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Generalities of the approaches for extraction of N* electrocouplings at high Q 2 Modeling of resonant / non resonant contributions is needed and should be focused on extraction of v NN* electrocouplings from measured observables in N and N 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 remaining part can be described at the level of phenomenological parameterization and fit to the data.
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How to define N* electrocouplings and check their values γvγv N N’N’ N*,△ A 3/2, A 1/2, S 1/2 G M, G E, G C N N’N’ + * v NN* electrocouplings can be defined in various ways, BUT should be related to: a) observables, b) transition amplitudes v p→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. Resonant amplitudes Non-resonant amplitudes
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v NN* electrocouplings from the CLAS data on N /N electroproduction N CLAS preliminary. N CLAS Good agreement between the electrocouplings obtained from the N and N channels. I. Aznauryan,V. Burkert, et al., PRC 80,055203 (2009). A 1/2 S 1/2 A 3/2 F 15 (1685) A 3/2 P 11 (1440) D 13 (1520) N world V. Burkert, et al., PRC 67,035204 (2003). N Q 2 =0, PDG. N Q 2 =0, CLAS M. Dugger, et al., PRC 79,065206 (2009).
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Partial wave (LSJ) amplitude of a b reaction: Reaction channels: Transition potentials: coupled-channels effect Dynamical coupled-channels model of EBAC For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) After dressing N* are poles at E complex N* production and decay amplitudesare complex BW ansatz projects s-channel N* ‘s
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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 f p, f MB are the -th N* electroproduction and -th N* hadronic decay amplitude to the meson-baryon (MB) final state; S is the operator for resonance propagation, taking into account all transitions between and N* states, allowed by conservation laws in the strong interactions. N* diagonal regular BW N* N* off-diagonal Off-diagonal transitions incorporated into JM: S 11 (1535) ↔ S 11 (1650) D 13 (1520) ↔ D 13 (1700) 3/2 + (1720) ↔ P 13 (1700) Energy dependencies, phases of N* production and decay amplitudes should be taken from coupled channel approaches together with MB dressing esrimates Inverse of the JM unitarized N* propagator:
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Quark degrees of freedom in non-resonant mechanisms Hand-bag diagrams for N and p channels. others…. How to combine quark and MB mechanisms to avoid double counting Driving MB mechanisms at Q 2 >5.0 GeV 2 Use of restrictions from unitarity and analyticity…. Content of the White Paper chapter, contributors….
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Future N* studies in π + π - p electroproduction with CLAS v NN*electrocouplings will become available for most excited proton states with masses less then 2.0 GeV and at photon virtualities up to 5.0 GeV 2 Needs to incorporate/check quark degrees of freedom in background 0.65 0.95 1.30 2.30 2.70 3.30 3.90 4.60 Q 2 (GeV 2 ) Resonance structures become more prominent with increasing Q 2. D 33, P 13, F 15 3/2 + (1720) D 13 Extension of JM model toward high Q 2 Coupling with Regge trajectory was increased by a factor 1.8!
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How to extend thus description toward W from 1.1 to 2.0 GeV? GPD parameterization Extension for and p final states
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Photon-nucleon current Composite nucleon must interact with photon via nontrivial current constrained by Ward- Takahashi identities DSE, BSE, Faddeev equation, current → nucleon form factors 9 Vertex contains dressed-quark anomalous magnetic moment Oettel, Pichowsky, Smekal Eur.Phys.J. A8 (2000) 251-281 Prospects to describe background within DSE fraework, attaching pion legs for N and replacing the final N by for final states?
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