Work in 2004: Note this is a Pseudo Leading Order Model

1. NUINT04 - Italy Arie Bodek, University of RochesterUn-Ki Yang, University of ChicagoUpdate on low Q2 Corrections to LO-GRV98 PDFs • Work in 2004: Note this is a Pseudo Leading Order Model • Vector PDFs: Extrat the low Q2 corrections to d and u valence quarks separately now by including all inelastic electron-hydrogen, electron-deuterium (including Jlab), photo-production on hydrogen and photo-production on deuterium in the fits (all fits include the c-cbar photon-gluon fusion contribution at high energy - this cross section is zero in leading order) • Compare to photo-production and Jlab electro-production Data in Resonance region (data not included in fit yet) • Compare to neutrino CCCFR-Fe, CDHS-Fe, CHORUS-Pb differential cross section (without c-cbar boson-fusion in yet - to be added next since it is high energy data) assume V=A • We aave a model for Axial low Q2 PDFs, but need to compare to low energy neutrino data to get exact parameters - next.

2. For applications to Neutrino Oscillations at Low Energy (down to Q2=0) the best approach is to use a LO PDF analysis (including a more sophisticated target mass analysis) and include the missing QCD higher order terms in the form of Empirical Higher Twist Corrections. Reason: For Q2>1 both Current Algebra exact sum rules (e.g. Adler sum rule) and QCD sum rules (e.g. momentum sum rule) are satisfied. This is why duality works in the resonance region (so use NNLO QCD analysis) For Q2<1, QCD corrections diverge, and all QCD sum rules (e.g momentum sum rule) break down, and duality breaks down in the resonance region. In contrast, Current Algebra Sum rules e,g, Adle sum rule which is related to the Number of (U minus D) Valence quarks) are valid.

3. Modified LO = Pseudo NNLO approach for low energiesApplications to Jlab and Neutrino Oscillations Original approach (NNLO QCD+TM) was to explain the non-perturbative QCD effects at low Q2, but now we reverse the approach: Use LO PDFs and “effective target mass and final state masses” to account for initial target mass, final target mass, and missing higher orders q mf=M* (final state interaction) P=M Resonance, higher twist, and TM x w= Q2+mf2+O(mf2-mi2) +A Xbj= Q2 /2 Mn Mn (1+(1+Q2/n2) )1/2 +B A : initial binding/target mass effect plus higher order terms B: final state mass mf2 , Dm2, and photo- production limit (Q2 =0) K factor to PDF, Q2/[Q2+C]

4. xIs the correct variable which is Invariant in any frame : q3 and P in opposite directions Initial quark mass m I and final mass,mF=m *bound in a proton of mass M Summary: INCLUDE quark initial Pt) Get x scaling (not x=Q2/2Mn )for a general parton Model q=q3,q0 PF= PF0,PF3,mF=m* PF= PI0,PI3,mI P= P0 + P3,M Special cases: (1) Bjorken x, xBJ=Q2/2Mn, x, -> x For m F2 =m I 2=0 and Highn2, (2) Numeratorm F2 : Slow Rescalingxas in charm production (3) Denominator: Target mass term x =Nachtman Variable x =Light Cone Variable x =Georgi Politzer Target Mass var. (all the same x ) • Most General Case: (Derivation in Appendix) • x ‘w= [Q’2 +B] / [ Mn (1+(1+Q2/n2) ) 1/2+A] (with A=0, B=0) • where 2Q’2 =[Q2+ m F2 -m I 2] + { (Q2+m F2 -m I 2 ) 2 + 4Q2 (m I 2+P2t) }1/2 • Bodek-Yang: Add B and Ato account for effects of additional m2 • from NLO and NNLO (up to infinite order) QCD effects. For case xw with P2t =0 • see R. Barbieri et al Phys. Lett. 64B, 1717 (1976) and Nucl. Phys. B117, 50 (1976)

5. http://web.pas.rochester.edu/~icpark/MINERvA/

6. Correct for Nuclear Effects measured in e/muon expt. Comparison of Fe/D F2 data In resonance region (JLAB) Versus DIS SLAC/NMC data In TM (C. Keppel 2002).

13. Note: All data has been radiatively corrected. Neutrino Experiments MUST apply radiative corrections - Tables can be provided (no consistent PDF type analysis can be done without radiative corrections - e.g. Bardin) ------------------------------------------------------ Work in Progress: Now working on the axial structure functions and next plan to work on resonance fits. Next: JUPITER at Jlab (Bodek,Keppel) will provided electron-Carbon (also e-H and e-D and other nuclei such as e-Fe) in resonance region. Next: MINERvA at FNAL (McFarland, Morfin) will provide Neutrino-Carbon data at low energies.

14. Apply nuclear corrections using e/m scattering data. (Next slide) Calculate F2 and xF3 from the modified PDFs with w Use R=Rworld fit to get 2xF1 from F2 Implement charm mass effect through w slow rescaling algorithm, for F2 2xF1, and XF3 Comparison of LO+HT to neutrino data on Iron [CCFR] (not used in this fit V=A) Last year’s fits Construction wPDFs GRV98 modified ---- GRV98 (x,Q2) unmodified Left neutrino, Right antineutrino The modified GRV98 LO PDFs with a new scaling variable, w describe CCFR diff. Cross sect. (En=30–300 GeV) well (except at the lowest x) En= 55 GeV is shown

15. Compare Last Year to this Year (this year also use R1998 instead of R world) V=A, lowest x no c-cbar contribution wPDFs GRV98 modified Very low X needs work ---- GRV98 (x,Q2) unmodified (maybe PDF f(x) needed) Left neutrino, Right antineutrino Last year

19. End CCFR neutrino and antineutrino Begin CDHS Neutrino Note, further studies needed. Are the data reliable at low x (rad corrections, resolution, flux). If R is smaller than R 1998 (nuclear shadowing) (waiting for Jlab data). What about c-cbar contribution (currently being calculated). Or make sure that differential cross section code has no bugs. With that caveat we show some data versus model. We we will be better agreement between data and model if R is smaller than R 1998, and if we include c-cbar NLO terms. However, Is the axial F2 larger? Whatabout shadowing for axial versus vector especially for iron and lead. All under investigation

26. Extra comparisons

32. End CCFR neutrino and antineutrino Begin CDHS Neutrino