High-Energy QCD Asymptotics of Photon-Photon Collisions

Abstract

The high-energy behaviour of the total cross section for highly virtual photons, as predicted by the BFKL equation at next-to-leading order (NLO) in QCD, is discussed. The NLO BFKL predictions, improved by the BLM optimal scale setting, are in good agreement with recent OPAL and L3 data at CERN LEP2. NLO BFKL predictions for future linear colliders are presented.

Figures (4)

• Figure 1: Photon--Photon collisions in QED: (a) electron-box diagram: $\sigma \sim \alpha^2 (\log s)/s$; (b) one-photon exchange diagram: $\sigma \sim \alpha^4 s^{0}$ ; (c) a typical higher-order diagram; its resummation leads to $\sigma \sim \alpha^4 s^{\omega}$, $\omega = \frac{11}{32} \pi \alpha^2$Gribov70.
• Figure 2: High-energy photon-photon collisions in QCD: (a) quark-box diagram: $\sigma \sim \alpha^2 (\log s)/s$; (b) one-gluon exchange diagram: $\sigma \sim \alpha^2 \alpha_S^2 s^{0}$; (c) a typical higher-order diagram; its resummation leads to $\sigma \sim \alpha^2 \alpha_S^2 s^{\omega}$, $\omega_{LO} = 12 \, \ln2 \, ( \alpha_S/\pi ) \simeq 0.55$FKL and $\omega_{NLO} =$ 0.13-0.18 BFKLP.
• Figure 3: The energy dependence of the total cross section for highly virtual photon--photon collisions predicted by the BLM scale-fixed NLO BFKL KLPBFKLP01BFKLP compared with OPAL OPAL and L3 L3 data from LEP2 at CERN. The (solid) dashed curves correspond to the (N)LO BFKL predictions for two different choices of the Regge scale: $s_0= Q^2$ for upper curves and $s_0=4 Q^2$ for lower curves.
• Figure 4: The energy dependence of the total cross section for virtual photon--photon collisions predicted by the NLO BFKL for future linear colliders. The solid curves correspond to the BLM scale-fixed NLO BFKL predictions with $s_0=Q^2$ (upper curve) and $s_0=4 Q^2$ (lower curve). The dotted curve shows the one-gluon exchange contribution.