Nuclear Effects from NuTeV Results

1. n / n - Iron Nuclear Effects from NuTeV Results Jorge G. Morfín Fermilab

2. Nuclear Effects in Neutrino Interactions • Target nucleon in motion - spectral functions (Benhar et al.) • Certain reactions prohibited - Pauli suppression • Quasi-elastic form factors are modified within the nuclear environment. (Butkevich/Kulagin, Tsushima et al.) • Produced topologies are modified by final-state interactions modifying topologies and reducing detected energy. • Convolution of ds(np) x formation zone uncertainties x p-absorption uncertainties yield larger oscillation-parameter systematics • Cross sections and structure functions are modified and parton distribution functions within a nucleus are different than in an isolated nucleon. Observations from an on-going CTEQ analysis.

3. 1.2 EMC NMC 1.1 E139 E665 1 0.9 0.8 0.7 1 0.001 0.01 0.1 Experimental Studies of Nuclear Effects with Neutrinos:essentially NON-EXISTENT Fermi motion shadowing EMC effect x sea quark valence quark • F2 / nucleon changes as a function of A. Measured in /e - A,not in  - A • Good reason to consider nuclear effects are DIFFERENT in  - A. • Presence of axial-vector current. • Different nuclear effects for valance and sea --> different shadowing for xF3 compared to F2.

4. Kulagin-Petti Model of Nuclear Effectshep-ph/0412425 • Global Approach -aiming to obtain quantitative calculations covering the complete range of x and Q2 available withthoroughphysics basis for fit to data. • Different effects on structure functions (SF) are taken into account: • Fermi Motion and Binding in nuclear structure functions is calculated from the convolution of nuclear spectral function and (bound) nucleon SFs: • Since bound nucleons are off-mass shell there appears dependence on the nucleon virtuality k2 = (M + e) 2 - k2 where we have introduced an off-shell structure function df2(x) • Leptons can scatter off mesons which mediate interactions among bound nucleons yielding a nuclear pion correction

5. Kulagin-Petti compared to e/m+Fe data F2 (e/m+Fe) / F2 (e/m+D) Charged Lepton

6. F2 (m+Fe) / F2 (m+N) compared toF2 (n+Fe) / F2 (n+N) Charged Lepton Neutrino

7. F2 (n+A) / F2 (n+N) Fe Pb

8. Kulagin-Petti: n-Fe Nuclear Effects F2 xF3

9. The Impact of new neutrino DIS and Drell-Yan data on large-x parton distributions Joey Huston - MSU, Cynthia Keppel - Hampton, Steve Kuhlmann - ANL, JGM - Fermilab, Fred Olness - SMU, Jeff Owens - Florida State, Jon Pumplin and Dan Stump - MSU Published in Phys.Rev.D75:054030,2007. e-Print: hep-ph/0702159

10. How well do we know quarks at high-x?CTEQ study of high-x PDFs • Ratio of CTEQ5M (solid) and MRST2001 (dotted) to CTEQ6 for the u and d quarks at Q2 = 10 GeV2. The shaded green envelopes demonstrate the range of possible distributions from the CTEQ6 error analysis. • In our study of high-x PDFs, we reached some interesting conclusions regarding neutrino induced nuclear effects.

11. CTEQ High-x Studyreference fit • Form reference fit mainly nucleon (as opposed to nuclear) scattering results: • BCDMS results for F2p and F2d • NMC results for F2p and F2d/F2p • H1 and ZEUS results for F2p • CDF and DØ result for inclusive jet production • CDF results for the W lepton asymmetry • E-866 results for the ratio of lepton pair cross sections for pd and pp interactions • E-605 results for dimuon production in pN interactions. • Correct for deuteron nuclear effects

12. NuTeV(Fe) and CHORUS (Pb) n scattering (unshifted) results compared to reference fitno nuclear corrections

13. NuTeV s(Fe) & CHORUS s(Pb) n scattering(un-shifted) results compared to reference fitKulagin-Petti nuclear corrections (no K-P errors yet available)

14. NuTeV s(Fe) & CHORUS s(Pb) n scattering (shifted) results compared to reference fitKulagin-Petti nuclear corrections

15. Nuclear PDFs from neutrino deep inelastic scattering I. Schienbein (SMU & LPSC-Grenoble, J-Y. Yu (SMU) C. Keppel (Hampton & JeffersonLab) J.G.M. (Fermilab), F. Olness (SMU), J.F. Olness (Florida State U) e-Print: arXiv:0710.4897 [hep-ph]

16. Formalism • PDF Parameterized at Q0 = 1.3 GeV as • PDFs for a nucleus are constructed as: • Resulting in nuclear structure functions: • The differential cross sections for CC scattering off a nucleus::

17. Same Reference Fit as Earlier Analysis • Form reference fit mainly nucleon (as opposed to nuclear) scattering results: • BCDMS results for F2p and F2d • NMC results for F2p and F2d/F2p • H1 and ZEUS results for F2p • CDF and DØ result for inclusive jet production • CDF results for the W lepton asymmetry • E-866 results for the ratio of lepton pair cross sections for pd and pp interactions • E-605 results for dimuon production in pN interactions. • Correct for deuteron nuclear effects

18. Sample NuTeV Data vs Theory Use ACOT - heavy quark mass Effects - in NLO QCD. Q > 2.0 GeV, W > 3.5 GeV Double-differential cross sections

19. Iron PDFs

20. F2 Structure Function Ratios: n-Iron

21. F2 Structure Function Ratios: n-Iron

22. F2 Structure Function Ratios: n-Iron

23. F2 Structure Function Ratios: n-Iron

24. xF3 Structure Function Ratios: n&n - Fe n Preliminary / Unpublished n Preliminary / Unpublished

25. Conclusions • NuTeV n-Fe scattering seems to see little or no evidence for shadowing • Differences in nuclear effects between n and n, Fe and Pb are small in the region 0.1 < x < 0.6 • The Kulagin-Petti corrections for Fe over-correct with respect to the reference fit when applied to the NuTeV Fe results. • Except at very high x, our correction factors differ in both shape and magnitude from charged lepton and K-P correction factors