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Modeling Neutrino Structure Functions at low Q 2

Modeling Neutrino Structure Functions at low Q 2. Arie Bodek University of Rochester Un-ki Yang University of Manchester. NuInt 2009, Barcelona, Spain, May 18 – 22, 2009. A Model for all Q 2 region?.

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Modeling Neutrino Structure Functions at low Q 2

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  1. Modeling Neutrino Structure Functions at low Q2 ArieBodek University of Rochester Un-ki Yang University of Manchester NuInt 2009, Barcelona, Spain, May 18 – 22, 2009 Un-ki Yang, Manchester

  2. A Model for all Q2 region? • The high Q2 region of lepton-nucleon scattering is well understood in terms of quark-parton model by a series of e/m/n DIS experiments. • But the low Q2 region is relatively poorly understood in neutrino scattering: very important for neutrino oscillation experiments. Many interesting issues… • PDFs at high x? • Non-perturbative QCD? target mass, higher twist effects? • Duality works for resonance region? • Axial vector contribution? • Different nuclear effects (e/mvsn )? • Build up a model for all Q2 region Un-ki Yang, Manchester

  3. Challenges at Low Q2 • A model to describe all Q2 region for e/m/nscatterings • [ DIS, resonance, even photo-production(Q2=0) ] • Resonance region is overlapped with a DIS region • Hard to extrapolate DIS contribution to low Q2 region from high Q2 data, because of non-pQCD effects • Describe DIS+resonance together using quark-parton model • Resonance scattering in terms of quark-parton model? • Duality works, many studies by JLab • Higher twist effects, PDFs at high x? SLAC, JLab data F2 GRV Un-ki Yang, Manchester

  4. Effective LO Approach mf=M* (final state) q P=M • Quark-Parton model: • NLO pQCD+TM+HT, and NNLO pQCD+TM: good for DIS and resonance • A HT extracted from the NLO analysis:~ NNLO pQCDterm: indep. of e/m/n • Effective LO approach: Use a LO PDFs with a new scaling variable to absorb TM, HT, higher orders • A reference for (,d): study nuclear effect Un-ki Yang, Manchester

  5. Fit withxw DIS F2(d) • Use GRV98 LO • xw= [Q2+B] / [ Mn (1+(1+Q2/n2)1/2 ) +A] • Different K factors for valence and sea • Ksea = Q2/[Q2+Csea] Kval = [1- GD2 (Q2) ] *[Q2+C2V] / [Q2+C1V], GD2 (Q2) = 1/ [ 1+Q2 / 0.71 ] 4 • Freeze the evolution at Q2 = 0.8 • Very good fits are obtained using SLAC/NMC/BCDMS p, dwith low x HERA/NMC F2 A=0.418, B=0.222, Csea = 0.381 C1V = 0.604, C2V= 0.485 2/DOF= 1268 / 1200 Un-ki Yang, Manchester

  6. DIS F2 at low x Un-ki Yang, Manchester

  7. Resonance and photo-production data F2(p) resonance Photo-production (p) s(g-proton) = 4pa/Q2 * F2(w, Q2) where F2(w, Q2) = Q2 /(Q2 +C) * F2(w ) Not included in the fit Un-ki Yang, Manchester

  8. 2xF1 data Jlab 2xF1 • All DISe/F2 data are well described • Photo-production data (Q2=0) also work: thus included in the latest fit • 2xF1 data (Jlab/SLAC) also work: using F2(w)+R1998

  9. Comparison withneutrinodata CCFR diff cross at En= 55 GeV • Assume vector = axial • Apply nuclear corrections using e/ scattering data • Underestimated at low x=0.015 • Totalanti-neutrino cross section lower by 5%? : red, : blue,(w)---- (x)

  10. NLO Correction to xF3? • Scaling variable, wabsorbs higher order effect on F2 , but not xF3; F2 data used in the fitting • Check double ratio => not 1 but indep. of Q2 NLO ratio: using VFS Un-ki Yang, Manchester

  11. Effect of xF3 NLO correction • Parameterized xF3 correction as a function of x • Neutrino cross section down by 1% • Anti-neutrino cross section up by 3% Un-ki Yang, Manchester

  12. Axial-vector contribution • In our neutrino cross section model • assumed Kaxial = Kvector • Toward axial-vector contribution • Kaxial= 1 • Extract Kaxial using existent neutrino data (underway) Un-ki Yang, Manchester

  13. Axial-vector contribution CCFR diff. cross at En= 55 GeV Kaxial = Q2/(Q2+C) Kaxial = 1 Un-ki Yang, Manchester

  14. Axial-vector contribution CCFR diff. cross at En= 35 GeV Kaxial = Q2/(Q2+C) Kaxial = 1 Un-ki Yang, Manchester

  15. Summary and Discussions • Effective LO model with wdescribes all DIS and resonance data as well as photo-production data: • Provide a goodreference for neutrino cross section, (,d) • Possible studies for axial vector contribution at Q2<1 and diff. nuclear effect • High energy neutrino data at low Q2 is in favor of additional axial vector contribution • Things to do • Need to tune axial vector contribution using existent neutrino data and possibly with coming MINERnA • Different nuclear effects (evsn, F2 vs xF3): Jlab and MINERnA data are very crucial Un-ki Yang, Manchester

  16. Comparison with CDHSW data En= 23 GeV

  17. F2, R comparison with NNLO pQCD+TM F2 R Eur. Phys. C13, 241 (2000)Bodek & Yang Un-ki Yang, University of Manchester

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