Virtual photon scattering at high energies as a probe of the short distance pomeron

TL;DR

The paper investigates high-energy, off-shell photon–photon scattering as a clean probe of perturbative QCD pomeron dynamics via the BFKL framework. It develops both Born two-gluon exchange and leading-log resummed calculations, detailing the energy dependence, polarization structure, and Regge-factorization properties through Mellin-space formulations and photon-color functions. It also assesses the virtuality and DIS connections, contrasts soft versus hard scattering regimes, and provides numerical estimates for event rates at LEP200 and a future linear collider, highlighting sizable theoretical uncertainties that motivate higher-order work. Overall, the study argues that gamma* gamma* scattering at high energies and large Q^2 offers a practical avenue to test BFKL predictions and to explore the transition to non-perturbative dynamics. The results indicate measurable enhancements over Born predictions and emphasize the role of scale choices and unitarity effects in shaping the observable outcomes.

Abstract

Perturbative QCD predicts the behavior of scattering at high energies and fixed (sufficiently large) transferred momenta in terms of the BFKL pomeron (or short distance pomeron). We study the prospects for testing these predictions in two-photon processes at LEP200 and a possible future e+ e- collider. We argue that the total cross section for scattering two photons sufficiently far off shell provides a clean probe of BFKL dynamics. The photons act as color dipoles with small transverse size, so that the QCD interactions can be treated perturbatively. We analyze the properties of the QCD result and the possibility of testing them experimentally. We give an estimate of the rates expected and discuss the uncertainties of these results associated with the accuracy of the present theoretical calculations.

Figures (17)

• Figure 1: The photon-photon scattering process in $e^+ e^-$ collisions.
• Figure 2: One of the two-gluon exchange graphs contributing to the high energy $\gamma^* \gamma^*$ cross section in the Born approximation. The gluons can be attached to the quark lines in $2^4$ different ways.
• Figure 3: The ${{\bf k}}^2 / Q^2$ dependence of the color functions $G_1$ (see Sec. \ref{['sec:notations']}) and $G_2$ (see Sec. \ref{['sec:polarization']}). We plot the normalized functions ${\tilde{G}} = G / (4 \, \alpha \, \alpha_s \, \sum_q e^2_q)$.
• Figure 4: The high-energy $\gamma^* \gamma^*$ cross section in the Born approximation as a function of the ratio $r \equiv Q_A / Q_B$ between the photon virtualities. The solid line is the rescaled cross section $\tilde{\sigma}(r)$ defined in Eq. (\ref{['tildesigmadef']}). The dashed line is the polarization asymmetry discussed in Sec. \ref{['sec:polarization']} (see Eq. (\ref{['convsiasymm']})), multiplied by $10^2$.
• Figure 5: Factorized structure of the virtual photon cross section in the high energy limit.