Quark-Antiquark Exchange in $γ^* γ^*$ Scattering

TL;DR

This work develops a perturbative QCD description of quark–antiquark exchange in high-energy γ^*γ^* scattering by summing leading double-logarithmic ladder diagrams. It presents three complementary methods—the Bethe–Salpeter ladder, infrared evolution equations (IREE), and reggeon Green’s functions—to obtain closed-form expressions for the even-signature amplitude, yielding a perturbative hard region with intercept $ω_0 = \sqrt{4λ}$ and capturing the energy dependence through Bessel-function structures like $I_0$ (and $I_2$ in certain regimes). The results imply a sizable perturbative secondary reggeon contribution to σ^{γ^*γ^*}_{tot}, with a mild dependence on the infrared cutoff μ_0$ and clear DIS low-$x$ limits, offering a bridge between LEP data and a perturbative mechanism. These findings highlight a perturbative alternative to nonperturbative reggeon exchange in the hard domain and set the stage for extending the analysis to flavor-singlet exchange and nonzero momentum transfer.

Abstract

We calculate the high energy behavior of quark-antiquark exchange in $γ^* γ^*$ elastic scattering by summing, to all orders, the leading double logarithmic contributions of the QCD ladder diagrams. Motivation comes from the LEP data for $σ_{tot}^{γ^* γ^*}$ which indicate the need for secondary reggeon exchange. We show that, for large photon virtualities, this exchange is calculable in pQCD. This applies, in particular, to parts of the LEP kinematic region.