Phenomenological πN→ππN amplitude and analysis of low energy data on total cross sections and 1--D distributions

Abstract

We develop the phenomenological amplitude of the πN → ππN reaction describing the exchanges of ∆ and N * along with the OPE mechanism. The contribution of the latter contains 4 independent low energy parameters (up to O(k 4 ) order). The terms of the polynomial background are added to stand for far resonances and for contact terms originating from the off-mass-shell interactions. These terms are introduced with the account of isotopic, crossing, C, P and T symmetries of strong interactions.The data consisting of total cross sections in the energy region 0.300 ≤ P Lab ≤ 500 MeV/c and 1D distributions from the bubble-chamber experiments for three reaction channels were undergoing fittings to determine free parameters of the amplitude. The best solutions are characterized by χ 2 DF = 1.16. At the considered energies the isobar exchanges are found to be more important than OPE. The obtained solutions reveal the need in more precise data and/or in polarization measurements because of large correlations of isobar parameters with the OPE ones.The theoretical solutions were used for modeling the Chew-Low extrapolation and the Olsson-Turner threshold approach. It is shown that the noncritical application of the former results in 100% theoretical errors, the extracted values being in fact the random numbers. The results of the Olsson-Turner method are characterized by significant systematic errors coming from unknown details of isobar physics. Sankt-Petersburg 1997

Scalar isoscalar pion pairs in nuclei and theA(π,ππ)Xreaction

“…Our understanding of the πN → ππN reaction at low energies has improved considerably in the last few years both experimentally and theoretically [20][21][22][23][24]. The model we present here follows closely that of ref.…”

Δ(1232)inπN→ππNreaction

“…(5)- (9). We summarize those matrix elements in Table II. TABLE II: The current matrix elements necessary to evaluate each diagram in Fig.…”

“…[2,3]. On the other hand, many types of interactions including the π∆∆ and ρN∆ interactions are considered in the global fits [8,9], but their individual roles in each channel of the πN → ππN reaction are not discussed. The π∆∆ and ρN∆ interactions still remain controversial in contrast to the well known πN∆ interaction.…”

Polarization properties of low energy amplitude for theπN→ππNreaction

“…The investigations of πN → ππN reactions are pronounced to be capable to discriminate between the ChPT and GChPT models for low-energy manifestations of QCD. Meanwhile the most recent attempts [9,10,11,12,13] of analysis of the πN → ππN data did not provide the necessary accuracy.…”

“…The relativistic version of the approach 3 was used recently [9] to treat the large set of the nearthreshold data on total cross sections and 1-D distributions in the energy region 300 ≤ P Lab ≤ 500 MeV/c. The phenomenological amplitude for the reaction πN → ππN, taking into account the exchanges of ∆ and N ( * ) along with the OPE mechanism and polynomial background derived with the account of isotopic, crossing, C, P and T symmetries of strong interactions, was fitted to the experimental data.…”