Statistics and rates

We plan to analyze the data with two main and complementary methods.

• global pile-up free data. Only events are analyzed which did not have another muon entering the TPC within $T_{PU}$typeset@protect @@footnote SF@gobble@opt Different time ranges from 10-20s will be investigated and the consistency verified. . This analysis is particularly clean and simple, and thus ideally suited for a precision experiment. Moreover it allows loose vertex cuts, thereby reducing the experimental sensitivity to deuterium diffusion. It has the disadvantage of pile-up losses according to .
• local pile-up free data. In order to reduce these losses the TPC volume is subdivided in smaller volumes during the analysis, by requiring no other local muon stop inside a cut volume around the electron reconstructed vector. In this way events can be analyzed where several simultaneous muons stop during the measurement/drift-time interval of the TPC. The vertex matching suppresses the accidental background from uncorrelated muons. The rate of accepted events is higher, but time dependent losses due to two event correlations and diffusion become a more serious correction.

The choice between the two analysis methods is made off-line, as in our experiment contiguous event-blocks containing all information are recorded always. Thus the data is collected simultaneously for both methods. The expected rates and measuring times for potential experimental setups and reconstructed events are compiled in table 8. In addition to the two present methods the table also indicates the potential of data taking with a chopped high intensity muon beam muon-on-request (MORE), which was proposed in Refs. [18,24,25]. The latter method would combine the advantages of the other methods, namely high event rates consisting of single isolated muons. As a bottom line, a net measurement time of 2x20=40 days is required for reconstructed and events. This running time seems acceptable for a fundamental precision experiment, consistent with the current trend to trade longer measuring times for smaller systematic corrections.

Table 8: Statistics estimates for the two main analysis methods and the potential future MORE beam

	local PU free	global PU free	MORE	source for estimate
incident flux(kHz)	30	30	70	measured
efficiencies
e acceptance	0.7	0.7	0.7	Monte Carlo
e efficiency, reconstruction	0.95	0.95	0.95	measured, MC
stopping	0.8	0.8	0.8	measured
fit time window	0.9	0.9	0.9	measured
reconstruction
pile-up free	0.70	0.40	1.0	estimate / equ. in sect 5.3
total acceptance	0.33	0.20	0.48
event rate (kHz)	10.	5.8	33.
days for reconst. events	11.5	20.0	3.5