Issues in the Quasi-free Delta Production Region Ryoichi Seki (CSUN/Caltech) in collaboration with Hiroki Nakamura (Waseda) RCCN International Workshop; Kahiwa, Japan; December 11, 2004

Q = ( ,q)  1. Nucleonic reactions + Ν  ℓ + Δ(1232) ℓ + Ν* a) (e,e’) SLAC J-Lab b) (,ℓ) Axial transition form factors 2. Nuclear reactions + A  ℓ + A* ℓ + A* +  …………. a) Spectral function b) Final state interaction c) Exchange current e) Other approaches Structure/ Response Function ( ,q )

Dufner-Tsai (1968), Fogli-Nardulli (1979)Paschos-Yu-Sakuda (2004)Dufner-Tsai (1968), Fogli-Nardulli (1979)Paschos-Yu-Sakuda (2004) Dufner-Tsai(1968), Fogli- Nardulli (1979)(Res2) Paschos-Yu-Sakuda (2004) (Res1)

1.Nucleonic reactions a) (e,e’) SLAC Target: p, d and inclusive  p and n responses A. Bodek et al., Phys. Rev. D20, 1471 (1979) A. Bodek and J. L. Richie, Phys. Rev. D23, 1070 (1981)

b) p (e,e’) J-Lab

Theoretical models 1) Unitary isobar model, MAID and Jlab/Yeveran D. Drechsel, S. S. Kamalov, and L.Tiator, Nucl. Phys. A645,145(‘99) I. G. Aznauryan, Phys. Rev. C68, (‘03); C67, (‘03) 2) Multi-channel K-matrix model, SAID R. A. Arndt et al., Phys. Rev. C52, 2120 (1995) Int. J. Mod. Phys. A18, 449 (2003) 3) Dynamical model, SL (Sato-Lee) and DMT (Dubna-Mainz-Taiwan) T. Sato and T.-S. H. Lee, Phys. Rev. C54, 2660 (1996) Phys. Rev. C63, (2001) S. S. Kamalov and S. N. Young, Phys. Rev. Lett. 83, 4494 (‘99) + D. Drechsel, O. Hanstein, L. Tiator, Phys. Rev. C64, (’02) * A recent review: V. D. Burkert and T.-S. H. Lee, nucl-ex/ (July’04) Phenomenological model H2 model, C. Keppel (1995)

a) n (e,e’) J-Lab 1) D (e,e’p) for Ee = GeV and Q 2 = 1.2 – 5 GeV 2 A. V. Klimenko, PhD thesis (Old Dominion Univ., 2004) 2) D (e,e’p) BONUS (2005)

Inclusive Neutron Resonance Electroproduction Again, a large uncertainty in neutron extraction….. …must consider deuteron wave function, Fermi smearing, off-shell effects, neutron structure function shape,... Courtesy of Thia Keppel

So, what will BONUS measure?… Inclusive Neutron Measurements in the JLab (large x, low Q) Kinematic Regime Elastic form factors Resonance structure –Transition form factors –Quark-hadron duality Data over a range of Q 2, x – Structure function moments –Large x nucleon structure Courtesy of Thia Keppel

BONUS RTPC Design 4 cm He 4mm x 10 cm 7.5 atm , z from pads r from time dE/dx from charge along track (particle ID) neonDME Courtesy of Thia Keppel

Courtesy of Thia Keppel Transition Form Factors from Inclusive Data – Projected Results Neutron n   Statistical uncertainties only Model uncertainty dominant, comparable to proton extractions

b) Nucleonic (,ℓ) *Scaling: A. Bodek, I. Park, and U. ki Yang, hep/ph/ (16 Nov 2004) * D. Rein and L. Sehgal, Ann. Phys. 133, 79 (1981) D. Rein, Z. Phys. C 35, 43 (1987)  BNL data (1990) and Int. Workshop on N* Physics (1997) * Alverez-Russo, Singh,and Vincent Vacas, Phys. Rev. C57, 2693 (‘98) E. Paschos, J.-Y. Yu, and M. Sakuda, Phys. Rev. D69, (‘04) * T. Sato, D. Uno, and T.-S. H. Lee, Phys. Rev. C67, (2003) p ( ,  ¯  ) p Data: BNL(1990) Data:ANL(1979)

2. Nuclear reactions a) Spectral function : * O. Benhar et al. (H. Nakamura’s talk in this workshop) Many-body nuclear matter calculation (correlated nuclear-state basis) + Shell model, in local density approx. * C. Ciofi degli Atti and S. Simula, Phys. Rev. C53, 1689 (‘96) b) Final state interaction : * Nucleon: Eikonal approx. of Lorentzian with optical potential * Pion: L. L. Salcedo, E. Oset et al., Nucl. Phys. A484, 557 (“88) (Note: Importance of the real part of the potential for low-E pions)

 nuclear effects in 16 O Probability of  0 – 16 O interaction in NEUT  + – 16 O cross section (NEUT vs. Data)

c) Exchange current 1) Current conservation + Off-energy/mass shell contributions * Electromagnetic  meson exchange models * Axial  Δ(1232) and pions in intermediate states modified propagators with their self-energy 2) Warning: % quenching of gA (GT) in beta decays Kirchbach and D. Riska, Nucl. Phys. A578, 511 (‘94) M. Hjorth-Jensen et al. Nucl. Phys. A563, 525 (1993) D. O. Riska, Phys. Rep. 181, 208 (1989) Effects on the form factors?

d) Other approaches 1) Valencia/Granada many-body calculations : A. Gil, J. Nieves, and E. Oset, Nucl. Phys. A627, 543 (1997) Many-body approach to the inclusive (e,e’) reaction … J. Nieves, J. E. Amaro, and M. Valverde, nucl-th/ (3 Aug 2004) Nuclear many-body theory of electroweak interactions … 2) Donnelly/I. Sick superscaling (RFG + phenomenological modifying function) J. E. Amaro et al., nucl-th/ (30 Set 2004) Using electron scattering superscaling to predict charge- changing neutrino cross sections in nuclei C. Maieron, T. W. Donnelly, I. Sick, Phys. Rev. C65, (2002) Extended superscaling of electron scattering from nuclei

16O(e, e’) Effects of form factor (Res1:Paschos et al.) Data M. Anghinolfi et al. Nucl. Phys. A602, 405 (1996)

Conclusion: Assessment of the present status of the Delta region 1) Quality: Presently available calculations and codes include all important physics except for that associated with the current (partial) conservation. 2) Predictability: More tuning of the calculations is desirable to the electron-scattering precision data, currently available or becoming available. 3) Experiment: More precise neutrino-nucleon data are critically needed 4) Codes: It is perhaps the best time for creating codes of higher quality than the presently available, by putting all together.