Nucleon Resonance Excitation with Virtual Photons

Abstract

Abstract. The unitary isobar model MAID is used for a partial wave analysis of pion photoproduction and electroproduction data on the nucleon. In particular we have taken emphasis on the region of the ∆(1232) resonance and have separated the resonance and background amplitudes with the K-matrix approach. This leads to electromagnetic properties of the dressed ∆ resonance, where all multipole amplitudes become purely imaginary and all form factors and helicity amplitudes become purely real at the K-matrix pole of W = M ∆ = 1232 MeV. The R EM = E2/M1 and R SM = C2/M1 ratios of the quadrupole excitation are compared to recent data analysis of different groups. The R EM ratio of MAID2005 agrees very well with the data and has a linear behavior over the whole experimentally explored Q 2 region with a small positive slope that predicts a zero crossing around 3.5 GeV 2 . The recent R SM data for Q 2 < 0.2 GeV 2 indicate a qualitative change in the shape of the ratio which can be explained by the impact of the Siegert theorem at pseudothreshold (Q 2 = −0.086GeV 2 ) in the unphysical region.

Combined parametrization of GEn and $\gamma^{\ast} N \rightarrow \Delta (1232)$γ*N→Δ(1232) quadrupole form factors

“…Since, according to chiral perturbation theory, the transition to the complex form factors is smooth [55,56], we can ignore the imaginary component of the form factors in first approximation, and treat the form factors in the timelike region as simple extrapolations of the analytic parametrizations derived in the spacelike region. Similar extrapolations to the timelike region can also be found in [44,73,74].…”

Improved empirical parametrizations of theγ*N→Δ(1232)andγ*N<

“…Note that the previous relation differs from the usual form E = √ 2 ω |q| S 1/2 [14,15], by a factor 1/|q|. This dif-ference has implications in shape of the parametrizations of the data, as we will show.…”

“…We will conclude at the end, that, an overall description of the data for low Q 2 and large Q 2 , including the pseudo-threshold, is possible using smooth representations of the helicity amplitudes. The presented parametrizations are compared with the MAID2007 parametrizations [14][15][16]. Parametrizations for very large Q 2 , that simulate the expected falloff from perturbative QCD (pQCD), will be proposed.…”

Transition form factors of theN*(1535)as a dynamically generated resonance

“…The empty triangles up are taken from Ref. [56]. The other data (empty circle and empty triangle down) are from Ref.…”