A bstract We consider the reaction γp → π _(+) π _(?) p at high energies. Our description includes dipion production via the resonances ρ , ω , ρ _(′)and f ~(2), and via non-resonant mechanisms. The calculation is based on a model of high energy scattering with the exchanges of photon, pomeron, odderon and reggeons. The pomeron and the C = +1 reggeons are described as effective tensor exchanges, the odderon and the C = ?1 reggeons as effective vector exchanges. We obtain a gauge-invariant version of the Drell-S?ding mechanism which produces the skewing of the ρ-meson shape. Starting from the explicit formulae for the matrix element for dipion production we construct an event generator which comprises all contributions mentioned above and includes all interference terms. We give examples of total and differential cross sections and discuss asymmetries which are due to interference of C = +1 and C = ?1 exchange contributions. These asymmetries can be used to search for odderon effects. Our model is intended to provide all necessary theoretical tools for a detailed experimental analysis of elastic dipion production for which data exist from fixed target experiments, from HERA, and are now being collected by LHC experiments.
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