Poles, the only true resonant-state signals, are extracted from a worldwide collection of partial wave amplitudes using only one, well controlled pole-extraction method

Each and every energy dependent partial-wave analysis is parameterizing the pole positions in a procedure defined by the way how the continuous energy dependence is implemented. These pole positions are, henceforth, inherently model dependent. To reduce this model dependence, we use only one, coupled-channel, unitary, fully analytic method based on the isobar approximation to extract the pole positions from the each available member of the worldwide collection of partial wave amplitudes which are understood as nothing more but a good energy dependent representation of genuine experimental numbers assembled in a form of partial-wave data. In that way, the model dependence related to the different assumptions on the analytic form of the partial-wave amplitudes is avoided, and the true confidence limit for the existence of a particular resonant state, at least in one model, is established. The way how the method works, and first results are demonstrated for the S11 partial wave.Comment: 22 pages, 8 figures, 2 table

Singularity structure of the pi N scattering amplitude in a meson-exchange model up to energies W < 2.0 GeV

Within the previously developed Dubna-Mainz-Taipei meson-exchange model, the singularity structure of the pi N scattering amplitudes has been investigated. For all partial waves up to F waves and c.m. energies up to W = 2 GeV, the T-matrix poles have been calculated by three different techniques: analytic continuation into the complex energy plane, speed-plot and the regularization method. For all 4-star resonances, we find a perfect agreement between the analytic continuation and the regularization method. We also find resonance poles for resonances that are not so well established, but in these cases the pole positions and residues obtained by analytic continuation can substantially differ from the results predicted by the speed-plot and regularization methods.Comment: 21 pages, 4 figures, 4 table

Stability of the Zagreb Carnegie-Mellon-Berkeley model

In ref. [1] we have used the Zagreb realization of Carnegie-Melon-Berkeley coupled-channel, unitary model as a tool for extracting pole positions from the world collection of partial wave data, with the aim of eliminating model dependence in pole-search procedures. In order that the method is sensible, we in this paper discuss the stability of the method with respect to the strong variation of different model ingredients. We show that the Zagreb CMB procedure is very stable with strong variation of the model assumptions, and that it can reliably predict the pole positions of the fitted partial wave amplitudes.Comment: 25 pages, 12 figures, 19 table

Relativistic O(q4)O(q^4) two-pion exchange nucleon-nucleon potential: configuration space

We have recently performed a relativistic $O(q^4)$ chiral expansion of the two-pion exchange $NN$ potential, and here we explore its configuration space content. Interactions are determined by three families of diagrams, two of which involve just $g_A$ and $f_{\pi}$, whereas the third one depends on empirical coefficients fixed by subthreshold $\pi N$ data. In this sense, the calculation has no adjusted parameters and gives rise to predictions, which are tested against phenomenological potentials. The dynamical structure of the eight leading non-relativistic components of the interaction is investigated and, in most cases, found to be clearly dominated by a well defined class of diagrams. In particular, the central isovector and spin-orbit, spin-spin, and tensor isoscalar terms are almost completely fixed by just $g_A$ and $f_{\pi}$. The convergence of the chiral series in powers of the ratio (pion mass/nucleon mass) is studied as a function of the internucleon distance and, for $r>$ 1 fm, found to be adequate for most components of the potential. An important exception is the dominant central isoscalar term, where the convergence is evident only for $r>$ 2.5 fm. Finally, we compare the spatial behavior of the functions that enter the relativistic and heavy baryon formulations of the interaction and find that, in the region of physical interest, they differ by about 5%.Comment: 27 pages, 33 figure

Soft-core meson-baryon interactions. II. πN\pi N and K+NK^+ N scattering

The $\pi N$ potential includes the t-channel exchanges of the scalar-mesons $\sigma$ and f_0, vector-meson $\rho$, tensor-mesons f_2 and f_2' and the Pomeron as well as the s- and u-channel exchanges of the nucleon N and the resonances $\Delta$, Roper and S_{11}. These resonances are not generated dynamically. We consider them as, at least partially, genuine three-quark states and we treat them in the same way as the nucleon. The latter two resonances were needed to find the proper behavior of the phase shifts at higher energies in the corresponding partial waves. The soft-core $\pi N$-model gives an excellent fit to the empirical $\pi N$ S- and P-wave phase shifts up to T_{lab}=600 MeV. Also the scattering lengths have been reproduced well and the soft-pion theorems for low-energy $\pi N$ scattering are satisfied. The soft-core model for the $K^+ N$ interaction is an SU_f(3)-extension of the soft-core $\pi N$-model. The $K^+ N$ potential includes the t-channel exchanges of the scalar-mesons a_0, $\sigma$ and f_0, vector-mesons $\rho$, $\omega$ and $\phi$, tensor-mesons a_2, f_2 and f_2' and the Pomeron as well as u-channel exchanges of the hyperons $\Lambda$ and $\Sigma$. The fit to the empirical $K^+ N$ S-, P- and D-wave phase shifts up to T_{lab}=600 MeV is reasonable and certainly reflects the present state of the art. Since the various $K^+ N$ phase shift analyses are not very consistent, also scattering observables are compared with the soft-core $K^+ N$-model. A good agreement for the total and differential cross sections as well as the polarizations is found.Comment: 24 pages, 20 PostScript figures, revtex4, submitted to Phys. Rev.

Electromagnetic Form Factors of Nucleons with QCD Constraints Sytematic Study of the Space and Time-like Regions

Elastic electromagnetic form factors of nucleons are investigated both for the time-like and the space-like momentums under the condition that the QCD constraints are satisfied asymptotically. The unsubtracted dispersion relation with the superconvergence conditions are used as a realization of the QCD conditions. The experimental data are analyzed by using the dispersion formula and it is shown that the calculated form factors reproduce the experimental data reasonably well.Comment: 14 page

On the pion cloud of the nucleon

We evaluate the two--pion contribution to the nucleon electromagnetic form factors by use of dispersion analysis and chiral perturbation theory. After subtraction of the rho--meson component, we calculate the distributions of charge and magnetization in coordinate space, which can be interpreted as the effects of the pion cloud. We find that the charge distribution of this pion cloud effect peaks at distances of about 0.3 fm. Furthermore, we calculate the contribution of the pion cloud to the isovector charges and radii of the nucleon.Comment: 7 pages, latex, 3 ps figures, minor change

Novel evaluation of the two-pion contribution to the nucleon isovector form factors

We calculate the two-pion continuum contribution to the nucleon isovector spectral functions drawing upon the new high statistics measurements of the pion form factor by the CMD-2, KLOE, and SND collaborations. The general structure of the spectral functions remains unchanged, but the magnitude increases by about 10%. Using the updated spectral functions, we calculate the contribution of the two-pion continuum to the nucleon isovector form factors and radii. We compare the isovector radii with simple rho-pole models and illustrate their strong underestimation in such approaches. Moreover, we give a convenient parametrization of the result for use in future form factor analyses.Comment: 9 pages, 2 eps figures, revtex4, CMD-2 and SND data included, conclusions unchanged, version to appear in Phys. Lett.

Dispersion-Theoretical Analysis of the Nucleon Electromagnetic Formfactors

Dispersion relations allow for a coherent description of the nucleon electromagnetic form factors measured over a large range of momentum transfer, $Q^2 \simeq 0 \ldots 35$ GeV$^2$. Including constraints from unitarity and perturbative QCD, we present a novel parametrisation of the absorptive parts of the various isoscalar and isovector nucleon form factors. Using the current world data, we obtain results for the electromagnetic form factors, nucleon radii and meson couplings. We stress the importance of measurements at large momentum transfer to test the predictions of perturbative QCD.Comment: 33 pp, RevTEX or plain LaTeX, 7 figures (in ffig.uu

Nucleon electroweak form factors: Analysis of their spectral functions

We investigate the imaginary parts of the nucleon electromagnetic and axial form factors close to threshold in the framework of heavy baryon chiral perturbation theory. For the isovector electromagnetic form factors, we recover the well known strong enhancement near threshold. For the isoscalar ones, we show that there is no visible enhancement due to the three--pion continuum. This justifies the use of vector meson poles only in dispersion--theoretical calculations. We also calculate the imaginary part of the nucleon isovector axial form factor and show that it is small in the threshold region.Comment: 14 pp, ReVTeX or LaTeX, uses epsf, 7 figure