2.1 The LEP Machine

As shown in figure 2.1,

Figure 2.1: Location of the LEP collider at CERN. The positions of the four experiments (DELPHI, OPAL, ALEPH, and L3) and the SPS accelerator are also shown.

LEP is located on the Swiss-French border near Geneva. It is roughly circular (actually eight straight sections on either side of each cavern, interspersed with curved sections), 26.7 km in circumference and between 50 and 170 m below ground level.

The injector system, which starts at the main CERN site, is shown in figure 2.2.

Figure 2.2: The LEP injector complex. The two closest detector caverns on the LEP beamline (DELPHI and L3) are also shown.

The LEP Injector Linacs (LIL) produce electrons and positrons (the positrons from the collision of 200 MeV electrons with a tungsten converter), which are separately accelerated to 600 MeV. After storage in the Electron-Positron Accumulator (EPA), they are injected into the Proton Synchrotron (PS) and thence into the Super Proton Synchrotron (SPS); these accelerate the particles to 3.5 and 20 GeV respectively. After injection into LEP, the counter-rotating electrons and positrons are accelerated to 45 GeV using a radio frequency (RF) acceleration system powered by sixteen 1 MW klystrons, operating in two of the straight sections of the ring. The beams are bent into orbit by 3368 dipole magnets and focused with 808 quadrupole and 504 sextupole magnets. Superconducting quadrupoles provide additional focusing around the four interaction regions, where the beams are squeezed to a RMS width of about $(200 \times 5)$ $\ensuremathbox{\mu\mathrm{m}}^2$ ( $\ensuremathbox{\mathrm{horizontal}} \times \ensuremathbox{\mathrm{vertical}}$).

The expected event rate is

$$N = \int \sigma {\cal L}(t) \d {t} \,,$$ (2.1)

where $\sigma$ is the cross-section for the process in question ($\sim 30$ nb for $\ensuremathbox{\mathrm{e^+ e^-}}\ensuremathbox{\rightarrow}\ensuremathbox{\mathrm{Z^0}}\ensuremathbox{\rightarrow}\ensuremathbox{\mathrm{q\bar{q}}}$ at the $\ensuremathbox{\mathrm{Z^0}}$ peak^2.4). In LEP, the luminosity, ${\cal L}$, defined by equation 2.1, is approximately

$${\cal L}= \frac{n_b f N_{e^-} N_{e^+}}{4 \pi \sigma_x \sigma_y}$$ (2.2)

The $n_b$ bunches in each beam circulate round the ring with a frequency $f$. Each bunch contains $N_{e^-}$ electrons or $N_{e^+}$ positrons and has RMS dimensions $\sigma_x \times \sigma_y$ (given above) at the interaction point. Typical 1994 values $n_b = 8$ and $f = 11.2$ kHz (corresponding to a beam cross-over rate of 11 $\ensuremathbox{\mu\mathrm{s}}$), with $N_{e^+} = N_{e^-} = 1.7\E{11}$ give a luminosity, ${\cal L}$, of $2.1\E{31}\ \ensuremathbox{\mathrm{cm}}^{-2}\ensuremathbox{\mathrm{s}}^{-1}$.

The LEP design and commissioning is described in [17], while its subsequent operation and performance is summarized in [18]. As well as higher currents and better operational efficiency, the luminosity was improved using the Pretzel [19] and bunch train [20] schemes, which increased the number of bunches of $\ensuremathbox{\mathrm{electrons}}+\ensuremathbox{\mathrm{positrons}}$ in the machine from $4+4$ (1989-92) to $8+8$ (1992-4), and thence to $12+12$ (1995). Table 2.1 summarizes the luminosity and number of events observed by DELPHI.

Table: Integrated luminosity and total number of hadronic $\ensuremathbox{\mathrm{Z^0}}$ events [23] recorded by DELPHI in the period 1989-95. $N_{\ensuremathbox{\mathrm{had}}}$ is higher in 1992 and 1994 relative to the integrated luminosity because during the other years a significant amount of data was taken off-peak, where the cross-section is much lower.