Can one measure C-odd asymmetry in e+e- --> pi+pi-

TL;DR

This paper discusses the potential to measure C-odd asymmetry in e+e- to pi+ pi- processes, highlighting the dominance of pion rescattering effects and their implications for understanding hadronic interactions.

Contribution

It introduces a method to measure C-odd asymmetry via angular distributions, emphasizing the role of rescattering diagrams and their enhancement, which was not previously quantified.

Findings

Asymmetry can reach about 10% at specific angles and energies.

Rescattering effects dominate the asymmetry and are enhanced by logarithmic factors.

The method allows measuring rescattering and phase but doesn't resolve existing spectral function discrepancies.

Abstract

C-odd asymmetry can be studied from an accurate measurement of the angular distribution due to the interference between the S- and P-waves in e+e- --> pi+ pi- at order alpha^3. The asymmetry is dominated by the pion rescattering diagram which is enhanced by the presence of the ln(s/m^2_e), and is quite large (10% at theta=30^0 and sqrt{s} < M_{f_2}) compared to alpha/pi=0.3%. This process can also be used for alternatively measuring the size of the rescattering term and the phase of the S-wave amplitude, but does not help to solve the present discrepancy between the hadronic spectral functions from e+e- and tau-decay data.