From soft to hard regime in elastic pion-pion scattering above resonances

Semihard and hard pion-pion scattering is of special interest because of its potential impact via final state interactions on the γ+→γπ⁺+π^- 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 $(2g)$ 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|1GeV^-2, but the PQCD exchange dominance is deferred to |t|3GeV^-2 because of competing multiple soft rescattering effects. Based on the NN and πN total cross section data and Regge factorization, we evaluate the dominant soft contribution to the ππ total cross section and find the results consistent with the ones deduced earlier from the absorption model analysis of the π→NXN, XΔ data.