Forward Muon +
Tracker Triggering
Update
D. Acosta, A. Ballado, M. Fisher, I.K. Furić, J. Gartner,
L. Kaplan, A. Madorsky, B. Williams
Overview
• Reminder: proposed three-phase trigger
• Phase 1: report regions of interest,
“match” (select) tracklets within
predetermined windows
• Phase 2: remove excess tracklets by
requiring high correlation
• Phase 3: combine tracker and muon
information to obtain better resolution
2
Reminder: Matching “Problem” Fixed
3x
• due to B field inhomogenities
in forward region
• solved with η-dependent
matching windows (≤0.4 rad)
3
Towards Phase 3: Muon
+ Tracker Fit
• Tracker momentum, cot(theta), z0
measurements are vastly superior to muon
• to properly combine (and gain), offline
framework is necessary
• combine muon + tracker = rely on tracker
momentum / cot theta / z0 fit seeded by
muon in matching phase
• fit components will provide natural objects
for Phase 2 selection of tracklets
4
Objective
• define algorithm which can be implemented
in firmware to fit for muon pt, cot theta, z0
• estimate necessary resources - the
algorithm has to be able to fit on a board
• today: estimate performance on generator
level information, due to digitization
• in progress - apply algorithm to fast/full sim
• measure resolutions, estimate trigger rates
5
R-Z algorithm
• in a homogenous B field, the R-Z analysis is a linear fit
• tracker construction implies most likely 3 hits = 2
pairs to combine
• stations 0 and X, 1and X (X=2,3,4)
• digitization - use strip pitch = 1 mm
• measure cot theta, z0
6
Ranges for Digitized z
We digitize measured z values with a scaling of 1 mm for each layer.
7
Computing
and
• After digitization of z for each individual layer we compute
• We compute
as
where
and
depending on layer we use for the base of the
lever arm to extrapolate the line.
8
resolution for different bits used
7 bits
10 bits
8 bits
11 bits
9 bits
12 bits
9
for different bits used
7 bits
10 bits
8 bits
11 bits
9 bits
12 bits
10
RMS Table (Bits)
Number of Bits
7
8
9
10
11
12
13
cotRMS
0.012599
0.006089
0.003197
0.002251
0.002034
0.001989
0.001977
z0RMS
0.998754
0.475577
0.224555
0.123699
0.089382
0.082022
0.080164
11
Creating Lookup Tables
• There is a clear leveling out for resolution RMS past the 10 bit
level. We therefore use this precision to digitize
in our
lookup tables.
• Lookup table 1
–
(with
hardcoded.)
• Lookup table 2
–
(with
hardcoded.)
• Resolution plots show the difference
where
is the actual and
is retrieved via digitization and the lookup
tables. Plots are divided up into how a specific combination of
layers hit measured the two variables in question.
12
RMS Table (cot)
Layer Combination
0,1
0,2
0,3
0,4
1,2
1,3
1,4
RMS (Chi-Squared)
0.003089
0.002164
0.001922
0.001810
0.003006
0.002126
0.001934
We see what would be expected: we get a more precise
answer when we measure cot0 with a longer lever arm, as
in combination 0,4 than we do with the shorter lever arm as
in combination 0,1.
13
RMS (Lo
0.00
0.00
0.00
0.00
0.00
0.00
0.00
RMS Table (z0 cm)
Layer
Z0 RMS
(cm)
LayerCombination
Combination
RMS
(Chi-Squared)
0,1
0,2
0,3
0,4
1,2
1,3
1,4
0.112099
0.066532
0.063353
0.056613
0.147737
0.088452
0.071203
RMS (Log Biased)
0.114375
0.077406
0.074436
0.070381
0.159280
0.112936
0.094238
14
Analogy for momentum fitting
• We use a factor of 0.01 cm to digitize
projected to
104 cm
• We look at changes in
for a combination of layers
(i,j).
• Lookup tables then convert each
to a
via the proper scaling:
We convert back in to digitized integers of
the following ranges. (on next slide)
to get
15
16
17
Ranges of
(pT = 10 GeV)
18
Ranges of
(pT = 10 GeV)
19
Base for resources
• have not attempted information reduction
study as done in r-z tracking (different bit
widths) - going for best performance
• 12x12 LUTs come from max deflection20 for
3 GeV track at 104 cm
Resources
• rΦ coordinate at 104 cm with 100 micron
precision requires 16 bits (encoding Φ position
of tracklet)
• trigger sector carries almost 4 bits of
information - reduces coordinate to 13 bits
• 5 13x13 bit LUTs (“alignment”) → global ϕ per
tracklet analyzed
• projection LUTs: 12x12 bit LUT per tracklet pair
(7 possible station combinations)
• combining the different pairs - average the Δϕ
(can do better with a weighted avg)
• Δϕ (0,4) is a measure of curvature
21
Computing
• With the hardcoded values for the slope we can make
lookup tables for
in terms of digitized
• Resolution plots for various momenta are below. And
continued on next page. (Units in GeV/c)
resolution at 3 GeV
resolution at 15 GeV
pT Resolution
[GeV/c]
Note: unusual display - blue point is the mean difference
error bar corresponds to ± RMS - resolution is ≤ 2%
23
Integration into framework
• first study was done at generator level
• study effects of digitization
• prepare framework and nominal LUTs
• have started merging into fastsim - expect
first fit results very soon
24
Conclusions
• reminder: problem with matching to CSC TF
tracks resolved - was due to B field
inhomogenities in the forward region
• presented results for a simple fitting algorithm
using LUTs at generator level
• CSC resolution (40%) → 2% from tracker
• expected spreads on fit inputs will drive cuts to
select at Phase 2 (cleanup)
• resources do not seem overwhelming (number
of pair combinations to consider?)
• we hope to have FastSim results very soon
25
(Fri?)