Final-state radiation in electron-positron annihilation into a pion pair

Abstract

The process of e + e − annihilation into a π + π − pair with radiation of a photon is considered. The amplitude of the reaction e + e − → π + π − γ consists of the model independent initial-state radiation (ISR) and model dependent final-state radiation (FSR). The general structure of the FSR tensor is constructed from Lorentz covariance, gauge invariance and discrete symmetries in terms of the three invariant functions. To calculate these functions we apply Chiral Perturbation Theory (ChPT) with vector and axial-vector mesons. The contribution of e + e − → π + π − γ process to the muon anomalous magnetic moment is evaluated, and results are compared with the dominant contribution in the framework of a hybrid model, consisting of VMD and point-like scalar electrodynamics. The developed approach allows us also to calculate the π + π − charge asymmetry.

Asymmetry observables ine+e−→π+π−γin theϕregion within a chiral unitar

“…The vector meson exchange was also included, but only at tree level ( fig. 2b), in [23,24,25,28] in a different way. In [10] the φ couples to ρπ through φω mixing since a direct coupling is OZI suppressed.…”

“…For the FSR in the the e + e − → π + π − γ reaction, there are some standard models like the scalar QED (sQED) for the final state Bremsstrahlung process [21,22,23,24]. This is the most important contribution for large invariant mass of the pions, but for the lowest part of the two pion spectrum other mechanisms related to φ radiative decay become competitive.…”

“…This is the most important contribution for large invariant mass of the pions, but for the lowest part of the two pion spectrum other mechanisms related to φ radiative decay become competitive. In [23,24,25] a correction from the vector contribution using the resonance chiral theory Lagrangians [26] was also considered. For the φ decay process there is a wider variety of models which differ on the treatment of the scalar mesons.…”

“…For this decomposition we follow the formalism of ref. [23] which is also used in ref. [25], (see ref.…”

Final-state radiation and the possibility to test a pion-photon interaction model near the two-pion threshold

“…It is convenient to parametrize the FS tensor in terms of three gauge invariant tensors (see [20] and Ref. [23,24] in it):…”