Vertexing and tracking software at LHCb

Transcription

1 Vertexing and tracking software at LHCb The 23rd International Workshop on Vertex Detectors Mácha Lake, Doksy, Czech Republic Espen Eie Bowen on behalf of the LHCb Tracking group 18 th September 214

2 Table of Contents 1 Introduction to LHCb 2 Track reconstruction 3 Primary vertex reconstruction 4 Performance 5 Summary Espen Eie Bowen (Universit at Z urich) Vertexing and tracking software at LHCb 18th September / 22

3 Introduction to LHCb The LHCb experiment The LHCb experiment LHCb is a dedicated heavy flavour physics experiment at the LHC Its primary goal is to look for indirect evidence of new physics in CP violation and rare decays of beauty and charm hadrons This requires: 1 Excellent tracking (momentum, impact parameter and primary vertex resolution) 2 Excellent decay time resolution 3 Excellent particle identification Candidates / (25 MeV/c 2 ) LHCb 1 s = 8 TeV candidates / (.1 ps) 4 2 LHCb Tagged mixed Tagged unmixed Fit mixed Fit unmixed Candidates / ( 5 MeV/c 2 ) LHCb Data ± Signal B D s K s Combinatorial Λ Λ + c (K,π b ) (*) Λ b D s p (*) B D (π +,ρ + s s ) ± ± B d D (K,π ) (*) ±(*) B (d,s) D s K ± ± ± arxiv: m( µ + µ ) [MeV/c 2 ] decay time [ps] New J. Phys. 15 (213) lab_massfitconsd_m m(d K ± ) [MeV/c 2 s ] arxiv: ± Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

4 Introduction to LHCb The LHCb detector Tracking system (TT,IT,OT) Rich detectors Muon system Vertex Locator Magnet Calorimeters Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

5 Introduction to LHCb The LHCb detector Tracking system (TT,IT,OT) Rich detectors Vertex Locator (VELO) Surrounds interaction point 42 silicon micro-strip stations with r-φ geometry Muon system Two retractable halves, 8 mm from beam when closed For more details see talk by C. Elsasser Vertex Locator Magnet Calorimeters Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

6 Introduction to LHCb The LHCb detector Tracking system (TT,IT,OT) Tracker Turicensis (TT) Upstream of magnet Four planes of silicon Vertex Locator micro-strip sensors (, -5, +5, ) Rich detectors Magnet T stations Downstream of magnet Consists of inner and outer detector regionsmuon system (Inner Tracker (IT) and Outer Tracker (OT)) IT: Three stations each with four planes of silicon micro-strip sensors (, -5, +5, ) OT: Three stations each withcalorimeters four planes of straw tubes (, -5, +5, ) Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

7 Track reconstruction Tracking Definitions Track types in LHCb Long tracks: Traverse full tracking system from VELO to the T-stations. VELO tracks: Have hits in both the r- and φ-sensors but are not matched to hits in other sub-detectors. Used for primary vertex reconstruction. Upstream tracks: Low momentum particles that are bent out of acceptance by the magnetic field. T tracks: Only reconstructed in the T stations, can originate from very long lived particles or material interactions. Downstream tracks: Made by charged daughters of long-lived particles with a vertex displaced from the interaction point (K s,λ). Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

8 Track reconstruction Track states Track states in LHCb In LHCb, a track consists of a series of straight line segments called track states As tracks are regarded as going in either the forward or backward direction, track states are parameterised as a function of z by a state vector x y x = t x t y with t x = x z and t y = y z q/p and a corresponding 5 5 state covariance matrix. Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

9 Track reconstruction Tracking Algorithms Velo tracking (VELO tracks) T seeding (T tracks) Velo-TT tracking (Upstream tracks) Forward tracking (Long tracks) Track Matching (Long tracks) Downstream tracking (Downstream tracks) Track Fit PV finding Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

10 Track reconstruction VELO tracking Velo tracking (VELO tracks) No B field in VELO so expect tracks to be straight lines Start track search from end of VELO Look for quadruplets of hits in r-sensors Extrapolate back to smaller z adding hits First forward going tracks, then backward Repeat process searching for triplets Starting from longest r-z track, search for φ hits that can make a straight line Fit tracks using a χ 2 minimization r z Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

11 Track reconstruction Upstream tracking Velo-TT tracking (Upstream tracks) Linearly extrapolate VELO track to TT Open search windows in each layer and calculate x between track and hits Scale x to reference plane at center of TT Choose clusters of hits consistent with coming from the same VELO track Fit each track candidate with a χ 2 fit and estimate q/p (δp/p 15%) Choose best candidate track based on # layers fired and χ 2 Hit VELO x z TT Track Extrapolation Reference plane Search Window Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

12 Track reconstruction Forward tracking Forward tracking (Long tracks) Linearly extrapolate VELO track to the T stations Open search windows in x each layer Use VELO track state and knowledge of the B field to project each selected hit to the z position of the reference plane Hits from same particle expected to be projected to same x position, while random hits uniformly distributed Hough transform Fit resulting clusters and remove outliers using χ 2 criterium Use a cluster search to add stereo hits Refit, remove outliers, select best track based on χ 2 /dof Hit Track Search Window Reference plane T1 T2 T3 x z Hough Space Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

13 Track reconstruction T seeding x z T seeding (T tracks) Search for track candidates in x-z projection Form a straight line between each suitable pair of x hits in T1 and T3 A compatible hit in T2 is added to form a parabola Hits compatible with this parabola are added to the track candidate A Hough transform is used to add stereo hits A weighted least-squares fit is applied to each of the track candidates T1 T2 T3 Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

14 Track reconstruction Track matching Track matching (Long tracks) Use reconstructed VELO and T tracks as input Extrapolate both seeds to magnet bending plane (end of T stations) and calculate their difference in x (y) x, y, t x, t y used to form a matching criterion χ 2 Fit track candidate and make estimate of the q/p track estimate x track estimate x VELO Magnet T stations z Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

15 Track reconstruction Downstream tracking Downstream tracking (Downstream tracks) Extrapolate T track back to find the (x, z) point at the center of the magnet Form a track estimate from this point and the nominal interaction point Find hits in TT consistent with the track estimate For each x hit, form a new track estimate and collect consistent x hits Fit in xz projection and remove outliers Add stereo hits, fit and remove outliers Choose the best track candidate with the most hits and smallest χ 2 x z track estimate K s IP TT Magnet T stations Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

16 Track reconstruction Duplicate track removal Duplicate track removal Two independent algorithms form long tracks and several track types are subtracks of other types necessary to avoid/remove duplicate tracks found by multiple algorithms This is accounted for in two different ways: 1 Some algorithms only use tracks/hits that have not been used by a previous algorithm 2 Where overlap does exist, the track with the smallest number of associated hits is discarded The remaining tracks are fitted using a Kalman filter Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

17 Track reconstruction Track fit Kalman Filter The purpose of the track fit is to obtain the most accurate estimates of the track parameters together with their corresponding covariances These estimates are used to match to particle identification objects (e.g. RICH rings), find primary and secondary vertices and calculate invariant masses of particle combinations Tracks can be regarded as a collection of measurements and tracks states The Kalman filter is divided into three steps: 1 Prediction: The parameters of a state at z k are predicted given a state at z k 1 2 Filtering: The state at z k is updated with information of the measurement at this position These two steps are repeated until all measurements have been added 3 Smoothing: All other track states are updated in the reverse direction x pred k x k+1 x k x pred k+1 x k 1 z k 1 Material z k z k+1 Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

18 Primary vertex reconstruction Overview PV Finding Primary vertex (PV) reconstruction consists of two steps: 1 Seeding: Find PV candidates 2 Fitting: Fit each PV seed High multiplicity PVs reconstructed first to reduce incorrect reconstruction of B secondary vertices as primary vertices Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

19 Primary vertex reconstruction PV seeding 1 Find PV candidates - the points at which a sufficient number of tracks pass close to each other Seeding For each track (base track), select tracks with a distance of closest approach to the base track below a threshold If insufficient tracks are selected, the next base track is considered For each selected track, the point of closest approach (POCA) to the base track is determined The average POCA for all the selected tracks is determined in a two step approach: 1 The truncated mean is calculated iteratively If sufficient tracks remain: 2 The weighted average is calculated Tracks used for the weighted average are marked as used and the process is repeated Set of space points become seeds to the PV fit Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

20 Primary vertex reconstruction PV fitting 2 Fit each PV seed - using an adaptive weighted least square method Fitting The standard least square iterative procedure for PV fitting is not optimal Tracks from B decays not yet known and are likely to be assigned to the PV Systematic shift towards the secondary vertex An adaptive weighted least square method using the Tukey biweight is employed A weight is assigned to a track according to the value of its χ 2 IP and the Tukey constant C T : W T = (1 χ 2 IP /C 2 T )2, if χ 2 IP < C 2 T or W T =, if χ 2 IP > C 2 T The position of the reconstructed primary vertex is determined iteratively, by minimizing n tracks χ 2 PV = i=1 χ 2 IP,i W T,i until the convergence conditions are satisfied: 1 The shift in the z position of the PV is less than a threshold value 2 Sufficient tracks are associated to the PV Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

21 Performance Track reconstruction efficiency Track reconstruction efficiency The long track reconstruction efficiency can be defined as the probability that the trajectory of a charged particle that has passed through the full tracking system is reconstructed This can be measured in data using a tag-and-probe method with J/ψ µ + µ decays One of the daughters is fully reconstructed (tag), the other only partially (probe), i.e. as a TT-muon track The tracking efficiency is obtained by matching the probe to a full reconstructed long track arxiv: LHCb Preliminary LHCb-DP (in prep.) p [GeV/c] Efficiency 1.4 LHCb Preliminary LHCb-DP (in prep.) Efficiency N track The average efficiency is above 96% and is only slightly affected in high multiplicity events Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

22 Performance Mass and momentum resolution Mass and momentum resolution The momentum resolution for long tracks can be extracted using J/ψ µ + µ decays For two muons of similar momentum, neglected muon masses, the momentum resolution can be approximated as: ( ) δp 2 ( σm ) 2 ( pσθ ) 2 = 2 2, p m mθ where m is the J/ψ mass, σ m is the Gaussian width obtained from a mass fit and the second term corrects for the opening angle θ between the two muons where σ θ is the mean per-event error on θ. [%] δp/p LHCb 1 Preliminary LHCb-DP (in prep.) p [GeV/c] Candidates/(1.6 MeV/c 2 ) Candidates/(22 MeV/c 2 ) LHCb [MeV/c 2 ] M µµ LHCb M µµ [GeV/c 2 ] Candidates/(1.6 MeV/c 2 ) Candidates/(.6 GeV/c 2 ) LHCb [MeV/c 2 ] M µµ 45 4 LHCb M µµ [GeV/c 2 ] σ m / m [%] LHCb Preliminary 4 1 LHCb-DP (in prep.) 5 1 m [MeV/c 2 ] Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

23 Performance Vertexing and decay time resolution Vertexing and decay time resolution 1 PV resolution: Precise vertex reconstruction is crucial in order to resolve production and decay vertices. A PV with 25 tracks has a resolution of 13 µm in x/y and 71 µm in z. IP 2 resolution: Selections on IP are used extensively in LHCb analyses to reduce contamination from prompt backgrounds. At asymptotically high p T the IP x resolution is about 13 µm. Decay time resolution: The most stringent requirements on the decay time resolution stem from the requirement to resolve the fast oscillations induced by Bs -Bs mixing. The typical decay time resolution in LHCb is 45 fs for a 4 track vertex. PV resolution [µm] x y 5 LHCb Preliminary LHCb-DP (in prep.) N resolution [µm] IP x LHCb LHCb data Simulation JINST 9 (214) P97 1/p [GeV -1 c] JINST 9 (214) P97 p [GeV c -1 ] T resolution [fs] 1 The data driven methods to measure such quantities are given in the backup 2 The impact parameter (IP) of a track is defined as its distance from the PV at its point of closest approach Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

24 Summary Summary The track reconstruction and primary vertex finding of LHCb performs to very high standard It gives excellent performance in terms of: Track reconstruction efficiency Mass and momentum resolution Decay time resolution Future The LHCb experiment will be upgraded during Long Shutdown 2 ( ) to allow data taking at s = 14 TeV and L = cm 2 s 1 For details see: Upgrade of the LHCb VELO - H. Schindler LHCb Upgrade: Upstream Tracker - F. Lionetto Espen Eie Bowen (Universit at Z urich) Vertexing and tracking software at LHCb 18th September / 22

25 Backup Primary vertex resolution The PV resolution is strongly correlated to the number of tracks used to reconstruct the vertex The analysis is done on an event-by-event basis The principle is to reconstruct the PV twice and determine the difference between these two PV positions Achieved by randomly splitting the set of tracks in an event into two and reconstructing the PV in both sets Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

26 Backup Impact parameter resolution Governed by three main factors: 1 Multiple scattering of particles by the detector material 2 The resolution of the hit positions from which tracks are built 3 The distance to extrapolate a track between its first hit and the interaction point. An approximate analytical expression is used: ( ).136 σip 2 = 2 x/x [ ln(x/x )] r σ σ2 2 p T ( 2 1 ) 2, where the first term is due to multiple scattering and the second term due to the detector resolution. The particle has a transverse momentum p T and it passes through a piece of material, of thickness x, and with radiation length X. The track is extrapolated over a distance 1 between the first hit on a track and the PV, and the distance from the PV to the second hit is 2. The resolution of the first and second hits on the track are σ 1 and σ 2. Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22

27 Backup Decay time resolution The reconstructed decay time in the rest frame of the decaying particle can be expressed in terms of the reconstructed decay length l, momentum p and mass m of the particle in the LHCb frame as: t = m l p. The decay time resolution depends on the topology of the decay and is calibrated for each final state using prompt combinations that fake signal candidates The shape of the prompt peak is determined only by the resolution function events /.1 ps data, rms = 5 fs mc, rms = 44 fs LHCb decay time [ps] R Aaij et al 214 JINST 9 P97 Espen Eie Bowen (Universität Zürich) Vertexing and tracking software at LHCb 18 th September / 22