Semihard and hard pion-pion scattering is of special interest because of its potential impact via final state interactions on the $\gamma +\overrightarrow{\gamma }{\pi }^{+}+{\pi }^{-}$ reaction in which perturbed QCD (PQCD) quark-exchange contribution is known to be short of strength. At moderate energies one can model large-angle pion-pion scattering by the PQCD two-gluon $\mathrm{}\left(2g\right)\mathrm{}$ exchange contribution. We discuss the onset of the dominance of the Glauber-Gribov-Landshoff (GGL) component of hard $2g$ exchange, which in the nonrelativistic approximation is free of suppression by the pion form factor, whereas in the relativistic light-cone approach it acquires a residual, albeit a weak, suppression and is free of the end-point contributions. Evaluation of the GGL amplitude with a model light-cone wave function consistent with the pion electromagnetic form factor data suggests that PQCD $2g$ exchange becomes substantial already at $|t|\gtrsim 1{\mathrm{GeV}}^{-2},$ but the PQCD exchange dominance is deferred to $|t|\gtrsim 3{\mathrm{GeV}}^{-2}$ because of competing multiple soft rescattering effects. Based on the NN and $\pi N$ total cross section data and Regge factorization, we evaluate the dominant soft contribution to the $\pi \pi$ total cross section and find the results consistent with the ones deduced earlier from the absorption model analysis of the $\pi \overrightarrow{N}XN,$ $X\Delta$ data.

• Received 15 February 2002

DOI:https://doi.org/10.1103/PhysRevC.66.055206