VELO Vertexing and Tracking Algorithms of the LHCb

VELO Vertexing and Tracking Algorithms of the LHCb Trigger System Juan P. Palacios University of Liverpool

Overview • The challenge at LHCb • LHCb trigger overview • L 0 – Overview – Algorithms • L 1 – Overview – Algorithms – Timing • Conclusions Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 2

The challenge at LHCb • • pp interactions at s 1/2 = 14 Te. V 40 MHz bunch crossing Average luminosity “modest” 2*1032 cm-2 s-1 Visible interactions at 10 MHz – 100 k. Hz bb events – 15% with all decay products of at least one B contained in detector – Branching ratio of interesting channels 10 -3 to 10 -7 • Write events at 200 Hz – Not just any old events but very interesting b ones of course! Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 3

Meeting the challenge LIKE LOOKING FOR A NEEDLE IN A SHARK-INFESTED OCEAN FULL OF HAYSTACKS • Fortunately B events have – Displaced vertices – High p. T particles from B decays • Exploit this in a three-level trigger system – L 0 hardware – L 1, HLT software on dedicated PC farm This talk will concentrate on the L 0 and L 1 vertexing and tracking algorithms Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 4

LHCb trigger overview KA BO p OM !!! p DISK 40 MHz L 0 Charged track multiplicity Number of interactions Total hadronic ET Large p. T, ET lepton, hadron, Hardware on customised electronics Synchronous Latency 4 s, 2 s for data processing Vertex 2004, Como, 9/9/2020 1 MHz 200 Hz L 1 Track p. T Impact parameter invariant mass e, ET Software on Linux PC farm Asynchronous Latency up to 58 ms J. P. Palacios, Liverpool 40 k. Hz HLT High PT, ET Displaced vertex B candidate mass Software on L 1 PC farm Use vacant CPU power Close to offline quality reconstruction Full LHCb tracking Particle ID Channel-specific event selection 5

Detectors in Trigger VELO: primary vertex impact parameter displaced vertex. L 1 Trigger Tracker: p, p. T L 1 SPD: Charged multiplicity L 0 Calorimeters: PID: e, , 0 Trigger on hadr. L 0, L 1 Muon System L 0, L 1 Pile-up system: multiple interactions, charged multiplicity L 0 Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 6

GLOBAL VARIABLES “L 0 OBJECTS” L 0 trigger in a nutshell 4 2 highest p. T muons CHAMBERS Highest ET , electron, hadron candidates CALORIMETERS ET CALORIMETERS L 0 decision unit L 0 DU z and # tracks in 1 st, 2 nd vertex PILE-UP SYSTEM Charged particle multiplicity SPD, PILE-UP SYSTEM Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool BUT HOW DOES IT ALL WORK? 7

L 0: pile-up system • For CP studies, multiple collisions aren’t favored (potential issues with tagging or primary vertex association) • Cut out events with multiple vertices • Two planes of R-measuring sensors • Identical to VELO sensors • Places up-stream from interaction point • Strips ORed in groups of 4 • Determines R resolution Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 8

Pile-Up Veto: principle Tracks from same ZPV have the same ratio k RA k R = B B k’ A ZPV - ZB Silicon r-sensors (backward!) RA RB k ZB ZA ZPV’ • Calculate vertex for all combinations of 2 points a and b. • Find highest peak (= prim. vtx) • Remove the hits and find 2 nd peak • Veto if peak>threshold • (Zvtx) 2. 8 mm, (beam) 53 mm Vertex 2004, Como, 9/9/2020 2 nd peak mult. cut tunable parameter J. P. Palacios, Liverpool 9

Pile-up Veto performance L 0*L 1 efficiency for different channels as a function of PU cut on 2 nd peak multiplicity. All other L 0 cuts are modified to fill the allowed bandwidth Vertex 2004, Como, 9/9/2020 Expected annual yield for B _Ds. K as a function of luminosity for different PU cuts J. P. Palacios, Liverpool 10

L 0 decision GLOBAL VARIABLES Tracks in 2 nd vertex Pile-up system multiplicity SPD multiplicity Total HCAL ET Pass ALL global cuts AND at least one ET threshold OR Pass p. T( ) cut (2 highest p. T muons) Reject events that are busy, empty or having multiple interactions B DECAY CANDIDATE THRESHOLDS ET of hadrons, electrons, , p 0 p. T of Good B-decay candidate p. T of two highest p. T Special di-muon trigger Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 11

0. 1 mm < IP < 3 mm? L 1 algorithm in a nutshell 2 D rz VELO tracking PV search ~58 tracks/event Allow for up to three PV 2 D track selection ~8 tracks/event L 0 muon match? 3 D rfz VELO tracking 3 D confirm Join VELO 3 D track to TT segment and re-fit L 0 match 3 D IP VELO-TT matching p, p. T estimation L 1 decision Vertex 2004, Como, 9/9/2020 Use VTT track + fringe B field OR VELO track + L 0 muon p. T of to tracks with highest p. T Highest L 0 invariant mass Highest L 0 and electron ET J. P. Palacios, Liverpool 12

L 1 2 D VELO tracking / 1 • rz tracking motivated by speed – Tracks from beam line form straight lines in rz – This is the reason VELO has rf geometry TRIPLET SEARCH 3 z-consecutive hits in up to 4 sensors, all same 45 o f sector TRIPLET EXTENSION Search for additional r hits compatible with triplet f segmentation 45 o for pattern recognition + speed GHOST + CLONE KILLING Overlap region, Shared hits, Number of hits Vertex 2004, Como, 9/9/2020 Reconstruct ~58 tracks/event J. P. Palacios, Liverpool 13

L 1 2 D VELO triplet search – Take first hit such that line satisfies angular criteria* • Project into S 1 and look for closest hit – 0. 9*pitch search window – If no hit found go to next S 2 hit • m ra • Start from hit in most downstream sensor, S 0 Loop over hits in S 2 S 0 40 0 • S 1 d S 2 vertex *compatible with coming from vertex and slope < 400 mrad BAD GOOD If good triplet found, start again from next S 0 hit – Exclude hits in found triplets from search ALLOW FOR ONE INEFFICIENT DETECTOR Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 14

L 1 2 D VELO Triplet extension • Project rz track to next sensor and look for hits in 3. 5*pitch window – Allow for off-axis tracks, not straight in rz – Flag good hits as used • Fit straight line to rz points and continue • After all extensions done – Non-extended triplets discarded and hits flagged as unused – All hits in extended tracks flagged as used – Go back to triplet search with remaining unused hits, moving towards the interaction point 2 D tracking performance: Efficiency: 98. 2% Ghost rate 6. 5% Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool Reconstruct ~58 2 D tracks/event 15

L 1 primary vertex search Start with 2 D tracking rz histogram Select tracks compatible with PV 1. 2. 3. 4. Project rz tracks to centre of each f sector Fit rz PV of ALL sectors Reject outliers Iterate three times Allow up to 3 PV Localise track in average f of sector Combine tracks from orthogonal f sectors to perform “xy” 3 D PV fit Treat individual rz tracks as xz, yz projections of same track in cartesian space BETTER EXPLAINED WITH THE AID OF A CLEAR DIAGRAM! Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 16

4, 0 20 Y’ , mo Co . P J. P os, i c ala ol o erp v i L Glo y x l a b x e m a fr Track pairs in perpen d ular sub-sectors tr measurements in 2 ic rotated Cartesian coeate ord PV is then constructe d as with XYZ g 20 /20 9/9 (0 , 0)

PV performance NTracks z x, y z NTracks • 1 st PV <tracks> = 38 x, y = 19 m z = 85 m 2 nd PV <tracks> = 15 x, y = 30 m z = 130 m With 2 D tracks + limited f information – Fast reconstruction: 0. 33 ms on 1 GHz PIII – Good resolution • 30 to 40 PV 2 D tracks/event contain enough info to “saturate” the resolution – Half as many effective 3 D tracks – At some point the PV resolution does not vary drastically with number of tracks • Remember: no momentum information. Errors due to multiple scattering not known. Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 18

2 D and 3 D VELO track matching to L 0 • 2 D matching – For selection of 2 D tracks to be reconstructed in 3 D – Compare dr/dz slopes • Construct c 2 using uncertainties in rz slopes of tracks and L 0 objects, f information from VELO sectors, B-field kick • 3 D matching – Rejection of 2 D mismatches – Improvement of VELO track p. T estimate • Construct c 2 using uncertainties in xz , yz slopes of tracks and L 0 objects, B-field kick c 2 max Purity Efficiency p/p 16 16 21. 0% 51. 2% 96. 5% 94. 7% 37% 6% 2 D 3 D Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 19

VELO 3 D tracking algorithm • • Sort 2 D tracks by length and start with longest Work in 45 o sectors independently Search inwards from sensor furthest from PV Look for compatible hits in neighbouring f sensor – Calculate r of track in f sensor, check sector, look for hit – Build list for each compatible f hit • Search in following f sensors – Project 3 D lines with rz from track and f from each hit in list – Build new lists for each good f hit found near projection • Select best 3 D track for given 2 D one – Scan through tree of lists, select track with most clusters or best c 2 • Mask all hits used and start again with next 2 D track Combined 2 D and 3 D Efficiency: 94. 8%, 96. 4% for B tracks Ghost rate 5. 0% Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool Reconstruct ~8. 5 3 D tracks/event 20

VELO-TT matching Get an estimate of p for good IP tracks! • • • Project 3 D VELO tracks into TT for pattern recognition Use as seeds to form TT track segments with 4 or 3 planes Pick one with best c 2 – • • c 2 based on slopes and B field kick Re-fit VELO and TT tracks allowing slopes to vary – Demand both meet at nominal place in centre of fringe field – L 1 optimised: good purity for high p. T tracks Momentum obtained from re-fitted slopes and integrated bending field For p. T > 1 Ge. V: 79% efficiency 98. 7% purity (p. T) ~ 20 -30% Vertex 2004, Como, 9/9/2020 Good p. T resolution at low p. T means we are unlikely to mistake low p. T tracks for high p. T ones J. P. Palacios, Liverpool 21

L 1 decision • Use ln(p. T) of 2 tracks with highest p. T and 0. 15 mm < 3 D IP < 3 mm • Information highest di-muon invariant mass, highst ET and electron above 3 Ge. V – Give weight to specific decay modes • tuned for retention of 4% of minimum bias L 0 triggers (40 k. Hz L 1 output rate) Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 22

L 1 timing • Timing of L 1 algorithms crucial – Balance between quality of reconstructed information available to make L 1 decision and complexity of L 1 algorithm process – But algorithms can be slow for reasons other than complexity • Separate L 1 s/w algorithm implementations benchmarked in search for inefficiencies – Technical changes • Information caching • Look-up tables • Static memory allocation where necessary Remember: L 1 trigger implementation in off-line style S/W environment. In general quality and conceptual speed of algorithms was of essence. Actual fine tuning of timing performance wrt technical s/w implementation details comes after validation… still, gains in speed can allow changes in conceptual approach… Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 23

L 1 Timing performance L 1 phase Time [ms 1 GHz PIII] VELO initialisation 0. 46 2 D tracking 0. 82 PV search/fit 0. 33 2 D track selection 0. 21 3 D tracking 1. 1 L 0 3 D track matching 0. 01 VELO-TT matching 1. 49 3 D track preparation 0. 16 L 1 variables calculation 0. 04 Decision 0. 02 Total 4. 64 • Time measured between start and stop of each algorithm • Minimise number of calculations needed to reject event • Granularity 1 s • Time for min. bias L 0 accepted events L 1 algorithms can provide fast efficient background rejection and signal retention with reasonably complex reconstruction in 1 ms (2007) Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 24

Conclusions • The three-level LHCb trigger reduces rate from 40 MHz (10 MHz visible) to 200 Hz • L 0*L 1 efficiency between 20% and 70% • L 1 efficiency between 60% and 80% • Within tight time and CPU budget • System is highly flexible and scalable, allowing to change retained event composition at all three levels – Possibility of adjusting thresholds in L 0 – Possibility of adjusting logic in L 1 – Possibility of bringing other detectors into L 1 • At a cost! More network, but same CPU power – Possibility of doing pretty much anything in HLT, except using RICH information… so far at least • L 1 performs high quality reconstruction within 1 ms time budget Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 25

Aknowledgements Many thanks in particular to the following : Mariusz Witek Hans Dijkstra Ivan Kisel Olivier Callot Thomas Schietinger Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 26

BACKUP SLIDES Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 27

The LHCb experiment • A dedicated B-physics CP violation experiment – Good primary, secondary vertex resolution – Good particle ID A small angle forward spectrometer with excellent PV and IP resolution HCAL Muons ECAL TT 1 VELO RICH 1 Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool Tracker RICH 2 28

LHCb Trigger Overview • L 0 – Reduce rate from ~10 MHz visible interactions to 1 MHz accept rate to L 1 – Use global varialbes • Charged track multiplicity • Number of interactions • Hadronic ET to reject empty events – Use B signatures • Large ET lepton, hadron or – Latency 4 ms (2 ms for data processing) • L 1 – – Shall concentrate on these. Emphasis on tracking/vertexing Maximum accept rate ~40 k. Hz High p. T, ET Impact parameter information Electron, hadron ET, di-muon invariant mass • HLT – – Accept rate ~200 Hz, use CPU power not used by L 1 High PT, ET Displaced vertex B candidate invariant mass Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool Close to offline quality data No RICH PID Use of full LHCb tracking system Large S/W commonality with L 1 algorithms 29

L 0 high p. T , • Use M 3 hits as seeds • Look in FOI in M 2, M 4, M 5 along extrapolation to (0, 0, 0) • Assume single B-kick at given z • Pick hit in M 2 FOI closest to extrapolation • Extrap M 3, M 2 to M 1. Pick closest M 1 hit • p. T determined from M 1, M 2 and lookup tables FOI size depends on station, background level, required min bias retention level Resolution ~ 20% for from b quark decays Overflow bin Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 30

L 0 high ET e, and h • • SPD: e/ separation Pre. Shower: 2. 5 X 0 pb. Identify EM particles ECAL: shaslik, EM shower energy HCAL: Fe scintillator tiles, hadronic shower energy Vertex 2004, Como, 9/9/2020 Hadrons: Efficiency • • J. P. Palacios, Liverpool 31

L 0 Decision Unit (L 0 DU) Information for L 0 DU: • Calorimeters: – ET of all candidates (hadron, electron, , etc. ) – ET (to avoid no collision + m from LHC bg) – SPD hit multiplicity • Muon trigger: – 4 2 largest PT muons • Pile-up detector: – z and number of tracks in 1 st and 2 nd vertex – total hit multiplicity • Variables used to find a B -meson signature Typical thresholds (Ge. V): • Electron ~ 2. 6 • Photon ~ 3 • Hadron ~ 3. 5 • ET ~ 5 • Muon ~ 1. 2 • Global variables used to enrich the triggered sample with “clean” events and avoid triggers due to e. g. large combinatorics L 0 DU performs simple arithmetic, with adjustable thresholds, downscaling, etc. Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 32

L 0 decision Global variable Tracks in vertex 2 nd Cut ET threshold 3 Pile-up veto multiplicity 112 SPD multiplicity 280 ET 5 Ge. V Global variable cuts. Reject events that are busy, empty or having multiple interactions Pass all global cuts AND at least one ET threshold Vertex 2004, Como, 9/9/2020 Value/Ge. V M. B. rate/k. Hz hadron 3. 6 705 electron 2. 8 103 photon 2. 6 126 p 0 local 4. 5 110 p 0 global 4. 0 145 Muon 1. 1 110 p. T( ) 1. 3 145 Thresholds for different L 0 inputs after combined optimisation OR Pass p. T( ) cut (two highest p. T muons) J. P. Palacios, Liverpool 33

L 1 in two nutshells/1 • Reconstruct 2 D VELO tracks (rf) ~58/event • Select 2 D tracks for 3 D reconstruction – Search for PV _select if 0. 1 < 2 D IP < 3 mm – Match 2 D tracks to L 0 m track segments _ select if good match • 3 D track reconstruction • Match 3 D tracks to L 0 objects – confirmation – Get estimate of track p and p. T • Match 3 D matched VELO tracks to TT track segments – Make so-called VTT tracks – Get first estimate of track p and p. T Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 34

L 1 in two nutshells /2 • Successfully reconstructed VTT 3 D or Velo-L 0 tracks used for decision • Use two highest p. T tracks – PT of tracks as discriminator • Combine with global variables – Highest L 0 invariant di-muon mass – Highest L 0 photon ET if > 3 Ge. V – Highest L 0 electron ET if >3 Ge. V Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 35

L 1 2 D VELO tracking rz Tracks in one 45 o azimuthal sector of the VELO Z vtx histogram X, Y vtx Event display showing 2 D tracks, Z vertex histogram and XY PV • Histogram 2 D z coord in preparation for PV search • Efficiency 97% for p > 1 Ge. V (get newest numbers!) • Purity 92% (get newest numbers!!!) Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 36

2 D VELO track matching to L 0 objects • Compare dr/dz slopes – Account for x-kick from B field for L 0 object dr/dz and f uncertainty – Use azimuthal information • 2 D tracks constrained to 45 o – Construct c 2 using uncertainties in dr/dz of tracks and L 0 objects, and f • Ignore 2 D track dr/dz uncertainty: small c. f. L 0 • Track f uncertainty 45 o*12 -2 • Cut on c 2 values to select matchings Muons Electrons Hadrons c 2 max Purity Efficiency p/p 16 4 4 21. 0% 11. 7% 16. 2% 96. 5% 98. 4% 98. 7% 36% 37% Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 37

p. T: 3 D VELO track matching to L 0 • In practice, only use L 0 muon objects • Construct c 2 from xz, yz slopes of 3 D track and L 0 object – Ignore 3 D track errors as negligible compared to L 0 object slope errors • Use track segment + VELO track and B kick to get accurate estimate of p. T ~ 4% • Performance: p/p c 2 max Purity Efficiency 16 51. 2% 94. 7% 6% Electrons 4 32. 9% 95. 8% 12% Hadrons 4 26. 9% 92. 8% 15% Muons Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 38

p. T: VELO 3 D track matching to TT • Project VELO tracks into TT – Straight line fit – Point errors • Detector resolution + 3 Ge. V for MS • Propagate downstream errors to upstream points to give most weight to last point on track • Use as seeds to form TT track segments with 4 or 3 planes – Fit straight line parametrised in xz, yz – x slope parametrised in terms of B field – Choose candidate with lowest c 2 • Re-fit VELO and TT tracks allowing slopes to vary – Demand both meet at nominal place in centre of magnet • Momentum obtained from re-fitted slopes and integrated bending field p. T ~ 30% Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 39

VELO-TT matching • Matching tuned to optimise L 1 performance: – need good purity for high p. T tracks! – c 2 for matching favours high p • p dependent • r dependent (multiplicity) – For p. T > 1 Ge. V • 79% efficiency • 98. 7% purity – p. T ~ 20 -30% for p. T > 1 Ge. V But this is all software, the trigger configuration For the VELO-TT matching can be changed for optimisation according to other criteria. Eg higher efficiency in HLT… Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool VELO-TT matching efficiency and p. T significance 40

L 1 decision / 1 • Use 2 tracks with ~6. 5/event – highest p. T – 0. 15 mm < 3 D IP < 3 mm • Construct discriminant: – D = distance to cut in ln(p. T) space • Construct other “bonus” discriminators b from – Highest di-muon invariant mass m • J/y a m+m- or B a m+m-(X) • Variable b dominates if m within 500 Me. V of J/y or B mass, otherwise linear with m – Highest ET above 3 Ge. V from L 0 ET max • B a K * • Variable b linear with ET max from 3 Ge. V – Highest electron ET above 3 Ge. V from L 0 ETemax • J/y a e+e • Variable b linear with ETemax from 3 Ge. V Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 41

Some words about HLT • Reject events not compatible with interesting b decay (p)/p from ~20 -30% to 0. 6% • Confirm L 1 decision – Add T 1 -T 3 information to improve p resolution of VELO-TT – Fast execution, reduces rate from 40 k. Hz to 20 k. Hz • Full pattern recognition + limited PID – Better VELO cluster resolution – Use full LHCb tracking system – close to offline quality – Identify electrons, muons (RICH PID to CPU demanding) • Exlusive selection – Very flexible, offline-like algorithms, relaxed cuts • Assuming 1 ms per L 1 event, have ~10 ms per event in HLT (2007 CPU) Vertex 2004, Como, 9/9/2020 J. P. Palacios, Liverpool 42