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

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?

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

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/ Form Factor model for  (1232) excitation O. Lalakulich, E. A. Paschos and G. Piranishvili, Phys. Rev. D 74 (2006) F2 underestimated in the FKR model Let’s introduce another Vector FF

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

Significant correction for small Q2

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

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.

SPP in NC N scattering W< 2 GeV

SPP in CC N scattering W< 2 GeV

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: ,2005

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 Only resonance contribution

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