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of the L1T operations are either simple arithmetic operations or functions using
memory lookup tables where an address of data produces a result previously written
into the memory.
The L1T requirements evolve with the experiment luminosity, energy and event
pile-up (number of p–p collisions per beam crossing). For example for the LHC
trigger systems [20], algorithms used by the ATLAS [13] and CMS [14] experiments
at the LHC during the period before 2014 (Run-1) were optimized for 7–8 TeV
center-of-mass energy, PU up to 40 due to the 20 MHz beam crossing frequency
and luminosities up to 7 × 10 −33 cm 2 s −1 , whereas afterwards (Run-2) these were
optimized for a 13 TeV center-of-mass energy and PU above 50 due to the 40 MHz
beam crossing frequency and luminosities exceeding 15 × 10 −33 cm 2 s −1 [15, 16].
12.1.3 Muon Triggers
The design of L1T muon trigger logic depends on the detectors being used to generate the trigger information. These detectors include those with timing resolution and
prompt signals that are generally less than the time between bunch crossings such
as Resistive Plate Chambers (RPCs) and Thin Gap Chambers (TGCs). They also
include special signal handling of detectors with individual signals and resolution
greater than the bunch crossing time, such as Cathode Strip Chambers (CSCs)
and Drift Tube Chambers (DTs). For these detectors, offset detector planes, frontend logic that processes over the drift time, and combinations of planes provide
identification of the bunch crossing associated with the muon passage. Another
important feature in muon trigger design is whether the muon chamber measuring
stations are placed in a magnetic field in air or embedded in iron. In the former case,
the muon momentum resolution is usually sufficient to provide an efficient threshold
up to relatively high p T . In the latter case, information from the tracking detectors
is needed to provide a sufficiently sharp threshold.
L1T muon algorithms depend on comparison of tracks of hits with predefined
geometrical patterns such as roads. For example, the ATLAS muon trigger employs
RPCs and TGCs in an air-core magnetic field and the trigger algorithm uses
Coincidence Windows that start with a hit in a central “pivot plane” and searches
for time-correlated hits within an η–φ window in a “confirm plane” [1]. Different
“confirm planes” are used for low and high p T muons, as is shown in Fig. 12.2.
The RPC barrel algorithm extrapolates hits in the middle RPC 2 station to a point
and coincidence window in the innermost RPC 1 station along a straight line to
the nominal interaction point. The size of this coincidence window depends on the
muon’s bend in the magnetic field. A low-p T candidate is found if there is one hit
in this window and hits in both views and planes of either RPC 1 or RPC 2. If there
is also a hit in RPC 3, then a high-p T candidate has been found. For Run 2 ATLAS
commissioned a fourth layer of barrel RPCs that improved the acceptance and added
new trigger logic to the end-cap requiring additional coincidences with the TGC’s
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