High-energy $\pi\pi$ scattering without and with photon radiation

We discuss the processes $\pi \pi \to \pi \pi$ and $\pi \pi \to \pi \pi \gamma$ from a general quantum field theory (QFT) point of view. In the soft-photon limit where the photon energy $\omega \to 0$ we study the theorem due to F.E. Low. We confirm his result for the $1/\omega$ term of the $\pi \pi \to \pi \pi \gamma$ amplitude but disagree for the $\omega^{0}$ term. We analyse the origin of this discrepancy. Then we calculate the amplitudes for the above reactions in the tensor-pomeron model. We identify places where ``anomalous'' soft photons could come from. Three soft-photon approximations (SPAs) are introduced. The corresponding SPA results are compared to those obtained from the full tensor-pomeron model for c.m. energies $\sqrt{s} = 10$ GeV and 100 GeV. The kinematic regions where the SPAs are a good representation of the full amplitude are determined. Finally we make some remarks on the type of fundamental information one could obtain from high-energy exclusive hadronic reactions without and with soft photon radiation.