Summary of π-π scattering experiments

Abstract

The ππ scattering amplitude at threshold is fully determined by the chiral symmetry breaking part of the strong interaction, and, thus, directly constrains the form of the low energy effective lagrangians. Current status of the study of the low energy ππ interaction is discussed, particularly the recent results on reactions πN → ππN near threshold. Present levels of experimental uncertainties and limitations inherent to the available analysis methods leave ample room for improvements in the determination of the s-wave ππ scattering lengths. Experimental improvements are expected from new measurements of K e4 decays and from attempts to study π + π − atoms, while further theoretical work is required in order to make full use of the extensive near-threshold πN → ππN data that has recently become available.

Form factors in the radiative pion decay

“…However the PIBETA collaboration [10] showed that a strong discrepancy between theory and experiment arises for the branching ratio of the process in a specific region of the electron and photon energies. Lately the same collaboration, after their 2004 analysis, concludes that the discrepancy has faded away [11]. Curiously enough this decay has a persistent story of deceptive comparisons between theory and experiment [12] that have prompted the publication of proposals beyond the Standard Model (SM) to account for the variance [13][14][15][16][17].…”

“…This is very much relevant on the experimental side because highstatistics experiments as PIBETA [11] already are able to determine, for instance, the slopes of the form factors involved in these decays. The procedure consists, essentially, in the construction of the relevant three-point Green functions (GF) in the resonance energy region with a finite spectrum of states at the poles of the corresponding meromorphic functions.…”

“…where p is the photon momentum 11 . The determination of f T involves QCD in its non-perturbative regime and, consequently, is a non-trivial task.…”

Polarization properties of low energy amplitude for theπN→ππNreaction

“…A review on the experimental opportunities for obtaining information on the ππ interaction and the discussion of the status of modern experiments planned to test the ChPT predictions might be found in the talks [7,8] by Počanić. 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.…”

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

“…(For more references and reviews of this approach as well as more recent trends one can use the book by Donoghue, Golowich an Holstein [29] and the review papers by Meissner [56] and Pich [65]; a deep insight into the contemporary interpretation of ChPT and the role of spontaneous symmetry breaking is provided by a series of preprints by Leutwyler [52]. ) The predictions of ChPT [32] (summary of the most interesting predictions as well as forthcoming experimental tests might be found in the talk [68]) explain the very sharp interest in the values of ππ-scattering lengths and other parameters of the ππ scattering. Since it is not possible experimentally to create the pionic target or the colliding pion beams there are only indirect ways for obtaining experimental data on the ππ scattering.…”