Baryon Resonance Analysis from MAID D. Drechsel, S. Kamalov, L. Tiator What is a resonance? What is a resonance? - a peak in the cross section ? - a peak in the imaginary part of a pw amplitude associated with a zero in the real part ? - a pole of the T-matrix in the 2nd Riemann sheet ! e.g. with a maximum in the speed-plots of pw amplitudes resonance part determines the pole background can be neglected possible requirements for an ansatz or a model of pion photoproduction gauge invariant covariant or at least relativistic crossing symmetric chirally symmetric fulfill low-energy theorems analytic unitary fulfill dispersion relations MAID Ansatz effective Lagrangian with fields on tree-level isobar model for N* and resonances (only with 4-stars) background partial waves are unitarized with K-matrix method for all S, P, D and F waves, higher background partial waves are taken from real Born terms P 33 (1232), P 11 (1440), S 11 (1535), S 11 (1650), S 31 (1620) are unitarized up to the region, above we fit a constant phase other resonances: D 13, D 33, D 15, P 13, P 31, F 15, F 35, F 37, we dont unitarize, but fit a constant phase as above MAID unitarization procedure K-matrix unitarization for all background partial waves up to L=3 MAID unitarization procedure a correction phase (W) for all Breit-Wigner resonance contributions the energy dependent width implicitly includes the coupling to other channels Definition of the electromagnetic NN* Couplings (e.g. Arndt et al, 1990 or PDG) reduced multipoles: therefore, we need a Partial Wave Analysis with resonance and background separation for helicity amplitudes and transition form factors we need the imaginary parts of the resonance multipoles Definition of the N-N* Form Factors helicity amplitudes: reduced multipoles from PWA: Sachs form factors: covariant (Dirac) form factors: for spin resonances as Roper P 11 or S 11 we get only 2 ff different sets of form factors can be defined as linear combinations of the reduced multipoles Delta: P 33 (1232) Roper: P 11 (1440) N*S 11 (1535) N*D 13 (1520) N*S 11 (1650) N*D 15 (1675) N*F 15 (1680) N*P 13 (1720) with MAID we have performed a detailed analysis of Transition Form Factors for the following Baryon Resonances data base for pion electroproduction data in the region up to W = 1.3 GeV data up to the 3rd resonance region up to W = 1.7 GeV JLab/Hall CFrolov1999 p0p0 Q = GeV BatesMertz et al.2001 p0p0 Q = GeV MainzPospischil et al.2001 p0p0 Q = GeV BonnBantes, Gothe2002 p0p0 Q = 0.6 GeV MainzElsner et al. / Stave et al.2006 p0p0 Q = GeV JLab/Hall AKelly et al.2007 n0n0 Q = 1.0 GeV JLab/CLASVillano et al.2008 prelim. p0p0 Q = 6.0 7.9 GeV JLab/CLASJoo et al.2002 / 2003 p0p0 Q = 0.4 1.8 GeV JLab/CLASJoo et al.2004 n+n+ Q = GeV JLab/Hall ALaveissiere et al.2004 n0n0 Q = 1.0 GeV JLab/CLASEgiyan et al.2006 n+n+ Q = 0.3 0.6 GeV JLab/CLASUngaro et al.2006 p0p0 Q = 3.0 6.0 GeV JLab/CLASPark et al.2008 n+n+ Q = 1.7 4.5 GeV E/M and S/M ratios for the N transition the analyses are based on 0 data from JLab, Mainz, Bonn and Bates analysis fit A fit B Ji, Ma, Yuan, PRL 90, 2003 pQCD with angular momentum effects Nucleon -> Delta on the Lattice C. Alexandrou et al., 2008 dynamical fermions m down to 360 MeV G M : main problems at small Q (pion cloud) R EM, R SM : in agreement within large uncertainties transition form factors of the Roper comparison of MAID and JLab analysis A 1/2 S 1/2 MAID analysis 2007/08 JLab analysis 2008 F2F2 F1F1 Huey-Wen Lin (JLab), ECT*, Trento 2008 Nucleon-Roper Transition Form Factors on the Lattice again problem with pion cloud at small Q Transverse Densities (Miller 2007 and Carlson, Vanderhaeghen 2007) for unpolarized nucleons or resonances: for polarized nucleons or resonances: the Breit frame, mostly used in nuclear physics, is not a propriate frame for the nucleon or nucleon resonances e.g. Z- graphs spoil the density interpretation these problems do not exist in the infinite momentum frame (on the Light Cone), where q + =0, and Z- graphs are suppressed in this frame transverse densities can be defined as 2-dim. Fourier transforms of the Dirac form factors Transverse Charge Densities of the Nucleon and N -> Roper (in collaboration with Marc Vanderhaeghen, Phys. Lett. B 672 (2009) 344) N S 11 (1535) MAID analysis 2007/2008 JLab analysis 2008 longitudinal: S 1/2 transverse: A 1/2 N D 13 (1520) A 3/2 A 1/2 longitudinal: S 1/2 MAID analysis 2007/2008 JLab analysis 2008 Transverse Charge Densities of the Nucleon and N -> Roper (in collaboration with Marc Vanderhaeghen, in preparation) N F 15 (1680) resonances with some forbidden amplitudes forbidden resonances with some forbidden amplitudes Summary and Conclusions MAID: set of single-channel partial wave analysis programs on the basis of isobar models recent results from channel (Maid2007/08): N->N* transition form factors for 13 N*/ resonances with **** PDG rating reasonably well for: I=3/2: P 33 (1232) I=1/2 proton: P 11 (1440), S 11 (1535), D 13 (1520), F 15 (1680) S 11 (1650), D 15 (1675), P 13 (1720),