Incoherent pair generation in a beam-beam interaction simulation

This paper deals with two topics: the generation of incoherent pairs in two beam-beam simulation programs, GUINEA-PIG and CAIN, and the influence of the International Linear Collider (ILC) beam parameter choices on the background in the micro–vertex detector (VD) induced by direct hits. One of the processes involved in incoherent pair creation (IPC) is equivalent to a four fermions interaction and its cross section can be calculated exactly with a dedicated generator, BDK. A comparison of GUINEA-PIG and CAIN results with BDK allows to identify and quantify the uncertainties on IPC background predictions and to benchmark the GUINEA-PIG calculation. Based on this simulation and different VD designs, the five currently suggested ILC beam parameter sets have been compared regarding IPC background induced in the VD by direct IPC hits. We emphasize that the high luminosity set, as it is currently defined, would constrain both the choices of magnetic field and VD inner layer radius.

Figure 1

${log}_{10}(P_t)$ distribution of the pairs per bunch crossing before (empty histogram) and after (solid histogram) electromagnetic deflections from the opposite beam, $P_t$ being in $\mathrm{GeV}/c$.

Figure 2

$P_t$ versus $\theta$ distributions for IPC particles before (left-hand plot) and after (right-hand plot) electromagnetic deflections from the opposite beam.

Figure 3

${log}_{10}(E)$ spectra for the three incoherent pair creation processes, BH, LL, and BW modeled in GUINEA-PIG (left plot) and CAIN (right plot), $E$ being in GeV.

Figure 4

Transverse momentum, $P_t$, versus polar angle, $\theta$, for $e^{\pm }$ from IPC processes modeled in CAIN.

Figure 5

${log}_{10}(E)$ spectrum for the Landau-Lifshitz process in GUINEA-PIG (upper line), CAIN (lower thin line) and BDK (dashed line), $E$ being in GeV.

Figure 6

${log}_{10}(P_t)$ with $P_t$ in $\mathrm{GeV}/c$ (left plot) and polar angle (right plot) distributions for the Landau-Lifshitz process in GUINEA-PIG and BDK (dashed line).

Figure 7

Distribution of $P_t$ versus $\theta$ for electrons from IPC processes. The region corresponding to particles reaching the VD (circles) is indicated with the two dashed lines for the detector configuration described in the text. A thick dotted line highlights the edge of the beam-beam deflection induced accumulation zone.

Figure 8

Distribution of $P_t$ versus $\theta$ for electrons from IPC processes reaching the VD, before electromagnetic deflections (triangles) and after (circles).

Figure 9

Comparison of GUINEA-PIG and BDK (dashed thick line) photon virtuality decimal logarithm spectra, $Q$ being in GeV. The vertical dashed line indicates the position of the electron mass.

Figure 10

${log}_{10}(Q_{{\gamma }_1})$ versus ${log}_{10}(Q_{{\gamma }_2})$ in BDK simulation, $Q_{\gamma i}$ being in GeV. The highlighted points correspond to events with pair particles reaching the VD. The dashed lines indicate the position of the electron mass.

Figure 11

$P_t$ versus $\theta$ plane for the background electrons reaching the VD for $r_1=15\mathrm{mm}$. The black points are all the IPC particles, generated including the beam-size effect (see Sec. 2). Blue square-shaped points correspond to the background in the VD for a magnetic field of 5 T. Adding the green circle-shaped (red triangle-shaped) ones, it corresponds to the background for 4 T (3 T). The thick line indicates the edge of accumulation limit for the nominal design.