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
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Revised: 11 July 2013
Published online: 3 September 2013
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.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013