Baryon resonance analysis from MAID

CPC(HEP & NP), 2009, 33(12): 1069- -1076Chinese Physics CVol. 33, No. 12, Dec., 2009Baryon resonance analysis from MAIDL. Tiator2;1) D. Drechsel'S.S. Kamalov2 M. Vanderhaeghen'1 (Institut fir Kernphysik, Universit&t Mainz, D 55099 Mainz, Germany)2 (Bogoliubov Laboratory for Thooretical Physics, JINR, Dubna, 141980 Moscow Region, Russia)Abstract The unitary isobar model MAID2007 has been used to analyze the recent data of pion electropro-duction. The model contains all four. star resonances in the region below W =2 GeV and both single-Q2 andQ2 dependent transition form factors could be obtained for the Delta, Roper, D13(1520), S11(1535), Sal(1620),Su(1650), D1s(1675), Fis(1680) and P:3(1720). From the complete world data base, including also π dataon the neutron, also Q2 dependent neutron form factors are obtained. For all transition form factors we alsogive convenient numerical parameterizations that can be used in other reactions. Furthermore, we show howthe transition form factors can be used to obtain empirical transverse charge densities and our first results aregiven for the Roper, the S11 and D13 resonances.Key words pion photo and electroproduction, non-strange baryons, transition form factorsPACS 14.20.Gk, 13.30.Eg, 13.75.Gx1 Introductiontudes A1/2 and A3/2 at the real photon point, whichare tabulated in the Particle Data Tables. For finiteOur knowledge about the excitation spectrum ofQ2 the information found in the literature is scarcethe nucleon was originally provided by elastic pion-and until recently practically nonexistent for the lon-nucleon scattering. All the resonances listed in the gitudinal amplitudes S1/2.Particle Data Tables'1 have been identified by partial-A big step forward was done during the lastwave analyses of this process with both Breit- Wignerdecade by the experiments at JLab, where electro-and pole extraction techniques. From such analysesproduction of π0 and π+ have been measured on thewe know the resonance masses, widths, and branch-proton. Most of these experiments did not use po~ing ratios into the πN and TrN channels. Theselarization degrees of freedom, but the virtual photonare reliable parameters for the four-star resonances,in electroproduction always carries longitudinal andwith only few exceptions. In particular, there remainstransverse polarizations which are accessible in exper-some doubt about the structure of two prominent res-iments with large azimuthal angle coverage. In addi-onances, the Roper P1(1440), which appears unusu-tion, also some experiments, especially in the 0(1232)ally broad, and the S11 (1535), where the pole can notregion were performed with polarized electrons, po-be uniquely determined, because it lies close to thelarized target and even an almost complete experi-ηN threshold.ment was done in Hall A with 16 unpolarized andOn the basis of these relatively frm grounds, ad-recoil polarization observables at Q2 = 1.0 GeV2.ditional information can be obtained for the elec-With our unitary isobar model MAID we have an-tromagnetic (e.m.) γNN* couplings through pionalyzed the electroproduction data and have obtainedphoto- and electroproduction. These couplings aretransition form factors for all 13 four-star resonancesdescribed by electric, magnetic, and charge transitionbelow w = 2 GeV. For the proton target in most casesform factors (FFs), G(Q"), GM(Q"), and GC(Q"), orwe could obtain both single-Q" and Q2-dependentby linear combinations thereof as belicity amplitudestransition form factors, for the neutron target we pa-A1/2(Q2)，A3/z(Q2), and Sr/z(Q"). So far we haverameterized the Q2 dependence in a simpler form a8some reasonable knowledge of the transverse ampli-far as the, existinσ data from the world data base中国煤化工Received 7 August 2009HCNMHG* Supported by Deutsche Forschungsgemeinechaft through SFB 443 and Jount Rtussian-German neusenDerg-Landau program1)E-mail: tiator@kph.uni- mainz.de⑥2009 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and tbe Instituteof Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd1070Chinese Physics C (HEP & NP)Vol. 33allows.mixing parameters and coupling constants were deFurthermore, the precise e.m. FF data, extractedtermined from an analysis of nonresonant multipolesfrom experiment, allow us to map out the quarkin the appropriate energy regions. In the latest ver-charge densities in a baryon. It was shown possible tosion, MAID2007, the S, P, D and F waves of thedefne a proper density interpretation of the form fac~-background contributions are unitarized as explainedtor data by viewing the baryon in a light-front frame.above, where the pion-nucleon elastic scattering am-This yields information on the spatial distribution ofplitudes,境= [7a exp(2ida)- 1]/2i, are described bythe quark charge in the plane transverse to the line-the phase shifts &a and the inelasticity parameters naof- sight. In this way, the quark transverse charge den-taken from the GWU/SAID analysisl7.sities were mapped out in the nucleon!3.3, and in theFor the resonance contributions we follow Ref. [8]deuteron!4 based on empirical FF data. To under-and assume Breit-Wigner forms for the resonancestand the e.m. structure of a nucleon resonance, it isshape,of interest to use the precise transition FF data to reth*(W,Q2)=veal the spatial distribution of the quark charges thatinduce such a transition. In this way, using the empir-碍(w,Q)fuv(W)rr Mafrn(W)eon, (3)ical information on the N - + N* transition form factorsM在- W2- iMpTotfrom the MAID analysis'l, the N - + O(1232) transi-where fnN is the usual Breit-Wigner factor describingtion charge densities have been mapped out in Ref. [3]the decay of a resonance R with total width To(W)and the N→N*(1440) in Ref. [6]. In this work, weand physical mass MR. The expressions for fyN, fnNwill extend this method to map out the quark transi-and Trot are given in Ref. [8]. The phase中R(W)tion charge densities inducing the N→S11(1535) andin Eq. (3) is introduced to adjust the total phaseN→D13(1520) e.m. excitations.such that the Fermi-Watson theorem is fulflld below two pion threshold. For the S- and P-wave mul-2 The MAID ansatztipoles we extend this unitarization procedure up toW = 1400 MeV. Because of a lack of further infor-In the spirit of a dynamical approach to pionmation, we assume that the phases中n are constantphoto- and electroproduction, the T-matrix of theat the higher energies. In particular we note thatunitary isobar model is set up with the fllowingthe phase中R for the P33(1232) excitation vanishes atansatzW = Mr= 1232 MeV for all values of Q*. For thistrn(W)=tu(W)+ 鼎(W)(1)multipole we may even apply the Fermi Watson the-orem up to W≈1600 MeV because the inelasticityof a background and a resonance T-matrix, whereparameter na remains close to 1. For the D- and F-each of them is individually unitary. This is a verywave resonances, the phases帆are assumed to be .important starting point that will allow us later toconstant and determined from the best fit. .clearly separate resonance and background ampli-While in the original version of MAID onlytudes within a Breit-Wigner concept.he 7 most important nucleon resonances were inFor a specific partial wave the background T-matrix is set-up by a potential multiplied by pioncluded with mostly only transverse e.m.cou-nucleon scattering amplitudes in accordance with theplings, in our new version all 13 four-star reso-nances below W = 2 GeV are included. TheseK-matrix approximation,are P33(1232)， Pl(1440)， Dr3(1520)， S11(1535),t(W,Q2)= uB*(W,Q2){1+it(W)，(2)S3(1620)，Ss(1650)， D1s(1675),Frs(1680),where only the on-shell part of the pion nucleonD33(1700)，P3(1720)， F3s(1905)， P31(1910) anrescattering is maintained and the off-shell part fromF3r(1950). .pion loop contributions is neglected.At thresholdit is well known that this is a bad approximation for'3 Transition form factorsγ, π0 production, however in the resonance region it iswell justified as the main contribution ftom pion loop中国煤化工;Q2) in most caseseffects is absorbed by the nucleon resonance dressing.areCNMHGergy and dependThe background potential opBna(W,Q2) is deonly:IH.denceoypivai CLiCIBy uoyendence occurs inscribed by Born terms obtained with an energy de-MAID2007 e.g. for the O(1232) resonance in termspendent mixing of pseudovector- pseudoscalar πNNof the virtual photon three -momentum k(W,Q2). Forcoupling and t-channel vector meson exchanges. Theall other resonances which are discussed here, how-No. 12L. Tiator et al: Baryon resonance analysis from MAID1071ever, we can assume a simple Q2 dependence, Aa(Q).tails see Ref.[5].They can be taken as constants in a single-Q2 anal-In Tables 2, 3 and 4 we give the numerical valuesysis, e.g. in photoproduction, where Q2 = 0 but alsoof the parameters for our Q2 dependent,“"superglobalat any fixed Q2, where enough data with W and θits". Our parametrization of the 0(1232) form fac~-variation is available, see Table 1. Alternatively theytors are more complicated, in particular due to build-can also be parameterized as functions of Q2 in anin requirements ftom low energy theorems in the longansatz likewavelength limit, details are discussed in Ref. [5].(A(2)= A.(0)(1+a,Q2 +oaqQ* +aQ)e-n.2. (田)Table 1. Database of pion electroproduction forenergies above the 0 resonance u to W =With such an ansatz it is possible to determine the1.7 GeV, used in our single-Q2 transition formparameters Aa(0) from a fit to the world database offactor analysis.photoproduction, while the parameters a; and b1 canreferenceyearreactionQ2/GeV2be obtained from a combined ftting of all electropro-Jooet al.:002pπ00.4-1.8duction data at different Q2. The latter procedure weJoo et al.10])200nr+0.4-0.65call the "superglobal ft". In MAID the photon cou-evissiere et al.1]1.0plings A。are direct input parameters. They are di-Egiyan et al.12]20060.3-0.6rectly related to the helicity couplings A1/2,A3/2 andUngaro et al.12|pr'3.0-6.0S1/2 of nucleon resonance excitation. For further dePark et al.14120081.7-4.5Table 2. New parameterizations of our transition form factors, Eq. (4), for proton targets.N", △*Aa(0)(10-3GeV-1/2)a1/GeV-2a2/GeV-4a3/GeV-8by/GeV-2_P(440)pA1/2-61.40.871-3.516-0.1581.36S124.240.01.501.75D13(1520)p-27.48.580-0.2520.3571.20A3/2160.6-0.8200.541-0.0161.06S1/2-63.54.193.40Dis(1675)p15.30.102.0021.61.910.180.69S1/z1.1oFrs(1680)p-25.13.780-0.2920.0801.25134.31.0160.2220.2372.41-44.03.7830_1.85D33(1700)226. .1.77210.0.881.712.02Pa3(1720)p73.01.891.55-11.510.83-0.660.43-53.02.46Table 3. Maid2007 parameterizations, Eq. (4),have been recently included in our database, we findfor proton targets (a2= 03= 0).differences compared to our MAID2007 parametriza-tion for the following 6 proton transition form fac-N",o°Aa(0)21bS1(1535)p66.40.70tors to P1u(1440), D13(1520), D33(1440), D1s(1675), .Frs(1680) and P3(1720).-2.0_23.90.81Above the third resonance region there is an en-Sa1(1620)65.61.862.50Sy/216.22.83ergy中国煤化工V, where no four-S1(1650)p33.31.450.62star IEpd this gap and up-3.52.880.76to 2MHc N M H Gnances, Fs(1905), .P3r(1910) and F3r(1950) are reported by the PDG,For all other resonances the parameters are listedwhich are also included in MAID. In electroproduc-in the three tables. Due to the 2008 π+ data thattion nothing is practically known about these states1072Chinese Physics C (HEP & NP)Vol. 33and we have just introduced their reported photonnegative, but reaches large magnitudes of around 25%couplings, multiplied with a simple gaussian form fac~at the Q2≈6 GeV2 in the JLab analysis, whereas intor, exp(-2.0Q2/GeV2). In MAID their main role isthe MAID analysis the magnitude is only around 10%to define a global high-energy behavior that is neededwith an asymptotically almost zero slope as predictedfor applications with dispersion relations and sumin calculations by Buchmann!5] and Ji et al.I6l.rules. Future experiments in this region will give usthe necessary information to map out these form fac-3.2 Second resonance regiontors in more details.Above the two pion threshold, we can no longerapply the two-channel unitarity and consequently theTable 4. Same as Table 3 for neutron targets.Watson theorem does not hold anymore. Therefore,Aa(0)a1b1the background amplitude of the partial waves doesPr1(1440)nA1/254.10.951.77not vanish at resonance as this was the case for theS1/2-41.52.981.550(1232) resonance. As an immediate consequenceD13(1520)n-76.5-0.53the resonance background separation becomes model-A3/20.581.75dependent. In MAID2007 we choose to separate the13.61.57background and resonance contributions according toS1(1535)n-50.74.751.69the K-matrix approximation, Eqs. (2), (3). Further-28.50.36Su(1650)nA/29.30.13more, we recall that the absolute values of the he-10.-0.50licity amplitudes are correlated with the values usedDr<(1675)n-61.70.012.00for the total resonance width IR and the single-pionAs/2-83.7branching ratio βn, giving rise to additional uncer-0tainties from these hadronic resonance parameters.F1s(1680)n27.91.20On the experimental side, the data at the higher en--38.44.09ergies are no longer as abundant as in the 0 region.However, the large data set recently obtained mainlyPr3(1720)n-2.912.70by the CLAS collaboration (see Table 1) enabled us5.00to determine the transverse and longitudinal helicitycouplings 88 functions of Q2 for all the four-star reso-nances below 1800 MeV. These data are available in3.1 First resonance regionthe kinematical region of 1100 MeV < w < 1680 MeVThe 0(1232)P33 is the only nucleon resonanceand 0.4 GeV2