Pomeron Odderon interference in production of two pi+ pi- pairs at LHC and ILC

We propose to look for the Odderon through the production of two pion pairs in photon collisions at high energies. We calculate the corresponding matrix elements in kT-factorization and discuss the possibility to reveal the existence of the perturbative Odderon by charge asymmetries, relying on models for the generalized distribution amplitudes of pi+ pi-. The application of this strategy to ultraperipheral collisions at the LHC suffers from the difficulty to trigger on interesting events and is plagued with severe background problems in p-p mode. Electron - positron colliders like ILC seem to better suit this physics.