1. LVL1 Workshop, CERN, 16/07/99Alan Watson (by proxy) ATLAS Jet Trigger Algorithm Performance Requirements:  Good jet E T resolution Sharp threshold Minimise rate for inclusive trigger  Good multijet performance Ability to resolve nearby (non-overlapping) jets Ability to classify events by multiplicity  Good jet coordinate precision Required for RoI-driven Level 2  Robustness and flexibility Robust against noise & pileup Flexible as do not know what we will want to trigger on in 2005/6/7/8/... Technical Requirements:  Manageable complexity of implementation! Not necessarily minimal complexity Must integrate well with rest of system

2. LVL1 Workshop, CERN, 16/07/99Alan Watson (by proxy) Elements of Jet Algorithm Overlapping, sliding windows  Architecture forces sliding window algorithm  Overlapping to optimize jet containment Cluster Size  Main determinant of single jet resolution Jet E T containment vs noise/pileup summation  Same size may not be optimal for all conditions and tasks (e.g. low-E T multijets) Step Size  Constrains possible cluster sizes  Major factor in multijet performance Limits how close jets can be resolved  Limits RoI coordinate precision “Declustering” Algorithm  Resolves overlaps & allows jet count  Main factor in multijet performance Determines how close jets can be resolved  Major factor in RoI coordinate precision

3. LVL1 Workshop, CERN, 16/07/99Alan Watson (by proxy) Overlapping Windows: Problem of Boundaries:  Unless windows >> jets, overlap required to optimise E T containment Drawback of Overlap:  Several windows overlapping jet may all pass threshold  cluster of hits from 1 object  Additional “declustering” logic required to resolve overlaps and allow jet multiplicity to be determined Non-OverlappingOverlapping 2 mid-E T objects1 high-E T object

4. LVL1 Workshop, CERN, 16/07/99Alan Watson (by proxy) Declustering and RoIs Two Tasks:  Count jets, resolving overlapping objects  Identify RoI coordinates for LVL2 One Solution:  Define an “RoI Cluster” jet cluster or part of jet cluster (“jet core”)  Require it is more energetic than neighbouring objects of same type  Centre of such a “local ET maximum” = RoI coordinate  Since neighbouring RoI clusters cannot both pass, 1 jet cannot produce > 1 RoI  so same requirement resolves multiple- counting due to overlaps R      Allow for 2 adjacent RoI clusters having equal E T. Final algorithm uses 0.4  0.4 RoI cluster, sliding by 0.2

5. LVL1 Workshop, CERN, 16/07/99Alan Watson (by proxy) The ATLAS Algorithm Main Features  Self-contained algorithm Implement in independent 4  4 windows  Require RoI cluster = E T maximum Avoids multiple counting of single object Provides RoI coordinate for Level 2  Different cluster sizes available Can choose 0.4  0.4, 0.6  0.6 or 0.8  0.8 Can mix cluster sizes for different tasks Elements = 0.2  0.2 (= step by which window slides) RoI = 2  2 cluster (0.4  0.4) Window = 4  4 elements (0.8  0.8)

6. LVL1 Workshop, CERN, 16/07/99Alan Watson (by proxy) Main Properties Fine Step Size:  Precise RoI coordinate (  )  Ability to resolve nearby jets (  )  Allows  = 0.2 for E T miss trigger Variable Cluster Size:  Maximum size = 0.8  0.8 Good jet E T containment/inclusive trigger  Minimum size = 0.4  0.4 Useful where noise/pileup significant cf jet E T (e.g. very low E T multijet triggers or secondary RoIs)

7. LVL1 Workshop, CERN, 16/07/99Alan Watson (by proxy) Jet Definitions The Problem:  A “jet” is defined by a “jet finder” No single, unambiguous definition Many different algorithms used  So, what should trigger performance be judged against? What we used:  Fixed-width Cone Algorithm (width = 0.8) Most widely used in ATLAS physics studies Most similar to trigger algorithms (risk of biassing trigger algorithm choice?)  KT algorithm (M. Seymour) Variant on widely-used Durham scheme, modified for hadron colliders  In all studies, performance of different trigger algorithms was compared with both types of jet finder.

8. LVL1 Workshop, CERN, 16/07/99Alan Watson (by proxy) Rate vs Cluster Size Threshold vs Cluster Size  Trade-off between containing jet E T and summing noise/pileup Favours larger clusters except for lowest E T Inclusive Rate vs Size  For thresholds giving 95% jet efficiency

9. LVL1 Workshop, CERN, 16/07/99Alan Watson (by proxy) Cluster & RoI Sizes & Multijet Triggers Jet Separation & Multijet Efficiency  Too large an RoI (poor jet separation) degrades efficiency for multijet trigger Top efficency of 4jet trigger vs Rate Multijet Efficency vs Cluster/Step Size  Choose thresholds for 1.5 kHz 4jet rate  Compare efficiencies for different physics processes.

10. LVL1 Workshop, CERN, 16/07/99Alan Watson (by proxy) RoI Multiplicities RoI multiplicity vs Cluster Size  Choose thresholds to give 95% efficiency for jet of required p T.  Compare mean RoI multiplicities for different cluster sizes.  Fast simulation used RoI Efficency vs p T  High L, full simulation