ReginaCaputoSandbox

Introduction

This is a place to collect the Level1 Topological Trigger (L1Topo) algorithms in a single repository to allow for precise and unambiguous communication between firmware developers and physics groups. L1Topo has the following features:

• Region of Interest (in L1Topo this is called a TOB) data used in the execution of algorithms based on event topology.
  • Information is identified by the L1Calo and L1Muon subsystems

This twiki page is laid out in the following way: First a list of inputs from the L1 systems is given. L1Topo receives information from the Level-1 calorimeters and the Level-1 muon systems. This provides jet, EM, muon and MET information. Next a detailed list of the types of output from these systems that L1Topo receives as input is given. These provide the inputs to the topological decisions that L1Topo makes. After the possible lists of input is given, a list and description of the current algorithms which L1Topo can perform is outlined.

Please make use of this twiki to help craft a topological based trigger that will fit the needs of your analysis while keeping in mind the trigger rate limitations that the ATLAS computing resource has. For the 2015 run, it will be very important to reduce trigger rates as much as possible while keeping excellent efficiency for signals of interest.

Inputs from L1 Systems

L1Topo receives the following inputs: Jets and forward jets, electrons and taus, muons, total and missing energy. The inputs are described below in detail.

Jets/Forward Jets

• Cluster size options: 0.4x0.4, 0.6x0.6, 0.8x0.8
• Energy bit information
  • jet cluster size 1: 10 energy bits: 0-1023 GeV, 1 GeV resolution (or alternatively 0-511.5 GeV with 0.5 GeV resolution)
  • jet cluster size 2: 9 energy bits: 0-512 GeV, 1 GeV resolution
• Position bit information: 5η + 5φ
  • 0.2 granularity (η x φ): |η|<2.4: ± [0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9, 2.1, 2.3]
  • 0.27 η x 0.2 φ granularity: 2.4<|η|<3.2: ± [2.67, 2.93, 3.2]
  • 1.7 η x 0.4 φ granularity: 3.2<|η|<4.9: ± [4.05]

Electrons/Taus

• Energy bit information
  • 8 energy bits: 0-255 GeV, 1 GeV resolution (or alternatively 0-127.5 GeV with 0.5 GeV resolution)
• Isolation bit information
  • 12 towers in each the EM and HAD calorimeters surrounding a 2x2 tower core
  • 5 bits total: each associated with a different isolation criteria. i.e.:EM isolation ring threshold, hadronic isolation ring threshold, hadronic veto (comes from 4 towers behind the 2x2 core)
• Position bit information: 6η + 6φ
  • 0.1 granularity (η x φ): |η|<2.5: ± [0.05,0.15,0.25,...,2.45]

Muons

The exact format of the muon input to L1Topo is still under discussion. This is the current proposal.

• 2 muons/half octant
  • 16 bits/octant and 16 total octants, A/C side, total of 256 bits: 0.1η + 0.1φ granularity + 1 p_T bit

Total and Missing Energy

• Sum E_T (15 bits): 16384 GeV, 1 GeV resolution
• Sum E_T restricted η region (15 bits): 16384 GeV, 1 GeV resolution
• Sum E_x and E_y (15 bits, plus sign): ±16384 GeV, 1 GeV resolution
• Sum E (15 bits): 16384 GeV, 1 GeV resolution
• From E_x and E_y can get MET² easily, MET is High Cost
• φ derived from E_x and E_y

Inputs to Algorithms

The following are the input object lists to the different L1Topo algorithm items. For example, one of the objects is a list of jets that would come from the level-1 calorimeter trigger. This list is then used as an input for one of the algorithms listed below.

Note: items that take up large computing resources are labeled in RED. These are also referred to as High Cost .

All Objects

These are the maximum number transmitted, if overflow issue a force accept.

• 2x96 jet objects total (can not be be directly connected to an algorithm without high cost)
• 240 electron and tau objects
• 2 muon objects per half octant
• 3xSum E_T (total and in quadrants), Sums E, E_x, and E_y

All Objects which pass requirement

The requirement is TBD, some options are p_T, η, etc - input is requested from physics groups to set the requirement such that a maximum of 10 objects would satisfy the requirement. If more then those objects would pass this, then the event would pass.

For example a requirement could be jets with p_T > 50 GeV

Sorted lists in E_T

This option sorts the All Objects list. In general sorting lists takes significant computing so doing an All Object sort is High Cost .

This sort would provide a maximum of 4 TOBs, the 4 highest E_T objects per list.

Sorted lists in E_T which pass requirement

This option sorts the All Objects which pass requirement list.

If the list is full: force pass (note: watch rates) The list of 10 objects can then be sorted in E_T, but recall sorting is High Cost .

Algorithms

This is a current list of algorithms and their definition in L1Topo: If there is an algorithm that a physics analysis team is interested in incorporating that is currently not on the list. Please contact someone in L1Topo. Keep in mind the cost in computing resources.

(Note: Multiplication/addition done in DSP logic blocks, cosh/cos done in Look Up Tables (LUTs))

• Δη - difference in η of two objects given granularity
• Δφ - difference in φ of two objects given granularity
• ΔR - not a circular cut, a combination of 2 cuts: |Δη| + |Δφ|
• H_T - Σp_T(jets)
• M_CT - use M_CT⁴ → (2E_T,1(1 + cosΔφ))²MET²
• M_T - use M_T⁴ → (2E_T,1(1 - cosΔφ))²MET²
• M - use M² → 2E_T,1E_T,2(coshΔη - cosΔφ)
• M_eff - High Cost Σ (H_T, MET)

Description of Algorithms

This is a detailed description of the Algorithms listed in the Algorithm section. A few quick notes:

• Algorithms are only used on Sorted lists and lists which satisfy some requirement, not on the All Object list
• Red items are High Cost in terms of computing resources
• Is overlap removal required in the algorithm requested? (input needed from physics groups)

Δη and Δφ

• Takes 2 input objects given granularity/range
• Calculates difference, makes decision

η and φ quadrant cut

• product of signs, can check quadrants. Simpler than a Δη and Δφ cut
• Note for our group... do we want to list this??

ΔR

• Two calculations: one Δη and then one Δφ
• Produces a square (or box) cut instead of the usual circular cut

H_T

• Sum of all E_T of the list of jets: specify which list

M_CT

• High cost if MET needed instead of MET²
• not high cost if M_CT⁴ is used for decision - check resolution
• Δφ is first calculated and the cos is calculated via LUTs
• result is added to 1, then multiplied by the E_T of the non-MET object
• the full result is squared then multiplied by MET²

M_T

• High cost if MET needed instead of MET²
• not high cost if M_T⁴ is used for decision - check resolution
• Δφ is first calculated and the cos is calculated via LUTs
• result is subtracted from 1, then multiplied by the E_T of the non-MET object
• the full result is squared then multiplied by MET²

M

• M² is used for the decision
• Δη and Δφ are first calculated and then cosh and cos are calculated via LUTs respectively
• results are subtracted then multiplied by the E_T of the two objects, then multiplied by 2

M_eff

• High Cost because MET is needed instead of MET²
• Sum of all E_T of the list of jets with MET included

Examples

Very nice studies were presented at the ATLAS Athens Trigger Workshop in December 2012.

• Please see the agenda page for examples

What we need from Physics Analyses

There are some items which are yet to be decided. Before decisions are made we would like input from the physics analysis groups. Some action items are:

• Threshold/requirements for "All Objects which pass requirement" object lists
• Algorithm functions which are missing (please make physics and resource case for adding algorithm)

Please keep in mind what is High Cost . Sorting lists and square roots in particular take up a lot of logic resources. Is it good enough to use the squared quantity in comparison? In general, don't use Lorentz vectors for making a decision - they take up too many resources since they require many square root functions. See the Algorithm list for examples in avoiding Lorentz vectors. Additionally with regard to the current algorithm list, specific lists of objects associated with current algorithms are needed from physics groups. The following is needed:

• Calculations of interest to your analysis
  • algorithm with object (object and list)
• Nature of calculation
  • type of list to use (sorted object vs unsorted, etc.)
  • bits of precision needed

Please keep in mind the resolution of the objects when requesting thresholds.

More information and references

• L1Topo reference from Sam
• On L1Topo Firmware
• On L1Topo Processor
• On JEM/CPM from L1Calo
• On CMX from L1Calo upgrade
• On L1Muon from ATLAS trigger workshop