Probing the QCD pomeron in doubly tagged e^+ e^- collisions

Abstract

We calculate the total cross-section for $γ^* γ^*$ collisions and for the process $e^+ e^- \to e^+ e^- + hadrons$ with two tagged leptons assuming dominance of the QCD pomeron exchange. We solve the BFKL equation including the dominant subleading effects generated by the consistency constraint which restricts the available phase-space of the emitted gluons to the region inwhich the virtuality of the exchanged gluons is dominated by their transverse momentum squared. Estimate of the possible soft pomeron contribution to the $γ^* γ^*$ cross-section is also presented. At very high CM energies $W$ the calculated total $γ^* γ^*$ cross-section exhibits effective power-law $(W^2)^λ$ behaviour with $λ\sim 0.3$. We confront our results with the recent measurements at LEP and give predictions for the energies which can be accessible at TESLA and at other future linear $e^+ e^-$ colliders.

Figures (2)

• Figure 1: The QCD pomeron exchange mechanism of the process $\gamma_1 ^* (Q_1 ^2) \gamma_2 ^* (Q_2 ^2) \to hadrons$.
• Figure 2: Energy dependence of the cross-section $\sigma^{TT} _{\gamma^* \gamma^*}(Q_1 ^2, Q_2 ^2, W^2)$ for the process $\gamma^*(Q_1 ^2) \gamma^*(Q_2^2) \to hadrons$ for various choices of photon virtualitities $Q^2 = Q_1 ^2 = Q_2 ^2$: a) Complete i.e. including soft and QCD pomeron contributions results corresponding to Eq. (\ref{['csx']}). For each choice of the virtualitity $Q^2$ four curves are shown taking into account hard effects only ("hard part"), hard amplitude with soft pomeron contributions added in the source term of the BFKL equation ("mixed"), the full cross-section including both soft and hard pomeron contributions ("full result"). We also show the "full result" with the low scale of $\alpha_s$ in the impact factors: $\mu^2 = (k^2 + m_q^2)/4$. b) Comparison of the complete contribution of the perturbative QCD pomeron to the cross-section $\sigma^{TT} _{\gamma^* \gamma^*}(Q ^2, Q ^2, W^2)$ (continous line) with its Born term component corresponding to the two gluon exchange mechanism (dotted line).