Muons are easily distinguishable from electrons and jets due to their relatively weak interaction with the detector material. At typical production energies their lifetime in the lab frame permits them to traverse the entire detector before decaying, leav- ing a unique signature in the form of an ID track, minimal energy losses in the calorimeters and a track in the muon spectrometer located beyond the calorimeters. Toroid magnets immerse the muon spectrometer in a magnetic field that allows for a separate momentum measurement (see section 2.3.4). Background rejection rates and momentum precision are both excellent, making muons ideal trigger signatures.
3.5.1 Muon Trigger in τ`τhad
The muon trigger follows the ATLAS three-level trigger design [120]. The L1 hard- ware level triggers on coincident hits in the RPC inside|η|<1.05 and TGC in the endcap region 1.05<|η|<2.4 of the muon spectrometer (MS). The muon momen- tum is estimated using the width of the coincidence window and is passed on to the subsequent trigger layers together with the geometrical location of the hits. The data output from L1 is reduced by defining regions of interest (ROI) around the set of hits. Cables and other equipment servicing the ID and calorimeters occupy the region at η = 0 producing a ‘crack’ that limits the acceptance of the MS and hence the L1 trigger. The software L2 trigger has access to precision tracking infor- mation from the MDT modules within the ROI. By referring to fast lookup-tables containing pre-defined track shapes matched to momentum values it is possible to quickly assign a transverse momentum estimate to the tracks. The tracks from the inner detector are also matched to the tracks from the MS to further increase the precision. Background rejection can be added to a chain through isolation variables calculated from neighbouring tracks to the muon candidate as well as reconstructed calorimeter energy deposits in cones around the muon candidate track (see also sec- tion 2.5). At EF level the employed algorithms are functionally very close to their offline counterparts and have access to the full detector information. Combined ID and MS tracks are reconstructed using two algorithms that use either an ID or MS track as the seed and subsequently extrapolate it outward to the MS or inward to the ID. These are called inside-out and outside-in algorithms respectively.
The τ`τhad decay channel uses a single muon trigger with the chain name
mu24i_tight. The number 24 following mu refers to the online transverse momen-
tum threshold imposed by the trigger in GeV, which has been chosen such that unprescaled operation is possible within the bandwidth of the trigger system. Thei
(probe) [GeV] T p 0 20 40 60 80 100 120 140 160 Efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ATLAS Preliminary = 8 TeV s , -1 L dt = 20.3 fb ∫ |<1.05 η | Data (2012) MC (probe) [GeV] T p 0 20 40 60 80 100 120 140 160 Data / M C 0.9 0.95 1 1.05 0 (a) (probe) [GeV] T p 0 20 40 60 80 100 120 140 160 Efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ATLAS Preliminary = 8 TeV s , -1 L dt = 20.3 fb ∫ |>1.05 η | Data (2012) MC (probe) [GeV] T p 0 20 40 60 80 100 120 140 160 Data / M C 0.9 0.95 1 1.05 0 (b)
Figure 3.7: Efficiencies of passing the single muon triggersmu24i_tightormu36_-
tight measured in Z → µµ events using a tag-and-probe method in the barrel (a)
or endcap (b) regions plotted as a function of the probe muon pT. The efficiency
ratios between data and MC are in good agreement within the momentum region shown [94].
indicates the use of isolation criteria to reduce backgrounds. A procedure similar to the electron case is used to determine the trigger efficiency by analysing a sample of Z→µµevents using a tag-and-probe method [120]. An isolated tag muon candidate track is required to be geometrically matched with the initial trigger object, while an isolated probe muon candidate must have opposite charge. Requiring that the invariant mass of the muon system must be compatible with theZ mass results in a high-purity sample with backgrounds from other processes representing less than 1% of the events. Trigger efficiencies at√s= 8 TeV are shown for both data and simulated samples in figure 3.7 as a function of the muon transverse momentum. Differences of a few percent between data and MC are used to correct the simulated samples used in the analysis.
3.5.2 Muon Reconstruction and Identification
The low-background environment for muons in ATLAS allows the reconstruction and identification algorithms to be designed with precision momentum measurements as the main goal. Three different reconstruction algorithms are defined depending on the available data from the detector subsystems [121]:
• Stand-alone (SA): Only MS information is included in the muon reconstruc-
tion. Tracks are extrapolated back to the interaction point while taking into account the expected energy loss in the calorimeters.
(a) (b)
Figure 3.8: Muon reconstruction efficiencies as a function of transverse momentum
(a) and pseudo-rapidity (b) measured in a Z → µµ sample using a tag-and-probe
method. Discrepancies of roughly 1–2% between data and simulated samples are observed [121].
• Segment-tagged (ST): These objects are constructed from ID tracks with at
least one possible associated MS track.
• Combined (CB): A subset of segment-tagged tracks, the combined muon ob-
jects combine ID and MS tracks while imposing quality criteria on the covari- ance matrices of the two track fits. The inclusion of both subdetectors and covariance matrix requirements ensures a higher momentum resolution and signal purity than the other reconstruction algorithms.
The analysis presented in this thesis uses only combined muons. An important pre- requisite to optimal muon reconstruction performance is detailed knowledge of the misalignment of the muon chambers. This can be measured in studies of cosmic ray events or in separate data runs where the toroid magnets are switched off. Tech- nical limitations of the detector result in pseudo-rapidity intervals where the muon reconstruction efficiency is significantly lower than in the rest of the tracking accep- tance inside |η|<2.5. As previously mentioned, the region at|η|= 0 has support structures and service equipment that limit the availability of the MS, while in the region 1.1 < η < 1.3 some chambers were not installed until Run 2, making them unavailable in the 2012 dataset. The efficiencies of muon reconstruction and identi- fication are measured in Z → µµ events following the same tag-and-probe method used to find the trigger efficiencies. Figure 3.8 shows the reconstruction efficiency as a function of transverse momentum and pseudo-rapidity, where the latter has visible drops at the mentioned regions with sub-optimal coverage. The efficiency
is well-described in simulation, having relative errors of 1–2% [121] compared to data. Scale factors are derived from these ratios and applied as corrections to the simulated samples.
In addition to efficiency discrepancies between data and MC, the scale of the muon momentum also needs to be investigated. The relative momentum resolution can be parametrised as
σ(pT)/pT =a⊕(b×pT), (3.6)
whereadenotes a constant contribution originating from multiple scattering and b is a contribution proportional to the transverse momentum due to the spatial resolu- tion of the detector. The parameters are derived in bins of pseudo-rapidity through studies using samples ofZ → µµ,J/Ψ→µµand Υ→µµevents. The momentum scale itself is accurate to within the order of a permille, while the constant and pT-dependent resolution terms are of the order±2%.