Eur. Phys. J. C (2013) 73: 2539
https://doi.org/10.1140/epjc/s10052-013-2539-y

Regular Article - Theoretical Physics

Unified dispersive approach to real and virtual photon-photon scattering at low energy

Groupe de Physique Théorique, Institut de Physique Nucléaire, Université Paris-Sud 11, 91406, Orsay, France

^* e-mail: moussall@ipno.in2p3.fr

Received: 24 May 2013
Revised: 11 July 2013
Published online: 3 September 2013

Abstract

Previous representations of pion-pair production amplitudes by two real photons at low energy, which combine dispersion theoretical constraints with elastic unitarity, chiral symmetry and soft-photon constraints are generalised to the case where one photon is virtual. The constructed amplitudes display explicitly the dependence on the ππ phase-shifts, on pion form factors and on pion polarisabilities. They apply both for space-like and time-like virtualities despite the apparent overlap of the left- and right-hand cuts, by implementing a definition of resonance exchange amplitudes complying with analyticity and consistent limiting prescriptions for the energy variables. Applications are made to the pion generalised polarisabilies, to vector-meson radiative decays, and to the σγ electromagnetic form factor. Finally, an evaluation of the contribution of γππ states in the hadronic vacuum polarisation to the muon g−2 is given, which should be less model dependent than previous estimates.