1. On description of resonance region in the FKR model Krzysztof M. Graczyk, Jan T. Sobczyk Institute of Theoretical Physics University of Wrocław Poland

2. Motivations  Modification of the FKR model  Rein-Sehgal model  MC generators Model which will better fit to experimental data in  (1232) region Model which will better fit to experimental data in  (1232) region I.Another idea of introducing form factors (effective)  We still keep only two form factors (vector and axial) II.Lepton mass in Charged Current N scattering III.7 new resonances How modification I affects cross section for Single Pion Production (SPP) in Neutral Current (NC) N scattering?

3. FKR and RS models Feynman, Kislinger, and Ravndal 71 Feynman, Kislinger, and Ravndal 71 Electroproduction: Ravndal 71Electroproduction: Ravndal 71 Neutrinoproduction: Ravndal 72, 73, Rein and Sehgal 81, Rein 87Neutrinoproduction: Ravndal 72, 73, Rein and Sehgal 81, Rein 87 Baryon wave function  Sym[SU(3)xSU(2)xO(3)] representationBaryon wave function  Sym[SU(3)xSU(2)xO(3)] representation Elastic Limit of the description ELASTIC SCATTERING Form Factors of the FKR/RS model are expressed by elastic nucleon form factors!!! Two Form Factors FKR MODEL This is not the only way of computing form factors

4. Electroproduction Neutrinoproduction F. Ravndal, Phys. Rev. D 4, 1466 (1971)F. Ravndal, Nuovo Cimento, 18A 385 (1973) M. Osipenko et al., The proton structure function F2 in the resonance regio, arXiv:hep-ex/0301033 Form Factor model for  (1232) excitation O. Lalakulich, E. A. Paschos and G. Piranishvili, Phys. Rev. D 74 (2006) 014009 F2 underestimated in the FKR model Let’s introduce another Vector FF

5. FKR Form Factor Evaluation Form Factor model for  (1232) excitation New effective vector form factor

6. Significant correction for small Q2

7. Axial part New effective axial form factor O. Lalakulich, E. A. Paschos, Phys.Rev.D71:074003,2005  interaction

8. SPP in NC N scattering We have different proportion of the vector and axial contribution!!! almost 2 times more D. Rein, L. Sehgal Annals Phys.133:79,1981.

9. SPP in NC N scattering W< 2 GeV

10. SPP in CC N scattering W< 2 GeV

11. The matrix elements of the J t and J z components of the hadronic current were computed separately Lepton mass Effect of the lepton mass We introduced lepton mass into the model. It was done in a different way than V. Naumov et al.. Nucl.Phys.Proc.Suppl.139:158-161,2005

12. Some difficulties !!! to get a space part of the resonances wave functions for third and fourth level of the oscillator, Hey et al. Phys. Rept. 96 (1983) 71. Does not contribute F2(ep) structure functions 18 25 Only resonance contribution

13. Summary  We proposed three improvements: 1. New form factors – the most significant, in particular for the 1 production in NC reactions 2. Lepton mass – relevant for small Q2 3. Heavier resonances – not significant