Accidental background

The accidental background which arrises from $\mu e$ events where the muon and the electron are uncorrelated to each other is expected to produce a flat distribution in time. A typical source of accidentals will be produced by electrons scattered on the TPC frames or on the wall of the pressure chamber into the acceptance cone of a stopping muon. In the test runs with the prototype TPC, we observed with the two scintillator telescopes (accepted solid angle $\sim 5\%$ each) at incident muon rates of 15-20 kHz the following accidental ratios (defined as accidental level divided by the true $\mu e$ signal at time 0):

• 4.5$\cdot 10^{-2}$ using no pile-up rejection, no e-tracking
• 0.9$\cdot 10^{-3}$ using global pile-up rejection, no e-tracking
• $<$0.8$\cdot 10^{-5}$ using global pile-up rejection and e-tracking
• 1.5$\cdot 10^{-4}$ using local pile-up rejection and e-tracking

Obviously, pile-up rejection and also electron back tracking to the muon stop location strongly reduces the accidental level. The global pile-up condition - on the other hand - may severely limit the data taking rate and thus the total reachable statistics. Fortunately, we can analyze the data in several ways using various rejection conditions, though the optimal beam rate is dependent on the choice.

We have made a study to understand which accidental levels are acceptable for reaching the statistical $10^{-5}$ accuracy of a $10^{10}$ event sample. A statistical exponential time distribution of $10^{10}$ events with a flat accidental admixture was generated using a fixed slope parameter $\lambda$ and then fitted back in a time region 0.6 - 20 $\mu s$ using CERN library routines (PAW). We found that even an accidental background of $10^{-2}$ yielded the correct $\lambda$ within the statistical errors and without any significant reduction of fitting accuracy. In reality, our experiment will produce data at much smaller accidental levels than $10^{-2}$. This helps to avoid systematic deviations which could arrise due to unexpected fluctuations of the accidental distribution.