Neutron structure functions from inclusive DIS data

1. Neutron structure functions from inclusive DIS data Neutron structure function Consistent comparison of data, calculations Systematics of the extraction procedure JA, F.Coester, R.J.Holt, T.S.-H.Lee, J.Phys.G36, 025005 (2009) Evaluation of model dependence JA, W. Melnitchouk, J. Rubin – work in progress John Arrington, Argonne National Lab Workshop on Nucleon Structure at Large Bjorken-x, Oct 13-15, 2010

2. E140 E139 Neutron Structure Function • Attempts to extract F2n(x) from deuteron and proton data yield large range of results, depending on the model of the deuteron • “Scaled EMC effect” approaches not realistic for high-x, neglect difference in F2p and F2n, but there is still a wide range if these are excluded • Extraction of F2nappears to be very sensitive to the deuteron model, limited by our understanding of nuclear structure for A=2

3. Recent F2n Extraction • Similar to previous extractions – emphasis onimproved treatment of the data, evaluation of systematics • Fit to F2p (from M.E.Christy) • Interpolate Rdp=F2d/F2p data to Q02=12 GeV2 • Fit Q2 dependence at fixed x using full Q2 range (3-230 GeV2) • Limited data included to 6<Q2<30 GeV2, require W2>3.5 GeV2 • Average Q2 for each bin always within factor of two of Q02 • Interpolation to fixed Q2 typically 0.5% • Deuteron evaluated in a light cone impulse approximation (neglect binding), with no “DIS” assumptions (e.g. doesn’t assume scaling, doesn’t neglect k┴), with a two-body effective N-N potential (CD-Bonn) • Parameterize Rnp = F2n/F2p, calculate Rdp and compare to data, get best fit using MINUIT • Functional form chosen with significant flexibility at large x

4. Neutron extraction • Global fit to F2n/F2p, yields good F2d/F2p [solid curves] • Take Sp, Sn as ratio of bound to free proton/neutron structure functions • F2d = F2pSp + F2nSn F2n = [ F2d–F2pSp ] / Sn or Rnp = [ Rdp – Sp ] / Sn convert D/p points & uncertainties to n/p Plot shows F2d per nucleon

5. Uncertainties related to the extraction • Overall normalization uncertainty in D/p ratio • Straightforward to propagate: Dominant effect at all x values • High-x behavior of the structure function • Modify large x behavior to the point where they start to be inconsistent with SLAC measurements • Uncertainty in Sn(x) • Increased falloff in F2n at large x yields increased Sn • Need to reevaluate Sn when varying F2n prior to making comparison to F2d/F2p data

6. Neutron Structure Function • Ratio of n/p falls with x, no sign of plateau • Agrees with Whitlow (on-shell) result • Lower thanThomas/Melnitchouk, EMC extrapolation • Results depend on nuclear model, deuteron disribution, etc… • Part II of talk • Whitlow extraction of D/p ratios has a large x-Q2 correlation; usually compared to deuteron calculations at fixed Q2 • We interpolate data to fixed Q2 • CTEQ6X calculates F2 at exact kinematics of each point

7. Q2-dependence Take Sp, Sn as ratio of bound to free proton/neutron structure functions • F2d = F2pSp + F2nSn F2n = [ F2d-F2pSp ] / Sn or Rnp = [Rdp – Sp ] / Sn The smearing functions have a large Q2 dependence at large x values Solid line – Q2 = 12 GeV2 Red points – Q2 matches Q2 of D/p ratio At largest x, Sp changes by ~0.12 between 12 and 24 GeV2 • Expect Rnp to go down by about 0.12 if account for this in Thomas and Melnitchouk extraction • Much smaller effect for Whitlow analysis, which took Q2=20 GeV2

8. First conclusions: F2n extraction • Suggests that a large part of the difference is related to the treatment of the Q2 dependence of the data • Extractions based on calculated deuteron structure are in reasonably good agreement • Need direct comparison using identical data, extraction procedure, deuteron wavefunction • Sensitivity to nuclear model is less than it appeared • Newer CTEQ6.1, CTEQ6x analyses (model similar to Melnitchouk and Thomas) yield consistent results(A.Accardi, et al., arXiv:0911.2254)

9. Large uncertainties or small uncertainties? • CTEQ6X: Huge variation in d/u at large x between different extractions A. Accardi, et al., arXiv:0911.2254 • CTEQ6X: Global behavior is extremely well constrained even at large x A. Accardi, et al., arXiv:0911.2254

10. Detailed investigations of model-dependence N3L0 Av18 CDBonn WJC2 WJC1 • Use same data, same extraction procedure, but vary N-N potential (top) and nuclear model (bottom) • Q02=16 GeV2: Closer to high-x data with large and poorly known Q2 dependence • Calculate Sp, Sn, using same input F2p,F2n and same N-N potential (CD-Bonn) REF: Arrington, et al., CDbonn, MST offshell Melnitchouk&Thomas WBA [CTEQ6X] Kulagin&Petti Arrington, et al Rinat, et al Solid: On-shell Dashed: Off-shell [MST or KP]

11. Detailed investigations of model-dependence N3L0 Av18 CDBonn WJC2 WJC1 • Use same data, same extraction procedure, but vary N-N potential (top) and nuclear model (bottom) • Q02=16 GeV2: Closer to high-x data with large and poorly known Q2 dependence • Calculate Sp, Sn, using same input F2p,F2n and same N-N potential (CD-Bonn) REF: Arrington, et al., CDbonn, MST offshell Melnitchouk&Thomas WBA [CTEQ6X] Kulagin&Petti Arrington, et al Rinat, et al Solid: On-shell Dashed: Off-shell [MST or KP]

12. Detailed investigations of model-dependence Comparison of different models, potentials using consistent D/p and F2p data as input, same procedure

13. Conclusions • Relatively small dependence on different deuteron calculations, off-shell prescriptions, N-N potentials • F2n/F2p relatively well known, barring significant extra nuclear effects (e.g. large exotic “EMC effect” in 2H) • Significant (but not ‘precise’) knowledge of F2n at large x • Includes SLAC D/p ratios, but not JLab or non-DIS input • Clean extractions of F2n/F2p at large x [3H/3He, BONUS, PVDIS, neutrino] still very important • Improved (needed) precision in extraction of F2n • Sensitive to additional modification of deuteron

14. Fin…

15. “Smearing ratios” for the calculations Melnitchouk&Thomas WBA [CTEQ6X] Kulagin&Petti Arrington, et al Rinat, et al Solid: On-shell Dashed: Off-shell [MST or KP]