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Generalities of the reaction approaches

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1 Generalities of the reaction approaches
Modeling of resonant / non resonant contributions is needed and should be focused on extraction of gvNN* electrocouplings from measured observables in Np and Npp electroproduction . Breit Wigner ansatz represents a reasonable parameterization for resonant amplitudes. It should account as much as possible for constraints imposed by unitarity and analyticity, employing inputs from coupled channel approaches. Non-resonant processes should be a mixture of driving terms, that incorporates both MB and quark degrees of freedom, while the remainig part can be described at the level of phenomenological parameterization and fit to the data.

2 How to define N* electrocouplings and check their values
Resonant amplitudes Non-resonant amplitudes p, h, pp,.. p, h, pp,.. γv * N*,△ + N N’ N’ A3/2, A1/2, S1/2 GM, GE, GC N gvNN* electrocouplings can be defined in various ways, BUT should be related to: a) observables , b) transition amplitudes gvp→N* at real energies equal to N* physical masses. Consistent results on N* electrocouplings from the analyses of major meson electroproduction channels should show their reaction and model independence.

3 Dynamical coupled-channels model of EBAC
For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) Partial wave (LSJ) amplitude of a  b reaction: Reaction channels: Transition potentials: core meson cloud meson baryon Physical N*s will be a “mixture” of the two pictures: coupled-channels effect exchange potentials of ground state mesons and baryons bare N* states

4 Unitarized Breit-Wigner Anstaz of JM model
The unitarization procedure proposed in I.J.R.Aitchison NP A189 (1972), 417 and modified to be consistent with N* propagators emplyed in JM mpdel: where fagp, fbMBare the a-th N* electroproduction and b-th N* hadronic decay amplitude to the meson-baryon (MB) final state; Sab is the operator for resonance propagation, taking into account all transitions between a and b N* states, allowed by conservation laws in the strong interactions. Inverse of the JM unitarized N* propagator: N*a N*a diagonal regular BW Off-diagonal transitions incorporated into JM: S11(1535) ↔ S11(1650) D13(1520) ↔ D13(1700) 3/2+(1720) ↔ P13(1700) N*a N*b off-diagonal Energy dependencies, phases of N* production and decay amplitudes should be taken from coupled channel approaches together with MB dressing esrimates

5 Quark degrees of freedom in non-resonant mechanisms
Hand-bag diagrams for Np, pD and rp channels. others…. How to combine quark and MB mechanisms to avoid double counting Driving MB mechanisms at Q2>5.0 GeV2 Use of restrictions from unitarity and analyticity…. Content of the White Paper chapter, contributors….


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