The gamma* gamma* Total Cross Section and the BFKL Pomeron at the 500 GeV e+e- Collider

TL;DR

The paper analyzes the γ* γ* total cross section at a 500 GeV e+e− collider within the BFKL Pomeron framework, deriving the ν-integral expression and explicit photon impact factors while assessing infrared diffusion effects. It demonstrates a clear BFKL energy rise that dominates over the 2-gluon baseline for realistic Q^2, and provides projected event rates under plausible luminosity and detector constraints. The study highlights the critical role of small-angle, double-tagging measurements to access the required kinematics, and discusses how unitarity corrections at high energy could manifest as deviations from the pure BFKL power law. Overall, it offers a concrete experimental path to test BFKL dynamics and potentially observe diffusion-induced effects at a future linear collider.

Abstract

We present a numerical estimate of the $γ^* γ^*$ total cross section at the designed 500 GeV $e^+e^-$ Linear Collider, based upon the BFKL Pomeron. We find that the event rate is substantial provided electrons scattered under small angles can be detected, and a measurement of this cross section provides an excellent test of the BFKL Pomeron.

Figures (4)

• Figure 1: Feynman diagram for the process $e^+e^- \to e^+e^- + \hbox{anything}$.
• Figure 2: The differential $e^+e^-$ total cross section, multiplied by $y_1y_2$, as a function of the rapidity $Y=\log s/s_0$. The full curves denote the numerical calculation based upon eq. (\ref{['4']}) and the dashed lines represent the 2--gluon approximation (no gluon production between the two quark pairs). The two curves on the left in each figure are for LEP I, the ones on the right for the 500 GeV $e^+e^-$ Linear Collider. We have chosen $y_1=y_2$ and $Q_1^2=Q_2^2 = 10 \,\hbox{GeV}^2$ (left hand figure) resp. $Q_1^2=Q_2^2 = 25 \,\hbox{GeV}^2$ (right hand figure).
• Figure 3: The total number of events per year ($3\cdot 10^7 \hbox{s}$), as a function of $y_1$. The variables $Q_i^2$ ($5<Q_i^2<200$ GeV$^2$) and $y_2$ ($0.1<y_2<0.9$) are integrated. The solid curve shows the results of the BFKL calculation and the dashed curve represents the 2--gluon result.
• Figure 4: The total number of events per 1000 $\hbox{pb}^{-1}$ with detector cuts in angle taken into account. This would typically correspond to one month of data taking at the design luminosity. We have chosen $E_{tag}>20$ GeV, $\log s/s_0>2$, $2.5 <Q_i^2 <200$ GeV$^2$. The acceptance cuts are $\theta_{tag}> 30 \,\hbox{mrad}$ (left) and $\theta_{tag}> 80 \,\hbox{mrad}$ (right). The $y$--binning is the same as in fig. 3. Solid lines are again the prediction based on BFKL, dashed lines represent the 2--gluon exchange.