DISPERSION THEORY METHODS FOR TRANSITION FORM FACTORS

Sebastian P Schneider

doi:10.1142/s201019451460461x

Abstract

Dispersion-theoretical analyses of transition form factors are stepping stones to a model-independent determination of the light-by-light scattering contribution to (g - 2)μ. We extend a calculation of the conversion decays of the lightest isoscalar vector mesons, ω/ϕ → π0ℓ+ℓ-, that builds on a previous dispersive analysis of the ω/ϕ → 3π partial-wave amplitudes and the pion vector form factor as its sole ingredients. We construct a good parametrization of e+e- → 3π that, together with information on the anomalous process γπ → ππ, allows us to obtain a description of the π0 transition form factor measured in e+e- → π0γ.

Highlights

Hadronic Light-by-Light Scattering The hadronic light-by-light scattering contribution is bound to be the dominant uncertainty in a precision standard-model determination of the anomalous magnetic moment of the muon in the near future
One of its largest contributions is given by pseudoscalar pole terms, whose strength is determined by processes involving a pseudoscalar (π0, η, η ) and two virtual photons, and by doubly-virtual transition form factors
Dispersion relations allow for a model-independent description of these transition form factors.[2]

Summary

DISPERSION THEORY METHODS FOR TRANSITION FORM FACTORS

SCHNEIDER Helmholtz-Institut fur Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universitat Bonn. Dispersion-theoretical analyses of transition form factors are stepping stones to a modelindependent determination of the light-by-light scattering contribution to (g − 2)μ. We extend a calculation of the conversion decays of the lightest isoscalar vector mesons, ω/φ → π0 + −, that builds on a previous dispersive analysis of the ω/φ → 3π partialwave amplitudes and the pion vector form factor as its sole ingredients. We construct a good parametrization of e+e− → 3π that, together with information on the anomalous process γπ → ππ, allows us to obtain a description of the π0 transition form factor measured in e+e− → π0γ

Introduction

Dispersion theory for transition form factor