The $γ^*γ^*$ Total Cross Section and the BFKL Pomeron at $e^{+}e^{-}$ Collider

Abstract

We present a numerical estimate of the $γ^* γ^*$ total cross section at LEP and at the designed $e^+e^-$ Next Linear Collider (NLC), based upon the BFKL Pomeron. We find for the linear collider 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. For LEP, although the number of events is substantially smaller, an initial study of this process is feasible.

Figures (5)

• Figure 1: Feynman diagram for the process $e^+e^- \to e^+e^- + \hbox{anything}$.
• Figure 2: The differential $e^+e^-$ cross section, multiplied by $y_1y_2$, as a function of the rapidity $Y=\log s/s_0$. The full curves denote the exact numerical calculation based upon eq. (4), the dashed curves belong to the analytic high energy approximation (7), and the dotted lines represent the Born approximation (no gluon production between the two quark pairs). The three curves on the left in each figure belong to LEP, the ones on the right to the Next Linear Collider NLC. 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, 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 left hand side corresponds to the LEP and the right hand side to the NLC situation. The solid curve shows the results of the exact calculation, the dashed curve shows the approximation and the dotted curve represents the Born result.
• Figure 4a: The total number of events per year ($3\cdot 10^7$ s) with detector cuts in angle taken into account. We have chosen $E_{tag}>20$ GeV, $\log s/s_0>2$, $2.5 <Q_i^2 <200$ GeV$^2$. The acceptance cut is $\theta_{tag}> 20 \,\hbox{mrad}$. The $y$-binning is the same as in fig. 3 and we have LEP on the left and NLC on the right hand side.
• Figure 4b: The same as in fig. 4a but with acceptance cut $\theta_{tag}> 60 \,\hbox{mrad}$.