2 behavior • Photonuclear absorption: resonances less apparent in nuclei than in the proton (beyond Fermi) • Nuclear moment analyses indicate higher twist occur at smaller Q2 current conservation

  18. At low Q2, L/T Separations are Crucial…. 1) F2 is sometimes referred to as the “transverse” SF. 2) F2 can’t be obtained precisely independent of R and L/T separations 3) Behaviour of F2 at low Q2 is not actually well determined (F2 0 at Q2 0). 4) R must be small for Q2 < 1 (R = 0 at the photon point, Q2 = 0). In fact F2s L + s T Except ate= 1 or Q2 large, F2 extracted from cross sections requires knowledge of R. This has not yet been observed in the data - in fact, quite the opposite…..

  19. Just an example…. At W2 = 4 GeV2 and Q2 < 1 GeV2, F2 will vary by 15% depending on the choice of R = 0 or R = 0.2. At higher Q2, this can be as much as 20%.

  20. R on the proton…E99-118, E94-110 + world Note: R still not small at low Q2 as expected! Precious little nuclear data available (E99-118 soon high W2, low Q2 H,D,C,Al,Cu,Au)

  21. E99-118 Ratio RD / RH Very limited previous data RD ~ 0.7 RH (within large uncertainty) V. Tvaskis, PhD Thesis, Vrije Universiteit, 2004

  22. LOTS of new, L/T separated, low Q2 nuclear data en route… Very preliminary data (just obtained January 2005) H,D,C,Al,Cu,Fe,Au resonance region Models: D resonance - JLab n/p - d/u = 1/5 EMC - SLAC DIS - F2allm (NMC) R - JLab e99118

  23. Data will be used for: Nuclear duality Neutrino modeling Deuterium (neutron) moments R on deuterium in resonance region A-dependence of structure functions (and moments) at low Q2 Search for nuclear pions (G. Miller prediction)

  24. Summary • Duality seems to hold even better in the nucleus, where Fermi motion naturally averages the structure function over resonances • EMC effect in resonance region same as deep inelastic regime • Fe momentum sum rule constructed from (d-p),p to within 5% • Use duality and the deuteron to extract • n-p structure function moments (lattice comparison) • n/p at large x (helicity conservation) • Challenges at low Q2 • Need L/T separations • When do R, F2 approach 0? • Nuclear Effects • *LOTS* of new data “in the can”…exciting times…

  25. 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 (pQCD) • Duality is described in the Operator Product Expansion as higher twist effects being small or cancelling DeRujula, Georgi, Politzer (1977)  k=1

  26. 1 Mn(Q2) = dxxn-2F(x,Q2) 0 F2 Need data covering wide range in x, at fixed Q2 Large x increasingly important at large n + elastics……

  27. Why is IGDH(Q2) interesting?

  28. Extended Baldin Sum Rule Q2 = 0, photoproduction Baldin Sum Rule GDH Sum Rule Q2 > 0, electroproduction Extended GDH Sum Rule Extended Baldin Sum Rule * Where κ : anomalous magnetic moment of the nucleon. α, β: electric and magnetic polarizabilities respectively ν0 : pion photoproduction threshold Need L/T separated data! * D. Drechsel, B. Pasquini, M. Vanderhaeghen hep-ph/0212124 Dec 2002

  29. Multiply with Q4/2M to emphasize transition of Baldin Sum Rule to Perturbative DIS Region Again, smooth transition ~ 2xF1 Moment

  30. Duality (F2) in Deuterium Resonance region and DIS F2 same, with same Q2 dependence, other than at smallest W

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