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Nuclear parton distribution functions and their effects on sin 2  W anomaly

Nuclear parton distribution functions and their effects on sin 2  W anomaly. Shunzo Kumano, Saga University kumanos@cc.saga-u.ac.jp, http://hs.phys.saga-u.ac.jp 12th International Workshops on Deep Inelastic Scattering (DIS04) Strbske Pleso, Slovakia, April 14-18, 2004.

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Nuclear parton distribution functions and their effects on sin 2  W anomaly

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  1. Nuclear parton distribution functions and their effects on sin2W anomaly Shunzo Kumano, Saga University kumanos@cc.saga-u.ac.jp, http://hs.phys.saga-u.ac.jp 12th International Workshops on Deep Inelastic Scattering (DIS04) Strbske Pleso, Slovakia, April 14-18, 2004 Refs. npdf:(1) M. Hirai, SK, M. Miyama, Phys. Rev. D64 (2001) 034003 (2) M. Hirai, SK, T.-H. Nagai, hep-ph/0404093 sin2W : (1) SK, Phys. Rev. D64 (2001) 034003 (2) research in progress (T.-H. Nagai) April 15, 2004

  2. Contents  Purposes  Determination of Nuclear Parton Distribution Functions (NPDFs) (1) used data, 2 analysis method (2) results  Nuclear modification effects on NuTeV sin2W (1) Paschos-Wolfenstein (PW) relation (2) valence-quark modification effects on the PW relation and sin2W

  3. Why nuclear parton distribution functions? Basic interest to understand nuclear structure in the high-energy region, Determination of sin2W perturbative & non-perturbative QCD sin2W in neutrino scattering (NuTeV) (2)Practical purpose to describe hadron cross sections precisely heavy-ion reactions:quark-gluon plasma signature long-baseline neutrino experiments: nuclear effects in n + 16O

  4. Parametrization of Nuclear Parton Distribution Functions Code for the obtained NPDFs could be obtained from http://hs.phys.saga-u.ac.jp/nuclp.html

  5. 1.2 EMC NMC 1.1 E139 E665 1 0.9 0.8 0.7 0.001 0.01 0.1 1 Nuclear modification Nuclear modification of F2A /F2D is well known in electron/muon scattering. Fermi motion original EMC finding shadowing x sea quark valence quark

  6. Experimental data (1) F2A / F2D NMC:He, Li, C, Ca SLAC:He, Be, C, Al, Ca, Fe, Ag, Au EMC: C, Ca, Cu, Sn E665: C, Ca, Xe, Pb BCDMS: N, Fe HERMES: N, Kr (2) F2A / F2A’ NMC: Be / C, Al / C, Ca / C, Fe / C, Sn / C, Pb / C, C / Li, Ca / Li (3) DYA / A’ E772: C / D, Ca / D, Fe / D, W / D E866: Fe / Be, W / Be

  7. Analysis conditions · parton distributions in the nucleon MRST 01 ( L = 220 MeV ) QCD · Q point at which the parametrized PDFs are defined : Q = 1 Ge V 2 2 2 · used experimental data : Q 2 ³ 1 Ge V 2 · total number of data : 951 606 ( F / F ) + 293 ( F / F ) + 52 ( Drell Yan ) A D A A ' – 2 2 2 2 · subroutine for the c analysis : CERN Minuit 2 – 2 ( R – R ) data calc S c = 2 i i ( s ) 2 data i i F A F A s pA R = , , , = ( ) + ( ) 2 2 DY s data s sys 2 s stat 2 s F F i i i D A ' pA ' 2 2 DY

  8. Comparison with F2Ca/F2D & DYpCa/ DYpD data (Rexp-Rtheo)/Rtheo at the same Q2 points

  9. Comparison with R=F2A/F2A’ data:(Rexp-Rtheo)/Rtheo are shown

  10. Comparison with R=DYpA/ DYpA’(Rexp-Rtheo)/Rtheo are shown

  11. Nuclear corrections of PDFs with uncertainties valence-quark antiquark gluon

  12. Nuclear Effects on sin2W Nuclear modification difference between uvA and dvA

  13. sin2W anomaly Others:sin2W = 1  mW2/mZ2 = 0.2227 0.0004 NuTeV:sin2W= 0.2277 0.0013 (stat) 0.0009 (syst) Paschos-Wolfenstein relation

  14. not so obvious: SK,PRD 66 (2002) 111301, research in progress Expand in v, n, s, c << 1 preliminary

  15. NuTeV kinematics G. P. Zeller et al. Phys. Rev. D65 (2002) 111103.  0.01  large error (preliminary!) at Q2=20 GeV2

  16. Summary (1) 2 analysis for the nuclear PDFs, and their uncertainties.  Valence quark: well determined except for the small-x region.  Antiquark: determined at small x, large uncertainties at medium and large x.  Gluon: large uncertainties in the whole-x region. (2) We provide nuclear PDFs for general users. http://hs.phys.saga-u.ac.jp/nuclp.html. (3) Effects on NuTeV sin2W progress (esp. error estimate) possibly (sin2W ) = 0.00X0.00X with a large error

  17. Supplements

  18. NuMI • test of shadowing models F3(valence) shadowing vs. F2 (sea) shadowing • accurate determination of nuclear PDFs Fe/D ratios F2 F3 S. A. Kulagin J. G. Morfin at NuFact02/NuInt02

  19. “surface” “volume” R= r0A1/3 A dependence Ref. I. Sick and D. Day, Phys. Lett. B 274 (1992)

  20. F2 large x small x Drell-Yan projectile target

  21. Error estimation Hessian method 2() is expanded around its minimum  0 ( =parameter) where the Hessian matrix is defined by In the 2 analysis, 1 standard error is The error of a distribution F(x) is given by

  22. 2 values Small nuclei are not well explained. Medium and large nuclei are reproduced. Drell-Yan data are reproduced.

  23. F2A/F2D data

  24. F2A/F2A’ data

  25. Q2 dependence

  26. Global analysis for F2 and Drell-Yan data for v(x)

  27. CTEQ, hep-ph/0312322, 0312323 • of the order of the NuTeV deviation • could not be “anomalous”

  28. Attempt to describe DIS & resonance region Empirical formula GRV94 Bodek-Yang NP B 112 (2002) 70 We need similar analysis for the NPDFs.

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