Overview

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Overview

Several important issues in the detector optimization and data analysis have to be addressed by Monte Carlo simulation.

Basic detector performance. A Monte Carlo program GMu based on Geant3 was developed which includes the main detector components of the proposed setup and tracks individual $\mu$ -e decay sequences. It establishes the expected detector performance and defines the granularity required in the tracking devices.
Simulation of overlapping events. Extensive studies of systematics associated with the reconstruction of overlapping events were performed with a simplified detector model, which allowed the generation and analysis of statistics samples of 10 $^{9}$ events with relatively modest means. These studies revealed subtle correlated losses (``double kill'') and are documented in report [2]. In the mean time we have drastically simplified the experimental strategy by avoiding electron tracking in the TPC for the main data sample. Accordingly the systematic problems discussed in this earlier report are significantly eleviated.
Simulation of specific physics processes. This includes mainly issues related to the physical processes of muonic hydrogen atoms relevant for the experiment, in particular diffusion of $\mu p$ and $\mu d$ atoms and related fusion processes. Some of these results are presented in section 5.4.3.
Distortions and background to high statistics time distributions. Their effect was studied by generating analytical expressions of the expected time distributions with appropriate disturbing effects, then smearing these ideal data points with Monte Carlo statistics and finally fitting them to quantify the effect on the lifetime measurement. Examples of this kind are studies of the effect of $\mu d$ diffusion, accidental background and $\mu SR$ oscillations.

**Figure 21:** Simulated event showing the different detector components included in the present Monte Carlo. The dashed lines are unobserved neutrinos.
$\resizebox*{0.6\textwidth}{0.5\textheight} {\includegraphics{for_peter2.eps}}$

These simulation studies will be further refined during the construction period of the final $\mu CAP$ detector. The main work will concentrate on detailed modeling of the detector response and the integration of the above mentioned special physics processes, not covered in Geant, into GMu. Furthermore the GMu generated data has to be mapped onto the event-block structure of the final experiment, so that the whole analysis chain is applied to and tested with MC data. In this way the following issues will be investigated:

Detailed studies of overlapping events (local pile-up free events). The analysis of overlapping events inherently is more complex, than that of single muon events (global pile-up free events). The time dependence of the efficiency due to two-event correlations has to be carefully modeled and compared to the data. Effects will be visualized with limited statistics by deteriorating critical parameters (like detection inefficiencies etc.) compared to the expected performance.
The selection cuts and efficiency for special classes of sub-events (like diffusion etc.) should be optimized with Monte Carlo and compared to the data, to improve the microscopic understanding of the detector.
Brute force Monte Carlo simulation of 10 $^{10}$ events is a major task. The current GMu generates about 3x10 $^{6}$ events/day on a 800 MHz Pentium. Thus about 5000 CPU days are required to obtain a 10 ppm statistics of reconstructed events. Such a calculation seems feasible at the Cray-T3E of the National Energy Research Center at LBNL, where the UC Berkeley group has an approved grant for this project. However, such an effort can only be made for the final analysis and even there the benefits of a full simulation have to be weighted against more direct experimental consistency checks. A problem, where medium scale computation is informative, is the local pile-up analysis. For that case, a large statistics can be generated by mixing events from a limited pool of fully simulated GMu events. The track reconstruction problems resulting from topologically overlapping events and potentially associated detector efficiencies and dead times can be studied with high precision by generating the random event ordering and some less CPU-intensive event properties (like decay time) during the mixing stage. (We have demonstrated this method in Ref. [21].)

Next: Basic detector performance Up: Detector simulation Previous: Detector simulation Contents

Peter Kammel 2001-02-04