Towards a high precision calculation for the pion-nucleus scattering lengths

We calculate the leading isospin conserving few-nucleon contributions to pion scattering on $^2$H, $^3$He, and $^4$He. We demonstrate that the strong contributions to the pion-nucleus scattering lengths can be controlled theoretically to an accuracy of a few percent for isoscalar nuclei and of 10% for isovector nuclei. In particular, we find the $\pi$-$^3$He scattering length to be $(62 \pm 4\pm 7)\times 10^{-3} m_{\pi}^{-1}$ where the uncertainties are due to ambiguities in the $\pi$-N scattering lengths and few-nucleon effects, respectively. To establish this accuracy we need to identify a suitable power counting for pion-nucleus scattering. For this purpose we study the dependence of the two-nucleon contributions to the scattering length on the binding energy of $^2$H. Furthermore, we investigate the relative size of the leading two-, three-, and four-nucleon contributions. For the numerical evaluation of the pertinent integrals, aMonte Carlo method suitable for momentum space is devised. Our results show that in general the power counting suggested by Weinberg is capable to properly predict the relative importance of $N$-nucleon operators, however, it fails to capture the relative strength of $N$- and $(N+1)$-nucleon operators, where we find a suppression by a factor of 5 compared to the predicted factor of 50. The relevance for the extraction of the isoscalar $\pi$-N scattering length from pionic $^2$H and $^4$He is discussed. As a side result, we show that beyond the calculation of the $\pi$-$^2$H scattering length is already beyond the range of applicability of heavy pion effective field theory.Comment: 24 pages, 14 figures, 10 table

Phenomenology of pp->pp eta reaction close to threshold

The recent high statistics measurement of the pp -> pp eta reaction at an excess energy Q=15.5 MeV has been analysed by means of partial wave decomposition of the cross section. Guided by the dominance of the final state 1S0 pp interaction (FSI), we keep only terms involving the FSI enhancement factor. The measured p-p and p-eta effective mass spectra can be well reproduced by lifting the standard on-shell approximation in the enhancement factor and by allowing for a linear energy dependence in the leading 3P0->1S0,s partial wave amplitude. Higher partial waves seem to play only a marginal role

Production of a0a_0-mesons in pp and pn reactions

We investigate the cross section for the reaction $NN \to NNa_0$ near threshold and at medium energies. An effective Lagrangian approach with one-pion exchange is applied to analyze different contributions to the cross section for different isospin channels. The Reggeon exchange mechanism is also considered. The results are used to calculate the contribution of the $a_0$ meson to the cross sections and invariant $K \bar K$ mass distributions of the reactions $pp\to pn K^+\bar K^0$ and $pp\to pp K^+K^-$. It is found that the experimental observation of $a_0^+$ mesons in the reaction $pp\to pn K^+\bar K^0$ is much more promising than the observation of $a_0^0$ mesons in the reaction $pp\to pp K^+K^-$.Comment: 26 pages, including 11 eps figures, to be bublished in J. Phys.

Study of the f2(1270)f_2(1270), f2′(1525)f_2'(1525), f0(1370)f_0(1370) and f0(1710)f_0(1710) in the J/ψJ/\psi radiative decays

In this paper we present an approach to study the radiative decay modes of the $J/\psi$ into a photon and one of the tensor mesons $f_2(1270)$, $f'_2(1525)$, as well as the scalar ones $f_0(1370)$ and $f_0(1710)$. Especially we compare predictions that emerge from a scheme where the states appear dynamically in the solution of vector meson--vector meson scattering amplitudes to those from a (admittedly naive) quark model. We provide evidence that it might be possible to distinguish amongst the two scenarios, once improved data are available.Comment: The large Nc argument improved; version published in EPJA

Eta physics at threshold

The production of eta and eta-prime mesons in elementary nucleon-nucleon collisions has been investigated at the synchrotrons CELSIUS, COSY and SATURNE. The magnitude and energy dependence of the total cross section as well as the occupation distribution of the phase space serve as observables for investigating the mechanisms underlying the production processes and the interaction of mesons with nucleons. The precise data on the eta and eta-prime creation via the pp --> pp eta(eta-prime) reactions allowed to settle the general features of the eta and eta-prime meson production and revealed the sensitivity of the mentioned observables to the nucleon-nucleon-meson final state interaction. The particular production properties, like for example the determination of the dominating exchange processes which lead to the excitation of the S_11 nucleon isobar in the case of eta creation, must be established by confrontation with other observables. The present status of this investigation with an emphasis on the results of the COSY-11 collaboration is briefly presented. The available data are interpreted in view of the production mechanism and the meson-nucleon interaction.Comment: 3 pages, 3 figures, Presented at Conference on Quarks and Nuclear Physics (QNP 2002), Julich, Germany, 9-14 Jun 200

Energy Dependence of the Near-Threshold Total Cross-Section for the pp --> pp eta' Reaction

Total cross sections for the pp --> pp eta' reaction have been measured in the excess energy range from Q = 1.53 MeV to Q = 23.64 MeV. The experiment has been performed at the internal installation COSY-11 using a stochastically cooled proton beam of the COoler SYnchrotron COSY and a hydrogen cluster target. The determined energy dependence of the total cross section weakens the hypothesis of the S-wave repulsive interaction between the eta' meson and the proton. New data agree well with predictions based on the phase-space distribution modified by the proton-proton final-state-interaction (FSI) only.Comment: 12 pages, 1 table, 4 figure

DN interaction from meson exchange

A model of the DN interaction is presented which is developed in close analogy to the meson-exchange KbarN potential of the Juelich group utilizing SU(4) symmetry constraints. The main ingredients of the interaction are provided by vector meson (rho, omega) exchange and higher-order box diagrams involving D*N, D\Delta, and D*\Delta intermediate states. The coupling of DN to the pi-Lambda_c and pi-Sigma_c channels is taken into account. The interaction model generates the Lambda_c(2595) resonance dynamically as a DN quasi-bound state. Results for DN total and differential cross sections are presented and compared with predictions of an interaction model that is based on the leading-order Weinberg-Tomozawa term. Some features of the Lambda_c(2595) resonance are discussed and the role of the near-by pi-Sigma_c threshold is emphasized. Selected predictions of the orginal KbarN model are reported too. Specifically, it is pointed out that the model generates two poles in the partial wave corresponding to the Lambda(1405) resonance.Comment: 14 pages, 8 figure

Eta meson production in nucleon-nucleon collisions within an effective Lagrangian model

We investigate the pp --> pp eta and pn --> pn eta reactions within an effective Lagrangian model for laboratory kinetic energies ranging from very close to eta meson production threshold to about 10 GeV. Production amplitudes include contributions from the mechanism of excitation, propagation and decay of N*(1535), N*(1650), and N*(1710) baryonic resonances. The initial interaction between two incoming nucleons is modeled by the exchange of pi, rho, omega and sigma mesons where the vertex parameters are taken to be the same as those used in the previous applications of this model. Parameters of the resonance vertices also have been taken from our earlier studies wherever applicable. Calculations have been done for total as well as differential eta production cross sections. To describe the data for energies closer to the production threshold final state interactions among the out-going particles have been included by means of a generalized Watson-Migdal method. Terms corresponding to the excitation of N*(1535) resonance and pion exchange process dominate the cross sections. With a single set of vertex parameters our model is able to describe the available data well on total cross sections for beam energies ranging from close to threshold to upto 10 GeV.Comment: 33 pages, 11 figures, one new appendix added, discussions extende

Determination of the pion-nucleon coupling constant and scattering lengths

We critically evaluate the isovector GMO sum rule for forward pion-nucleon scattering using the recent precision measurements of negatively charged pion-proton and pion-deuteron scattering lengths from pionic atoms. We deduce the charged-pion-nucleon coupling constant, with careful attention to systematic and statistical uncertainties. This determination gives, directly from data a pseudoscalar coupling constant of 14.11+-0.05(statistical)+-0.19(systematic) or a pseudovector one of 0.0783(11). This value is intermediate between that of indirect methods and the direct determination from backward neutron-proton differential scattering cross sections. We also use the pionic atom data to deduce the coherent symmetric and antisymmetric sums of the negatively charged pion-proton and pion-neutron scattering lengths with high precision. The symmetric sum gives 0.0012+-0.0002(statistical)+-0.0008 (systematic) and the antisymmetric one 0.0895+-0.0003(statistical)+-0.0013(systematic), both in units of inverse charged pion-mass. For the need of the present analysis, we improve the theoretical description of the pion-deuteron scattering length.Comment: 27 pages, 5 figures, submitted to Phys. Rev. C, few modifications and clarifications, no change in substance of the pape

Dynamical coupled-channel approaches on a momentum lattice

Dynamical coupled-channel approaches are a widely used tool in hadronic physics that allow to analyze different reactions and partial waves in a consistent way. In such approaches the basic interactions are derived within an effective Lagrangian framework and the resulting pseudo-potentials are then unitarized in a coupled-channel scattering equation. We propose a scheme that allows for a solution of the arising integral equation in discretized momentum space for periodic as well as twisted boundary conditions. This permits to study finite size effects as they appear in lattice QCD simulations. The new formalism, at this stage with a restriction to S-waves, is applied to coupled-channel models for the sigma(600), f0(980), and a0(980) mesons, and also for the Lambda(1405) baryon. Lattice spectra are predicted.Comment: 7 pages, 4 figure