Background Suppression by Time Information

Different simulation modes are used to study the suppression of combinatorial background through the time information. The expected background topologies are needed to estimate the suppression by the timing cuts whereas signal-like events are required to study the inef-ficiencies added by this cuts. Defaultµ → eee signal like events are generated with decay products randomly distributed in the allowed phase space. Table 10.3 gives an overview of the abundance of the different track types in the different simulation modes.

10.3. IMPACT OF THE SCINTILLATING FIBRE DETECTOR

Table 10.3:Abundance of different track types in different simulation modes: the actual muon de-cay is dominated by Michel dede-cays,µ →eee signal decays and Bhabha background.Recstands for reconstructed by the track finding algorithms andcandfor tracks which are part of a signal candid-ate triplet which fulfils the cuts presented in Table 10.2.

track type fraction [%]

Michel µ→eee Bhabha rec rec cand rec cand 4-hit tracks 24.7 25.1 20.1 26.0 24.2 6-hit tracks 65.4 65.0 68.2 63.9 60.6

8-hit tracks 9.9 9.9 11.7 10.1 15.2

tracks which reach the tiles 43.2 41.3 42.7 42.2 32.2

Simulation of Combinatorial Background for Time Suppression Studies The dominant combinatorial background consists of the superposition of a positron from a Michel decay which undergoes Bhabha scattering with an electron in the target material, with a second positron from another Michel decay. Besides the vectorial momentum (∑

⃗ p_i = 0), the energy (∑

E_i =m_µ) and spatial vertex constraints, the combinatorial background of this topology is additionally suppressed by the requirement of a time coincidence. It is assumed, that the time suppression factorizes from the other suppression factors. Hence topologies of Bhabha pairs in combination with a positron with a common vertex, and which also fulfil the momentum and energy signal candidate cuts shown in Table 10.2 are generated at a common vertex. Weighted events are used to speed up the simulation. The weight of an event is defined by the matrix element of the Bhabha scattering and the probability of the two Michel decays.

Time suppression of combinatorial background with the given event topology is studied through the random distribution of the decay time of the additional Michel positron,

Achievable Background Suppression

Figure 10.3 shows the distribution of the time separation, as defined in Equation 10.7, for signal and Bhabha background events. Furthermore, a detector with a perfect Gaussian distributed times according to the resolutions and efficiencies stated in Table 10.1 and track abundance as summarized in Table 10.3 is simulated denoted by refer-ence model. While the background events are distributed uniformly, the distribution of sig-nal candidates peaks towards zero. Note that the distribution of events from the simulation framework shows a larger tail than the reference model caused by tails in the simulated time resolution distribution with respect to a Gaussian shape.

The tracker is assumed to provide time information precise enough to assign the hits to individual 50 ns reconstruction frames. In the presented studies no further time information from the pixel tracker is used. Figure 10.4a shows the signal selection efficiency of the tim-ing cut and the Bhabha background suppression due to the additional time information from

CHAPTER 10. TIMING IN THE RECONSTRUCTION AND ANALYSIS FRAMEWORK

0 2 4 6 8 10

cut on time separation ts [ns]

counts

signal events

signal events (ref model) Bhabha background events

Figure 10.3:Distribution of the time separationt_sfor signal ( , ) and Bhabha background ( ) events. A reference model ( ) with event times following perfectly Gaussian distribution shown for comparison. The signal events from the simulation framework ( ) show larger tails than the refer-ence model ( ). The different distribution of signal and background events is used to distinguish them statistically.

the scintillating fibre and tile detector. Only track candidates with all three tracks detected in the timing detectors are shown. Such track candidates are denoted as timing required. This requirement results in a loss of signal efficiency of 2.7 %. Figure 10.4 shows the achievable sup-pression of Bhabha background by time information as a function of the signal event selection efficiency. The suppression is displayed forallevents and fortiming required events where the inefficiency due to this requirement is taken into account. The same reference model as above is shown as comparison. The tails in the simulated event time distributions cause the suppression to be slightly smaller than in the reference model. The efficiency converges slower towards one. Furthermore, the results obtained by cutting onχ²_timing, as described in Equation 10.4, is shown. For Bhabha background, a cut on the time separation t_sperforms better.

The working point of the time cut can be adjusted by the needs of an analysis, as theDAQ

works independently of these cuts. At a signal selection efficiency of 80 % a Bhabha back-ground suppression ofO(85) can be achieved.

The performance of the individual sub-detectors, either fibre or tile, for the different cuts are illustrated in Figure 10.5a. In the presence of only the tile detector, significant suppressions are only achieved⁵if all three particles of a candidate end up in this sub-detector. Hence, the efficiency for long tracks reduces to (53 %)³ =∼15 %. In the sole presence of the fibre detector and perfectly Gaussian distributed event times the suppression at a given efficiency is reduced to (66.7±0.5) %. Both timing detectors are required to achieve the presented suppressions.

5for cuts ont_s.

10.3. IMPACT OF THE SCINTILLATING FIBRE DETECTOR

0 2 4 6 8 10

cut on time distribution ts 0

(a)Additional Bhabha background suppression factor due to the tim-ing detectors and signal selection efficiency as a function of the cut on time separationt_s.

(b)Suppression versus efficiency for all track candidates ( ) and with required timing( ) for all three tracks. Furthermore, the performance of a cut onχ²_timing( ) can be compared to the default cut ont_s.

Figure 10.4:Suppression of Bhabha background due to the time information from the fibre and tile sub-detectors in relation to the relative signal selection efficiency. The additional suppression within 50 ns reconstruction frames is presented. Eitherall eventsor only those candidates which all three tracks have a hit in the timing detectors (timing required) can be used. A reference model (ref model) as in Figure 10.3 is shown for comparison.

CHAPTER 10. TIMING IN THE RECONSTRUCTION AND ANALYSIS

(a)Timing suppression of Bhabha background as a function of the relative selection efficiency of signal candidates.

(b)Timing suppression of Bhabha background at relative signal selection efficiency of 90 % as a function of the fibre detector’s mean res-olution. The expected resolution of 260 ps is highlighted.

Figure 10.5:Timing suppression of Bhabha background in the presence of only fibre detector ( ), only the tile detector ( ) and the combination of the two detectors ( ) The dashed lines ( ) show the suppressions ifall eventsare used, whereas the solid lines ( ) show the suppression if timing is required for all three tracks of a candidate (timing required). The here used reference model, where the event times are distributed according to a perfect Gaussian, yields upper limits.

The dependency of the suppression on the fibre detector’s resolution at a relative signal selection efficiency of 90 % is illustrated in Figure 10.5b. Purely Gaussian time distributions are employed to obtain upper limits. Small improvements in the detectors time resolution show significant effect on the possible Bhabha background suppression.