A track finding algorithm based on A track finding algorithm based - - PowerPoint PPT Presentation

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A track finding algorithm based on A track finding algorithm based on pixel detector for the ATLAS pixel detector for the ATLAS second level trigger second level trigger

Andrea Bar at ella – Mauro Dameri - Paolo Moret t ini – Fabrizio Parodi

I NFN Genova

Out line

• ATLAS t rigger st rat egy f or t he B-physics.
• PixTrig: a pixel based Level 2 t rack f inding algorit hm.
• Ef f iciency and perf ormances.
• Applicat ion t o t he select ion of rare B decays.
• Applicat ion t o t he b-t agging in mult i-b j et s event s.
• Conclusions

Pixel2000 - Genova - 6/6/00

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The ATLAS Level 2 Trigger The ATLAS Level 2 Trigger

Net work swit ch

Commercial Processors

R/ O Buf f ers R/ O Buf f ers R/ O Buf f ers

The ATLAS second level t rigger ref ines t he decision t aken at Level 1 using t he dat a f rom t he dif f erent sub- det ect ors, including t he t rackers. I t has t o t ake it s decision in 10-20 ms, reducing t he

• verall rat e by a f act or of 10

(f rom 100 KHz t o 10 KHz). The implement at ion of t his t rigger will be based on a f arm

• f commercial processors connect ed t o t he R/ O buf f ers

t rough a swit ch. Hardware co-processors, bot h at buf f er and f arm level, are also under st udy.

Pixel2000 - Genova - 6/6/00

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LVL2 Processing Modes LVL2 Processing Modes

The ATLAS t rigger is most ly based on “Regions of I nt erest ” (RoI ). This means t hat every t rigger component analyses only t he port ions of t he det ect ors ident if ied by t he previous component s; in t he case of t he LVL2, only t he region where a muon or a j et where f ound at LVL1 are reconst ruct ed. I n t he case of t he rare b decays reconst ruct ion however, t he int erest ing j et is usually not energet ic enough t o be seen at LVL1, so t he event is t riggered by a high pT µ in t he second j et . I n t his case a “Full Scan” is necessary at LVL2 t o reconst ruct t he charged t racks in t he whole inner t racker, and select t he vert exes using invariant mass and impact paramet er inf ormat ion.

Pixel2000 - Genova - 6/6/00

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PixTrig PixTrig: The Basic Idea : The Basic Idea

PixTrig is a t rack f inding algorit hm designed t o be used in Full Scan and RoI guided mode. Thanks t o t he high resolut ion and low noise of t he pixel det ect or it can provide f ull 3d t rack reconst ruct ion and impact paramet er measurement t o be used in st and-alone mode or as seed f or ot her algorit hms. PixTrig is a pure combinat orial algorit hm using t he ATLAS pixel det ect or space point s: combinat ions in t he t wo innermost layers are ext rapolat ed t o t he t hird if point ing t o t he primary vert ex. I f a point close t o t he ext rapolat ion is

∆ Z 3 ∆ φ

R

3

∆ φ

R

e xt

R o I

∆ Z e xt

f ound in layer 3, t he point s are kept as a candidat e t rack. Overlaps are solved on t he basis

• f

t he residuals in t he t hird layer.

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Logical Layers Definition Logical Layers Definition

The

• riginal

implement at ion

• f

PixTrig was based on t he t hree phisical layers of t he barrel pixel det ect or. To adapt t he algorit hm t o t he end- caps geomet ry (where we have f ive Link L1-L2 Link L1-L3 disks) we moved, in t he present C++ implement at ion wit hin t he ATLAS t rigger simulat ion, t o t he def init ion of “logical layers”. A logical layer is an arbit rary collect ion of det ect or modules. Logical f irst layers (every module in t he barrel B-layer of t he det ect or) have a link t o t he modules in t he corresponding second and t hird logical layers. This approach increase t he f lexibilit y of t he algorit hm and it s robust ness t o t he pixel inef f iciencies. However, we have t o keep in mind t hat More complexit y in t he Logical Layers More combinat ions Longer processing t ime and more f ake t racks

→ → → → → → → → → → → → → → → →

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Reconstruction Efficiency in jets Reconstruction Efficiency in jets

0.2 0.4 0.6 0.8 1

• 2

2 0.2 0.4 0.6 0.8 1

• 2

2

η Efficiency η Fake Trks Fraction

0.2 0.4 0.6 0.8 1

• 2

2 0.2 0.4 0.6 0.8 1

• 2

2

η Efficiency η Fake Trks Fraction

B B-

• jets

jets – – No pile No pile-

• up

up

The The reconst ruct ion ef f iciency reconst ruct ion ef f iciency in j et in j et RoI RoI is close t o is close t o 90% 90% and and f lat f lat over

• ver η

η and and p pT

T.

. At At low luminosit y low luminosit y t he f ract ion t he f ract ion

• f
• f f ake t racks

f ake t racks (combinat ion of (combinat ion of point s coming f rom dif f erent point s coming f rom dif f erent part icles) is always part icles) is always below 20% below 20% (it ’s higher in t he end (it ’s higher in t he end-

• caps

caps because more combinat ions are because more combinat ions are possible t her e). possible t her e). At At design luminosit y design luminosit y t he t he f ract ion of f akes reaches f ract ion of f akes reaches 60% 60% in t he end in t he end-

• caps

(spurious caps (spurious combinat ions lying on a st raight combinat ions lying on a st raight line can be pref err ed t o good line can be pref err ed t o good t racks). t racks).

B B-

• jets

jets – – 24 24 ev

• ev. pile

. pile-

• up

up

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Timing (jet Timing (jet RoI RoI) )

The processing t ime on a commercial Pent ium I I I 500 MHz syst em is of 3.7 ms per j et . As expect ed, t his t ime scales wit h t he number of clust ers in t he RoI f ollowing a cubic law; however t he coef f icient

• f t he t hird power is

small, so t he behavior is approximat ely quadrat ic. At design luminosit y, t he average t ime needed t o process a j et is close t o 90 ms.

20 40 60 10 20 30

a)

ID Entries Mean RMS UDFLW OVFLW 800 679 3.656 3.113 0.0000E+00 3.000

Processing time (ms) Events

b)

0.6536 / 11 P1 0.0000E+00 P2 0.6945E-01 P3 0.7165E-03 P4 0.6402E-04

Mean number of clusters per layer Processing time (ms)

5 10 15 20 10 20 30 40 50 10 20 30 40 50 100 200 300 400

a)

ID Entries Mean RMS UDFLW OVFLW 800 719 86.32 81.04 0.0000E+00 5.000

Processing time (ms) Events

b)

2.218 / 15 P1 0.0000E+00 P2 0.2935E-01 P3 0.1855E-02 P4 0.2302E-04

Mean number of clusters per layer Processing time (ms)

50 100 150 200 50 100 150

B B-

• jets

jets – – No pile No pile-

• up

up B B-

• jets

jets – – 24 24 ev

• ev. pile

. pile-

• up

up

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Z Zvertex

vertex Reconstruction with a LVL1

Reconstruction with a LVL1 µ µ µ µ µ µ µ µ

To reduce t he processing t ime we have t o decrease t he number of ext rapolat ion t o t he t hird layer . This could be achieved using a hard cut on t he Z impact paramet er of t he lay1-lay2 combinat ions, but t he posit ion of t he primary vert ex need t o be known wit h some precision. I n event s t riggered at LVL1 by a muon, it is possible t o use PixTrig it self wit h a high pT t hreshold, t o f ind t he muon and reconst ruct it s Z0 (which is close t o Zvert ex). I n 95.7% of t he event s one candidat e is f ound in t he µ

200 400 600 1 2 3 4

Reconstructed Tracks in µ RoI

Entries Mean RMS UDFLW OVFLW 718 0.1667E-02 0.6718E-01 5.000 2.000

Zrec - Zvertex

50 100 150

• 0.4
• 0.2

0.2 0.4

RoI , and in 99% of t he cases it s Z0 is less t han 5 mm apart f rom t he Z

• f vert ex .

The reconst ruct ion of t he vert ex t akes 0.5 ms.

Pixel2000 - Genova - 6/6/00

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Z Zvertex

vertex Reconstruction Inside a Jet

Reconstruction Inside a Jet

I nside a j et RoI , t he posit ion of t he vert ex can be reconst ruct ed as t he barycent er of t he Z0 of t he t racks in 55% of t he event s. This does not save processing t ime, but allows a clean-up of t he sample “a post eriori”. Using t his met hod, t he ef f iciency and purit y achieved at design luminosit y are similar t o t he low luminosit y ones.

1 10 10 2 10 3

• 20
• 10

10 20 Entries 1644

zrec-ztrue Number of events Good quality sample

1 10 10 2 10 3

• 20
• 10

10 20 Entries 1374

zrec-ztrue Number of events Bad quality sample

0.2 0.4 0.6 0.8 1 1.2 1.4 2 4 6 8 10

pT

Efficiency N(Fake Tracks)/Ntot

η

0.2 0.4 0.6 0.8 1 1.2 1.4

• 3
• 2
• 1

1 2 3

B B-

• jets

jets – – 24 24 ev

• ev. pile

. pile-

• up

up

Pixel2000 - Genova - 6/6/00

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Full Scan Efficiency and Timing Full Scan Efficiency and Timing

Full-scan on b event s wit h at least one µ wit h pT > 5 GeV/ c. Low luminosit y. Track reconst ruct ion pT cut at 0.5 GeV/ c. CPU: PI I I 500 MHz

ε:

95 % Fakes : 5% barrel 30% end-caps Tot al t ime: 35.3 ms, almost linear wit h t he number of clust ers.

0.2 0.4 0.6 0.8 1

• 2

2 0.2 0.4 0.6 0.8 1

• 2

2

η Efficiency η Fake Trks Fraction

20 40 60 100 200 300

a)

ID Entries Mean RMS UDFLW OVFLW 800 750 35.29 28.74 0.0000E+00 14.00

Processing time (ms) Events

b)

3.084 / 13 P1 0.0000E+00 P2 0.1457 P3 0.2473E-02 P4

• 0.5960E-05

Mean number of clusters per layer Processing time (ms)

50 100 150 50 100 150 200 250

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Track Parameters Resolution Track Parameters Resolution

The t r ack par amet er s ar e calculat ed wr it ing t he equat ion of t he helix connect ing t he t hree point in t he space. The resolut ions are all accept able, if we consider t hat no f it is perf ormed and all t he point s get t he same weight . The error on d0 is dominat ed by t he back ext r apolat ion t o t he vert ex

100

• 0.1
• 0.05

0.05 0.1 -0.1 0.1 5 10 15 100

• 0.2
• 0.1

0.1 0.2 -0.2 0.2 5 10 15 ∆d0 (cm) pT (GeV/c) ∆d0 (cm) ∆Z0 (cm) pT (GeV/c) ∆Z0 (cm)

34 10-3 30 10-3 1/ pT 1.9 mrad 1.3 mrad φ 2.2 mrad 1.8 mrad θ 324 µm 135 µm Z0 85 µm 68 µm D0 End-caps Barrel

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Exclusive B decays at LVL2 Exclusive B decays at LVL2

For t he select ion of exclusive B decays, a complet e t rack reconst ruct ion in t he inner t racker is perf ormed f ollowing t he direct ion of t he seeds given by t he f ull-

• scan. I n t his cont ext , P

ixTrig provides good perf ormances:

• it ’s f ast
• it produces f ew t rack candidat es
• it gives a f ull 3D def init ion of t he

t racks, limit ing t he volume scanned by t he second st age algorit hm

• it

gives good

• verall

resolut ion because it ’s less sensit ive t o t he int eract ions in t he mat erial of t he det ect or.

mππ (GeV) number of events

Si Kalman filter Pixel-guided TRT-guided 25 50 75 100 125 150 175 200 4 4.5 5 5.5 6 6.5 7

pT > 0.5 # of f ull t ot al seeds scan t ime PixTrig 39 36 ms 66 ms TRT scan 171 150ms 317ms

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B B-

• tagging at LVL2

tagging at LVL2

The B-t agging can be perf ormed in

• ne or more j et RoI using PixTrig
• alone. The met hod is t he classical
• ne, based on t he likelihood rat io

built on t he d0 dist ribut ions f or signal (b-j et s) and background (u- j et s). Since no error on d0 is calculat ed, we can use t he same weight f or all t he t racks or use a pT paramet rized error est imat e. The t wo met hods give similar result s: εb = 0.8 Ru = 4

εb = 0.5 Ru = 25

pT(GeV/c) σ(d0)(µm)

0.002 0.004 0.006 0.008 0.01 10 20 30 1 10 10 2 0.2 0.4 0.6 0.8 1

εb Ru

|d0| d0/σ

σd0 vs pT

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Comparison with the off Comparison with the off-

• line b

line b-

• tag

tag

I t is import ant t o check t hat t he on-line preselct ion does not spoil t he f inal

• f f -line perf ormances.

This plot compares t he pure of f -line result s wit h t hose obt ained running t he

• f f -line algorit hm over a

sample pre-select ed wit h t he on-line b-t agging t uned at εb = 90%

1 10 10 2 10 3 0.2 0.4 0.6 0.8 1 Offline algorithm Trigger algorithm Offline algorithm

• n a preselected sample

εb Ru

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Selection of H Selection of H → → → → → → → → hh hh→ → → → → → → → bbbb bbbb

The b-t agging can be used t o increase t he t rigger accept ance of mult i b-j et s event s, which are cut by high ET t hresholds at LVL1. The price t o pay is an increase

• f t he j et -t rigger rat es which

is signif icant at LVL1 and modest af t er t he LVL2 bt ag.

1 10 10 2 10 3 0.2 0.4 0.6 0.8 1

ε(4b) R(Dijets)

Single Jet Combined Single Jet Reference

19 % 1.0 St andard LVL1 53 % 1.5 LVL1 Loose + Bt ag t ight 58 % 2.0 LVL1 Loose + Bt ag loose 76 % 6.4 LVL1 Loose E on signal Rat e I ncrease Select ion

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Conclusions Conclusions

The f easibilit y of a f ast t rack f inding algorit hm based on t he ATLAS pixel det ect or has been demonst rat ed. The perf ormances are wit hin t he LVL2 specif icat ions bot h f or t he “f ull-scan” and t he “RoI guided” mode. They benef it f rom t he high precision and cleanness of t he pixel space point s. The b-t agging could be usef ul at LVL2 t o increase t he accept ance of mult i b-j et event s. Development is on-going in t he f ollowing sect ors:

• Fine t uning of t he algorit hm, especially in t he end-caps
• Robust ness

t o t he det ect or inef f iciency and misalignment

• Sensit ivit y t o t he clust ering algorit hm used