Pattern Recognition Comparison: Generic versus Standard

Transcription

1 Pattern Recognition Comparison: Generic versus Standard Analysis of the VErtex LOcator ACDC3 test run data Anne Keune Master Thesis - August 27 Supervisor: Dr T.J. Ketel Second reader: Dr A.P. Colijn B-Physics group, Nikhef Universiteit van Amsterdam Master: Physics Track: Particle and Astroparticle Physics

2 2 Abstract The standard VELO pattern recognition of LHCb is compared to a generic pattern recognition, using test run data. The test run was performed in November 26 using 4 GeV protons and 18 GeV pions of the H8 beam line at the CERN SPS accelerator. This was part of the VELO commissioning and allowed testing of the tracking and monitoring software on real data and the use of vacuum and cooling systems. The setup consisted of ten modules with silicon strip detectors with a possible readout of six modules at a time. For analysing the test run data the generic pattern recognition is especially developed to be very robust and to deal with all kinds of tracks. In the real LHCb experiment the standard VELO pattern recognition is used, which is optimised for fast dealing with tracks coming from the interaction region. Although initially the comparison of the two pattern recognition techniques brought to light several differences, adjustments to the algorithms have resulted in similar track reconstruction efficiencies for the tested data sets.

3 Contents 3 Contents 1 Introduction Theory Unitarity Triangles Quantum Mechanics of Mixing Box Diagrams CP Asymmetry The experiment with the VErtex LOcator Monitoring Pattern Recognition Techniques Standard Pattern Recognition Generic Pattern Recognition Feature Differences Tolerances Unique Seeds Cuts on tracks Data Analysis: Comparison of Pattern Recognition Techniques The Yield of Straight Beam Track Data using Original and Adjusted Pattern Recognition Techniques Residuals of Straight Beam Track Data using Old and Improved Alignment Resolution Improvement with η function for Straight Beam Track Data Residuals for Inner and Outer Target Data Target Reconstruction for Inner and Outer Target Data Speed of Pattern Recognition Techniques Conclusion

4 4 1 Introduction 1 Introduction When any type of particle collides with its antiparticle both particles can annihilate and equally, under the right circumstances, pairs of matter and antimatter particles can be created. At first sight there seems to be a perfect symmetry between matter and antimatter. But although it is assumed that during the Big Bang equal amounts of matter and antimatter were produced, nowadays the whole visible universe appears to exclusively exist of matter. Therefore it is believed that a difference in the behaviour of matter and antimatter must have contributed to this asymmetry. To study the properties of particles and their interactions at the highest energies, the Large Hadron Collider (LHC) is currently being constructed. The LHC is designed to collide two counter rotating beams of protons or heavy ions. LHCb is one of four main experiments along the LHC ring and is dedicated to the measurement of the difference between matter and antimatter. It will specifically focus on the violation of charge conjugation combined with parity transformation (CP violation) in hadrons containing a b or b quark. The theory behind this is explained in section 2. The VErtex LOcator (VELO) is the subdetector of the LHCb experiment closest to the proton interaction region. Its main goal is to measure particle trajectories and thus to reconstruct interaction and decay vertices with high accuracy. Hadrons containing a b or b quark that are created in the high energy proton interaction, can travel a small distance inside the VELO before they decay. The accuracy of the tracking within the VELO will allow to separate primary vertices from secondary ones, which is an important requirement in the measurement of asymmetries in the b/ b systems. Both the LHC and the LHCb detector are still under construction and at this stage parts of the detector are tested separately. In November 26 a test run was performed with the available VELO modules. This test run was given the name ACDC3, which stands for the third Alignment Challenge and Detector Commissioning. To replace beam collisions at the LHC, targets were used at different positions. By using these target data it was possible for the first time to study tracking accuracies and vertexing quality, with part of the final detector setup. A more detailed description of the VELO and of the test run setup is given in section 3. To analyse the test run data a monitoring program needs to be in place. Normally all the incoming data is stored in files and is analysed at a later time. During the test run it was also possible to analyse the data online, which means real-time monitoring while the data was coming in. This test run was the first run where VELO data was monitored online and considered a step towards using full online monitoring in the LHCb experiment. More information on monitoring is found in section 4. A part of track reconstruction is the pattern recognition. For the LHCb

5 5 experiment the so called standard pattern recognition is developed. This technique is optimised to deal with target data. The generic pattern recognition was developed to analyse the ACDC test run data. This generic pattern recognition is slower than the standard LHCb pattern recognition, but can handle tracks coming from all directions which is more suitable for test run analysis. The two pattern recognition techniques and their different features are presented in section 5. Different data sets are analysed using the two pattern recognition techniques. With the generic pattern recognition not all test run results were as expected. Therefore the standard pattern recognition is also made compatible for the test run data. This allows for testing how well both the standard and the generic pattern recognition perform using real data. The comparison of the two pattern recognition techniques is also important because a decision is needed on which of the pattern recognition techniques to use in the LHCb experiment. The analysis results and the comparison are given in section 6.

6 6 2 Theory 2 Theory The Standard Model (SM) is a theoretical model which describes all observed particles in terms of three generations of quarks and leptons, as well as the strong, weak and electromagnetic interactions between them. These elementary particles and their interactions, which involve symmetries and their conservation laws, form the basis of describing the physics of nature. For a long period of time the symmetry of parity transformation (P ) was assumed for all laws in physics, but in 1956 C.U. Wu observed that only lefthanded neutrinos were created in a weak decay and no right-handed neutrinos, which meant parity symmetry is violated in weak interaction [1]. However, parity transformation combined with charge conjugation (CP ) transforms the left-handed neutrino into a right-handed anti-neutrino which does exist and CP symmetry was still assumed. This changed in 1964, when J. Cronin and V. Fitch discovered CP symmetry violation in the decay of the neutral K meson [2]. The symmetry of CP T (where T stands for the operation of time reversal) is still assumed to be valid. Mesons are particles made of a quark and an antiquark. The B d meson contains a d and a b quark, as the B d meson contains a d and a b quark. These mesons are said to be of b and anti-b flavour, respectively. Weak interaction does not conserve flavour. The charged current couples to two different quark flavours. One of the consequences is that transitions between the flavour states B d and B d can take place; this is called B-mixing. The SM incorporates the CP violating parameters in the so called CKM (Cabibbo-Kobayashi-Maskawa) matrix, which contains the different strengths, V ij, of flavour-changing weak decays and defines the transformation from the flavour eigenstates to the mass eigenstates. The nine elements of the matrix initially each contribute two degrees of freedom; a real and an imaginary variable, but these are not all independent. Rephasing the matrix and using the constraints of unitarity, results in just four degrees of freedom [3, 4]; three so called generalised Cabibbo angles (θ 12, θ 13, θ 23 ) and one phase factor (δ 13 ), see equation (1). CP violation is present if this phase factor is non-zero. V CKM = = V ud V us V ub V cd V cs V cb V td V ts V tb c 12 c 13 s 12 c 13 s 13 e iδ 13 s 12 c 23 c 12 s 23 s 13 e iδ 13 c 12 c 23 s 12 s 23 s 13 e iδ 13 s 23 c 13 s 12 s 23 c 12 c 23 s 13 e 1δ 13 c 12 s 23 s 12 c 23 s 13 e iδ 13 c 23 c 13 (1) Here c ij stands for cos θ ij and s ij for sin θ ij. In the next section a parametrisation of this matrix will be used to exploit its unitarity.

7 2.1 Unitarity Triangles Unitarity Triangles In this section the CKM matrix and its unitarity properties are discussed in more detail. Because of the unitarity of the CKM matrix the following equations V ij Vik = hold for all i {u, c, t} and j, k {d, s, b} with j k. i Each of these six equalities represents a triangle in the complex plane. It suffices to introduce the Wolfenstein parameterisation [5], which uses the parameters λ, A, ρ and η where s 12 = λ, s 23 = Aλ 2 and s 13 e iδ 13 = Aλ 3 (ρ iη). V CKM = 1 λ2 2 λ λ 3 A(ρ iη) λ 1 λ2 2 λ 2 A λ 3 A(1 ρ iη) λ 2 A 1 Most applicable to the B d meson is the unitarity relation V ud V ub + V cdv cb + V tdv tb = Using the Wolfenstein parameters, this relation - normalised to the real term V cd Vcb - can be written as ( ρ iη) ( 1 + ρ + iη) = which can be represented as a unitary triangle in the ρ-η complex plane. (fig 1). Fig. 1: Unitary Triangle for the equality: V ud Vub + V cdvcb + V tdvtb =, illustrating the current experimental constraints on this unitarity triangle. Image by the CKMFitter group [6]. A non-zero area for such a triangle implicates the existence of CP violation. In other words, if the inner angles (α, β and γ) of the triangles are found to be non-zero then CP violation has been demonstrated.

8 8 2 Theory 2.2 Quantum Mechanics of Mixing The time evolution of B d (t) and B d (t) can be described by an effective Hamiltonian [7, 8]. H = M i ( M i 2 Γ = 2 Γ M 12 i 2 Γ ) 12 M12 i 2 Γ 12 M i 2 Γ The off-diagonal terms are responsible for the (off-shell as well as on-shell) mixing between states, whereas the imaginary part of the diagonal terms are responsible for the decay. The solution, Ψ(t), of the Schrödinger equation, using this Hamiltonian, is given by: Ψ(t) = α B L (t) + β B H (t) where α and β depend on the initial conditions and the time dependent mass eigenstates B L (t) (light) and B H (t) (heavy) are defined as: B L (t) = e i(m L i 2 Γ L)t B L B H (t) = e i(m H i 2 Γ H)t B H and B L = p B d + q B d B H = p B d q B d with m H/L = M ± m/2 and Γ H/L = Γ ± Γ/2. Here m and Γ follow directly from the Hamiltonian. The complex variables p and q satisfy normalisation p 2 + q 2 = 1 and q p = M12 i 2 Γ 12 M 12 i 2 Γ 12 which can be derived from the eigenvalue calculation. If q/p = 1, then B L and B H would also be the CP eigenstates and no CP violation would occur in mixing. Directly from the time evolution of B L (t) and B H (t), the time evolution of B d (t) and B d (t) can be derived. B d (t) = g + (t) B d + q p g (t) B d B d (t) = p q g (t) B d + g + (t) B d where g ± (t) = 1 2 e i(m L i 2 Γ L)t ( 1 ± e i( m i 2 Γ)t) 2.3 Box Diagrams For neutral mesons transitions between the meson and it antiparticle can occur. These oscillations can have either on-shell, Γ 12, or off-shell, M 12, intermediate

9 2.3 Box Diagrams 9 states. These intermediate states can be formed by u, c, t quarks, but the contributions of the charm- and the up-quark as good as cancel each other due to their similar mass, according to the GIM mechanism [9]. In addition, with the top quark as intermediate particle it is impossible to create on-shell intermediate states because of the heavy top mass. Thefore off-shell oscillations with the top quark as intermediate state are dominant. These oscillations can be represented by so called box diagrams. For the B d meson, the process of mixing is depicted in figure 2. Fig. 2: Box-diagrams showing the dominant transitions from the Bd meson to its antimatter particle. For the B d meson, the phase, φ d, of this mixing process is given by φ = 2 arg (V td V tb ) = 2β with β the angle of the unitarity triangle, fig 1. For B-mixing the off-shell contributions dominate the on-shell contributions, therefore often the approximation M 12 Γ 12 is used. The fraction q/p becomes q p M 12 M 12 = e i2β (2) Here the direct link between the CKM matrix elements and how the flavour eigenstates linearly combine to mass eigenstates can be seen [1]. Note that applying this approximation, q/p = 1 is obtained and therefore no CP violation in the mixing. This is consistent with the theoretical expectations which indicate that CP violation in the mixing of the B system is very small [11]. Using this approximation the rate of oscillation from B d to B d is given by I(B d B d ; t) = q 2 p g (t) 2 I = q 2 e Γt [ ( ) ] Γt p cosh cos ( mt) I 2 2 e Γt 2 cos ( mt)i

10 1 2 Theory Similarly I(B d B d ; t) = g + (t) 2 I e Γt cos ( mt)i 2 I( B d B d ; t) = p 2 q g (t) 2 I e Γt cos ( mt)i 2 I( B d B d ; t) = g + (t) 2 I e Γt 2 cos ( mt)i The way to measure oscillations is to tag the flavour of the neutral B meson at time of production and to use a flavour specific final state to determine the flavour at time of decay. For each measured proper time the probability of whether the meson has oscillated can be determined (figure 3). The VELO is responsible for the accurate measurement of the proper time. It also determines the angles between the trajectories to determine the invariant masses of the particles. Fig. 3: The mixing of neutral mesons. The blue line depicts the probability of finding a B meson at time t, given a B meson at t =. The red line depicts the probability of finding a B meson at time t, given a B meson at t = 2.4 CP Asymmetry Final states which are CP eigenstates are of special interest to study the CP asymmetry in the interference between B d f and B d B d f, with f a CP eigenstate. Before looking at decay widths, it is sufficient to introduce the variable λ f = qāf pa f (Note that this is not the same λ as used in the Wolfenstein parametrisation.) A f and Āf are the amplitudes for the decays of B d f and B d f, respectively.

11 2.4 CP Asymmetry 11 The decay width for B d f ( Γ = ) can now be given by Γ (B d f) = A q f g + (t) + Āf p g (t) 2 e Γt 2 A f 2 [ 1 + λ f 2 + ( 1 λ f 2) cos ( mt)) + 2I (λ f ) sin( mt/2) ] The term A f g + (t) describes the decay B d B d f and Āf q p g (t) describes the part of the decay through B d B d f. Similarly, for the B d f decay Γ ( Bd f ) = p Āf g + (t) + A f q g (t) e Γt 2 2 Ā f 2 [ 1 + λf 2 ( 1 λ f 2) cos ( mt)) + 2I (λ f ) sin( mt/2) ] The CP asymmetry can now be written in terms of these decay widths a CP = Γ (B d f) Γ ( Bd f ) Γ (B d f) + Γ ( Bd f ) = λ f 2 1 λ f cos ( mt) + 2I (λ f ) λ f sin( mt) = A dir cos ( mt) + A mix sin( mt) (3) The coefficients A dir and A mix are the amplitudes for direct CP violation in decay amplitudes and for CP violation due to the interference between mixing and decay, respectively. The value of λ f, and thus also I (λ f ) depends on the final state which is looked at. In case of the so called golden mode : f = J/ψKs, a value of I (λ f ) = e 2iβ is found. The number of B and B (which flavour is tagged at production time t = ) decays to J/ψKs is measured as a function of proper time, measured accurately by the VELO. This directly measures the asymmetry a CP which gives information about the angle β and thus the CP violating parameters of the CKM matrix. Using this decay channel, the current value of sin 2β is measured to be.725 ±.37 [12]. In order to measure this type of CP asymmetries in the B s system, a particularly accurate measurement of the proper time with the VELO is crucial, given the fast oscillation rate of the B s mesons, see figure 3.

12 12 3 The experiment with the VErtex LOcator 3 The experiment with the VErtex LOcator The VErtex LOcator (VELO) is the detector of LHCb which is closest to the interaction region and it is separated from the beam vacuum by only a thin foil of aluminium. The VELO is contained within a vacuum vessel of 1.7 m length and 1.1 m diameter (figure 4), which is part of the LHC beam pipe and is sealed by a 2 mm thick aluminium exit window. The LHC beam pipe extends throughout the complete LHCb detector. The VELO strip detectors are distributed over two secondary vacuum boxes which are separated from the LHC beam vacuum. Fig. 4: A schematic drawing of the VELO contained within a vacuum vessel. Its strip detectors contained by two secondary vacuum boxes separated from the LHC beam vacuum. The main goal of the VELO is to reconstruct particle trajectories with small polar angles using high resolution silicon strip detectors. For triggering purposes it is important to be able to select events in which the decay of a B meson occurs. This kind of event is characterised by secondary decay vertices. In the later analysis the distances between the primary and the secondary vertex are used to precisely determine the life times of the B mesons. In addition to this the precise angles between the trajectories of the decay particles is determined and used, together with their momentum which is determined in the magnet, to calculate the invariant masses of the secondary decays. As seen in the previous section, these accurate measurements are necessary to precisely reconstruct the production and decay vertices of hadrons containing a b(c) quark, which are needed to tag their flavour and thus to calculate CP violating parameters.

13 13 The VELO contains 21 detector stations, positioned perpendicular to the beam line as shown in figure 5. The VELO is designed to maximise the number of tracks and vertices it can reconstruct, while keeping the amount of material traversed by particles to a minimum. All particles at an angle between 1 and 4 mrad, covering the angular acceptance of the LHCb spectrometer, traverse at least three stations, which is the minimum number of stations required to reconstruct a track. The outer radius of each strip detector is limited in size because of manufacturing reasons to 42. mm. Due to these two constraints on angle and radius, the distance between two stations in the central region of the VELO is chosen to be about 3 mm. The central part of the VELO is covered by 16 stations. In addition there are 5 stations towards the LHCb detector covering the small angle tracks with a larger distance of about 6 mm between the stations to minimise the amount of material. In total the stations are distributed over a length of about 1 meter. Because the VELO is used to reconstruct particle trajectories near the vertex, the innermost radius of these stations should be as small as possible, since a short track extrapolation distance leads to a more precise impact parameter reconstruction. The innermost radius of a VELO strip detector is 8.2 mm. Since this distance to the beam is smaller than the 3 mm aperture required by LHC during injection, each station is divided in two halves, a left and a right half module, each spanning 182 degrees to allow for a small overlap to obtain full φ-coverage and to accommodate for the relative alignment. The stations reside on a common support system that can be retracted during injection to a save position clear from LHC s required aperture. This retracted position is called the open VELO mode. When the beams have stabilised the VELO returns to its closed mode. In order to protect the modules from the RF radiation coming from the beam bunches, the same aluminium box which separates the modules from the primary LHC beam vacuum also acts as a wake field guide [13]. The RF foil has a complicated structure shown in figure 5b. Deep inner corrugations close to the beam axis reduce the material, traversed by particles before the first measured point, to a minimum. The side corrugations also allow for the overlap of the left side and right side detector box. The thickness of the foil is only 3 µm. More details about the mechanical design can be found in [14, 15].

14 14 3 The experiment with the VErtex LOcator Fig. 5: Sensor positions of the VELO. The two colours represent the alternating upstream/downstream position of the R and Φ sensors per module (a). The complicated structure of the RF foil. The inner corrugations minimise the material the particle crosses. The outer corrugations allow the detector halves to overlap (b). A module consists of two 3 µm thick silicon sensors, a Φ sensor and an R sensor. The two sensors of a module are each mounted on a hybrid. The hybrids are glued back to back on a carbon fibre paddle and base, leaving a distance of 2 mm between the sensors. Each hybrid is cooled to a temperature below zero degrees Celsius by direct thermal contact of cooling pads mounted on the base. The cooling is done using a mixed-phase CO 2 system and prevents thermal runaway and, in addition, reduces thermal noise in the sensors and electronics [13, 15]. As seen in figure 5, the upstream and downstream positions of the sensors alternate, where an upstream (downstream) sensor is the sensor furthest from (closest to) the rest of the LHCb spectrometer. The R sensors are numbered to 41, increasing in downstream direction. Here the odd numbers are reserved for the right half sensors and the even numbers for the left half sensors. The Φ sensors are numbered 64 to 15, where each associated R and Φ sensor in a module differ 64 in number. Both the R and the Φ sensor contain 248 readout strips. The R sensor contains curved concentric strips and determines the r radius of a transversing particle. The R sensor is divided into 4 azimuthal sectors ( - 3 for downstream, 3 - for upstream) of approximately 45 degrees each and thus they contain 512 strips each, with its closest strip 8.2 mm from the beam and its furthest 42. mm. Based on R measurements alone tracks can be tested if they come from a common vertex or from a secondary decay. Segmenting the R sensors into 4 sectors reduces the number of uncorrelated tracks per sector. The distance between the centre of strips, the pitch, varies linearly with R from 4 µm to 11 µm, with the smallest pitch closest to the beam axis. The smaller pitch closest to the beam line increases accuracy near the interaction region and results in a better spread of occupancy over the electronics readout channels, due to the

15 15 higher particle flux near the beam axis. The decision on which pitch distances to use is based on earlier test run studies, in which the sensor resolution was measured using different track angles as a function of pitch [16]. The Φ sensor contains straight radial strips and, together with the R coordinate, determines the φ angle. This sensor is divided into 2 radial sectors ( - 1), an inner and an outer sector. The Φ strips are tilted with a stereo angle, which is different in sign and magnitude for the inner (2 degrees) and outer (-1 degrees) sector. If extending the strips, their distance of closest approach to the beam axis would be 2.8 mm for the inner sector and 3.1 mm for the outer sector. The choice of the angle in the inner region is driven by the track reconstruction efficiency and the number of produced ghost tracks. The angle and its opposite sign in the outer sector follows from the condition to minimise the depth of the corrugations in the RF foil [15]. Its inner sector contains 683 strips and runs from r = 8.2 to r = 17.2 mm, with a pitch width varying from 35.5 to 78.3 µm. The outer sectors thus contains 1365 strips running from r = 17.3 to r = 42. mm, with its pitch varying from 39.3 to 96.6 µm. The geometries of the two sensor types are depicted in figure 6. Fig. 6: The geometries of the R and the Φ sensor. The 248 strips per sensor are read out using 16 Beetle chips (i.e. 128 strips are connected to the same Beetle chip), which are radiation hard front-end electronics chips (version 1.5, [17]). These chips are called Level- electronics (L) and are located on the hybrids of the detector. The data have to be stored in the chip for the 4 µs latency of the L trigger decision. After acceptance by the L trigger, which selects single proton-proton interactions with large p T hadrons, the signals from each Beetle chip are transmitted through 4 analogue data links to the Level-1 electronics (Off Detector electronics) for further processing. Due to the L trigger selection, the L1 electronics only have to deal with maximal one event per 4 µs. The L1 readout board is called Trigger ELectronics and Level-1 board (TELL1) and performs zero-suppression and clustering, which will be discussed in section 4. The L1 trigger selects events in which same reconstructed tracks have a significant rz-impact parameter, which may indicate B meson decay products. First reconstructing tracks in the rz-projects optimises the speed of this selection process. The standard LHCb pattern recognition therefore first only selects R clusters in order to create RZ tracks, before searching for matching Φ clusters. This process is discussed in

16 16 3 The experiment with the VErtex LOcator more detail in section 5.1. L1 accepted data are processed and sent to the data acquisition. Test Run ACDC3 The analysis is based on data taken during the test run performed in November 26. This test run was given the name ACDC3, which stands for the third Alignment Challenge and Detector Commissioning. In the same series test runs ACDC and ACDC2 were performed in April and August 26, respectively. Where previous test runs where for R&D and prototyping, these ACDC test runs are part of the VELO commissioning and allow for testing of the alignment algorithms on real data, testing of the monitoring software and the use of vacuum and cooling. The ACDC3 used 4 GeV protons and 18 GeV pions of the H8 beam line at the Super Proton Synchrotron (SPS) accelerator. The beam cycle consisted of 4.8 second spills every 16.8 seconds, each typically providing 1 7 particles. The beam intensity and the size of the beam spot could be adjusted from the H8 barrack. Ten right half modules were installed for testing, with a possible readout of six modules at a time due to a shortage of cables. A cooling system with limited capacity was built for the operation of the test run [18]. The VELO was first operated with the modules in air and afterwards was run with the modules in vacuum. In vacuum the beam had to pass two 4 mm thick aluminium windows which sealed the detector box. This window caused most of the background detected by the sensors. Scintillation counters upstream and downstream of the detector box were installed to provide a coincidence signal to replace the L trigger. Four different cable configurations were chosen to test the modules. For this analysis only data taken with the fourth cable configuration (HP4) are used. Fig. 7: Position of the R sensors read out in the HP4 cable configuration, with their relative distances in mm. The position z = corresponds to the origin of the LHCb coordinate system. The HP4 cable configuration consists of the R sensors: and the associated Φ sensors: There are two groups of three modules close to each other with 31 mm between them. The distances between the modules are depicted in figure 7. The test run coordinate system

17 17 is a right-handed Cartesian coordinate system as is the LHCb detector with the central interaction point at its origin. The z axis is aligned horizontally along the beam direction. Whereas in the LHCb setup the x axis horizontally points towards the outside of the LHC ring, the right half sensors used in the test run are turned upward so that here the x axis points upwards. The y axis points horizontally to the right when following the beam direction. With the HP4 cable configuration straight beam track data, consisting of beam particles perpendicular to the silicon sensors, and target data, consisting of secondary particles produced by the beam hitting lead targets positioned above the silicon sensors was taken. The straight beam track data were used for alignment studies and the target data were used for vertex studies. Fig. 8: Installation of the targets.

18 18 3 The experiment with the VErtex LOcator Fig. 9: Schematic figure of the position of the targets relative to a VELO sensor. The inner targets are positioned at (x, y) = (, ), the outer targets at (x, y) = (15, ). Positions in mm. targets the detector was moved vertically. The targets used were 2 and 3 µm thick lead coins with a radius of 1. mm for the inner targets and 2.5 mm for the outer targets 1. In total four pairs of an inner and an outer target were glued onto Mylar foil, which are held by rings mounted in the test run setup (figure 8), such that each inner target was positioned at x = mm, y = mm and each outer target at x = 15 mm, y = mm. The pairs of targets were installed in four different z-positions, but the only 2 targets which are discussed in this analysis were positioned at z = and had a thickness of 3 µm. Therefore the inner target data correspond to interaction point collisions with a closed VELO, while the outer target data correspond to a half open VELO. In order for the beam to hit the different Quoted from VELOG 12 Nov 26 Another great morning for science! We have just seen the first vertices from the outer targets 1 and 2! by Mark, Torkjell, JC and Aras (see figure 1) Fig. 1: The z position of the vertices reconstructed using outer target data. The three peaks show the z positions of - from left to right - the beam window and outer targets 1 and 2. Image submitted by Tomas, VELOG 12 Nov All targets used were made by Frans Mul (FEW mechanical workshop, Vrije Universiteit)

19 19 The money shot. Quoted from VELOG 6 Nov 26 Tonight we took our first beam data with the velo half in the beam. As Jan said, it has been baptized. Bring out the champagne!... Aras and Anne are signing out after a very exciting night shift! by Anne and Aras (see figure 11) Fig. 11: Correlation of channels over threshold on R sensors 3 and 27 (first cable configuration). In addition to the uncorrelated noise, the correlated points between channel 6 and 14 indicate straight beam tracks in sectors 1 and 2 of the R sensors 3 and 27.

20 2 4 Monitoring 4 Monitoring In addition to monitoring the test run data offline, i.e. the monitoring of data which has already been stored in files, it was possible to monitor data realtime during the operation of the ACDC3 test run. The monitoring of real-time data is called online monitoring. Monitoring data online allows quick tests on cable connections, which was particularly useful during the test run where four different cabling schemes were used. This test run was the first run where VELO data could be monitored online and a first step towards using online monitoring in the real experiment was made. The online monitoring was made possible using software packages which were written for the offline analysis. Offline Monitoring To monitor the test run data Vetra was developed: a VELO specific piece of software for data analysis. Vetra is based on the standard LHCb software Gaudi [19], which implies that code written in Vetra can also be used in the real experiment. Currently Vetra is used for the commissioning of the detector and analysis of the test run data. During the test run the acquired data are stored into data files. These data files contain two formats, called non zero suppressed (NZS) and zero suppressed (ZS) data. The NZS data are raw data. To obtain ZS data TELL1 clustering is performed before storing the data. The clustering is performed real-time by the TELL1 readout board 2. Channels with a signal above a certain threshold, together with their neighbouring channels with a signal above strip noise are taken together to form a cluster. The data that contain the information of these clusters but hold no information on channels without signal, are therefore called zero suppressed. Storing only ZS data is faster and needs less storage space. The Vetra software can be used to analyse both ZS and NZS data. In this analysis ZS data will be used. Two packages for analysing ZS data are VeloClusterDataMonitor and Velo- TrackDataMonitor. The VeloClusterDataMonitor algorithm is used to read out the stored cluster container. It can for instance be used to analyse the sum ADC value and the number of strips (strip size) of the clusters. The package PatVelo selects sets of clusters from the cluster container which are used to create tracks using a tracking algorithm. This package contains two different pattern recognition algorithms and this will be discussed in more detail in section 5. The selected tracks are stored into a track container. The VeloTrackDataMonitor algorithm reads out the stored track container and can therefore be used to analyse track parameters, hitmaps and residuals, but it is also possible to analyse cluster information of the clusters used in tracks. The plots created by the VeloClusterDataMonitor and the VeloTrackDataMonitor are stored in ROOT 2 During the test run a bug in the TELL1 clustering was discovered and corrected, but the ZS data taken with cable configurations HP1 and HP2 are therefore erroneous. The ZS data for these cable configurations can be reconstructed offline using an emulator. This analysis is based on HP4 data for which real-time TELL1 clustering is used.

21 21 files. In order to give easier access to the monitored data stored in the ROOT files, several macros to plot the histograms are added to the Velo(ACDC) monitoring package. Using these standard macros users can plot histograms, including hitmaps and track residuals. In figure 12 two track hitmaps are depicted, plotted using the dedicated macro: akbeamspot. These hitmaps show the points of interaction of beam tracks; module 25 is the most upstream module and module 39 is the most downstream module for the HP4 cable configuration. The pattern recognition algorithm used to reconstruct these tracks is called the generic pattern recognition (section 5). Fig. 12: XY track hitmaps for modules 25 (left) and 39 (right) made using the generic pattern recognition technique. The horizontal axis represents the x position of the tracks in mm and the vertical axis the y position in mm. A third package used to analyse the ZS data, is the GenericVertexSeeding. This algorithm gets the track container as input and returns a vertex container, which contains the vertices satisfying certain conditions. For instance, one can choose how many tracks are needed in order to reconstruct a vertex. With the data from the vertex container target profile and resolution can be determined. In the real experiment this will have the shape of the interaction region. It is also possible to visualise tracks and clusters. This visualisation can be done using the software package Panoramix. In figure 13 an inner target event is depicted where two tracks are reconstructed to a common vertex. The outlines of the first R sensor and the last Φ sensor are drawn. Between these sensors all found clusters are shown and the reconstructed tracks. Although the tracks are only drawn in between the sensors, the extended trajectories intersect at the position of the inner target.

22 22 4 Monitoring Fig. 13: Panoramix visualisation of tracks and clusters in one event. Online Monitoring With the offline monitoring in place only a few changes had to be made to run the online monitoring [2]. The software program GaudiOnline has the possibility to read in data directly from the detector and to pass it on to Vetra for real-time analysis. The same histograms which are created in VeloClusterDataMonitor and VeloTrackDataMonitor are used for the online monitoring, but instead of being stored in a ROOT file they are realtime exported to a DIM server [21]. In order to display these histograms, a ROOT viewer needs to be connected to the same DIM server. A ROOT viewer is a graphical interface to ROOT, with the ability to access histograms and counters over the internet as they are produced by Vetra [22]. Figure 14 depicts an image of such a ROOT viewer, which shows the actual test run data coming in. In the right menu one can select which histograms are to be shown in the left frame. It is also possible to select draw options for the histograms and to choose the time interval after which the histograms are updated (i.e. new incoming data are added to the histogram). The left upper histogram of the figure shows the number of monitored events. This histogram beautifully shows that every time the histogram is updated, the number of monitored events has increased.

23 23 Fig. 14: The ROOT viewer displays the histograms of real-time incoming data. How to run the monitoring. Quoted from VELOG 4 Nov 26 [HEALTH WARNING: These guidelines will evolve so don t become wedded to them] by Malcolm

24 24 5 Pattern Recognition Techniques 5 Pattern Recognition Techniques A pattern recognition algorithm gets a cluster container as input. Per event it selects sets of clusters, which lie on one trajectory and satisfy other chosen conditions as well. These sets of clusters are then stored into local tracks. Therefore these sets of clusters will often be referred to as tracks, but these must not be confused with the final tracks after the fitting algorithm has been applied. At the moment there are two pattern recognition techniques in use 3. The standard pattern recognition () is optimised for fast dealing with tracks coming from the interaction region for the closed VELO configuration. A second pattern recognition technique, the generic pattern recognition (Generic PR), was created for the analysis of the test run data. This technique is less fast, but it is more robust as it is developed to deal with all kinds of data, including angled beam track data and open VELO data. For the Standard PR, developed by David Hutchcroft, a note has been released describing the performance of the on simulation data [23]. For the Generic PR, developed by Tomas Lastovicka, no documentation has been written yet. In sections 5.1 and 5.2 will be discussed how the two pattern recognition techniques work. At the start of this analysis the was not yet compatible with test run data. Changes that were made to the algorithm during the course of this analysis are described in section 5.1 as well. The features of the two pattern recognition techniques which are mainly responsible for different results will be discussed in section Standard Pattern Recognition is designed to find VELO tracks for standard LHCb operation with the two VELO detector halves closed and centred around the beam interaction region. The vertex trigger of LHCb will select events with secondary vertices based on fast track finding of what are called RZ tracks. These are 2D tracks with only R measurements on them. Based on these preliminary tracks, 3D tracks are constructed by adding Φ measurements to the tracks, which is called Space tracking. The consists of RZ tracking and Space tracking and their implementation is described below. RZ Tracking RZ tracks are 2D tracks only based on R measurements at the z position of the R sensors. The R sensors are divided in sectors of about 45 degrees and in order to reduce ghost tracks and to optimise the speed of the selection process the RZ tracks are reconstructed for each sector separately. 3 A third and a fourth PR technique, PatVeloOpenTracking and PatVeloGeneralTracking, have been released after the completion of this analysis. These techniques have not been tested using real data yet and will not be discussed here.

25 5.1 Standard Pattern Recognition 25 For tracks coming from the interaction region for a closed VELO configuration, this does not cause any limitation on the tracks reconstructed. It is possible to set the options to allow for crossing between the outer two sectors to the inner ones, which is needed to deal with tracks coming from the interaction region for an open VELO configuration (section 6.4). Starting with the most downstream R sensor (in the HP4 cable configuration this is sensor 39) and working upstream (up to sensor 25), the algorithm searches for clusters in each sector of the sensor. When a cluster is found in a certain sector, the associated sectors of the two previous read-out [1] sensors are checked for clusters as well. If all three sensors contain at least one cluster in the same sector, it is then examined whether these three clusters can form a possible track. If one of the two previous sensors misses a cluster in the considered sector, one more consecutive sensor is checked for clusters in its associated sector, in order to create a triplet of clusters, also called a seed. In order for a seed to be valid, the r coordinate of the most downstream seed cluster has to be strictly larger than the r coordinate of the most upstream seed cluster. All target tracks satisfy this condition. Depending on the region from which tracks are selected, the cut on the r coordinate of the most upstream seed cluster can be increased. From the coordinates of the outer two seed clusters, the position of a cluster on the middle sensor is predicted. If a matching cluster near the predicted position is found, a seed containing these three coordinates is stored. Clusters which are used in a seed cannot be used again in other seeds. Fig. 15: Schematic figure depicting the opposite directions of the beam and the reconstruction process. The darker blue modules are read out in cable configuration HP4. The lighter blue modules are installed, but not read out in HP4. A seed can be propagated if clusters on other sensors are found where predicted by extrapolation. The estimated trajectory is updated each time a new cluster is added to the track. Tracks which do not satisfy given constraints, for instance on charge, will be dismissed. The tracks which are left are stored in the RZVelo track container. [1] The original code assumed that at most one R sensor was missing in four consecutive modules; either through detection inefficiency or by not being read out. In the ACDC3 test run setup 6 Velo modules are tested at a time and - in contrast to when the full VELO is installed - not all modules which are read out are consecutive. This often caused at least two missing R sensors in four consecutive modules and therefore a decrease in efficiency. The code now deals with multiple missing sensors, by skipping sensors which are not read out (in stead of dealing with them as read-out sensors, with missing clusters). This

26 26 5 Pattern Recognition Techniques modification will be used from now on. Space Tracking After the reconstruction of an RZ track, Φ clusters are added to the track in order to reconstruct Space tracks. All Φ sensors positioned between the first and last R sensor found in a track plus one additional sensor in each direction will now be evaluated. These Φ sensors are evaluated starting with the most downstream sensor, working upstream. A Φ sensor consists of two sectors, an inner and an outer sector. For each Φ sensor it is first determined in which sector the estimated RZ trajectory intersects the sensor. In this sector the best matching Φ cluster is searched for. A condition for this cluster is that it lies within the boundaries of the R sector that the RZ was constructed in. For the clusters in the first tested Φ sensor, new seeds are created (A Φ seed contains a single Φ cluster) [2]. For each of the following sensors, a cluster gets added to a seed if it is the best match and within a certain maximum distance of estimated trajectory. If it is not the best match to any seed, a new seed is created. This way Φ lists are constructed. A selection process will follow to only select the best Φ lists. If the found Φ lists share a certain number of clusters, the two lists are merged. Of all the Φ lists found, the longest list with lowest χ 2 value is selected. This list, with a small tolerance on its properties, is used as a standard for comparison to other lists. If other lists are found within this pre-defined tolerance (and with a minimum of 3 clusters), they are accepted as well and multiple solutions for the same RZ track can be found. Together with the R clusters of the RZ track, the Φ clusters of a selected list are saved as a Space track. Again, only tracks which satisfy given constraints, for instance on charge, are accepted. The accepted tracks are now stored in the local track container. [2] In the original code new seeds were created for the first two Φ sensors. This often caused identical lists with two different seeds, which were merged at the end of the algorithm. The problem was that Φ lists are required to contain a minimum of 3 clusters in order to be merged and thus two Φ lists of each 2 clusters could not be merged to a minimal required 3 cluster list. The code assumed there were two Φ sensors per module. Now the code has been simplified to look at modules in stead of sensors. Only for the Φ clusters found in the first module new seeds will be created. This modification will be used from now on. Problems Compatibility Test Run Data Before being able to apply the Standard PR to the test run data, there was a problem of rotated R sensors to overcome. In comparison to the standard geometry, the R sensors are rotated 18 degrees in the test run geometry. Φ clusters are selected given they are

27 5.2 Generic Pattern Recognition 27 found within the boundaries of a certain R sector. Consistently searching in the wrong area of the Φ sensor, caused no Space tracks to be found. Solving this problem simply meant redefining which R sensors are positioned upstream and downstream. This problem was also discovered last year and had already been adjusted for the Generic PR. 5.2 Generic Pattern Recognition The Generic PR was built especially to analyse test run data. In contrast to the, the Generic PR was developed to deal with tracks coming from all origins. The test run was also used to study for example charge sharing using angled tracks. Because of this robustness of the Generic PR, it is not implemented to first create 2D tracks for fast triggering, but it searches for R and Φ clusters at the same time. This increases simplifies the algorithm, but does slow the process of recognising pattern down (section 6.6). The Generic PR, in contrast to the only considers sensors which are read out. The algorithm starts with the most downstream R sensor, working its way upstream searching for clusters per sector of the considered sensor. If a cluster is found the algorithm looks for the associated sectors in the two previous sensors. The first three R clusters of a track are constrained to be in the same R sector. When coordinates are found in all 3 consecutive sectors, Φ clusters are looked for in both sectors of the two Φ sensors associated to the first and the last of the three consecutive R sensors. All possible cluster combinations are created using the clusters on the first and last R sector and associated Φ sensor. The only constraint on the clusters is that it has not been stored in a track before. For the R/Φ cluster pairs it is tested whether the found R cluster lies in the right Φ sector and whether the Φ cluster is found in the associated R sector. If this is the case, a matching (unused) R and Φ cluster is searched for in the middle module. All the valid three pairs of R and Φ clusters are stored as track seeds. Clusters are only tagged as used when they are stored in a track. Therefore when creating seeds, it is possible that the same cluster is used in different seeds. The found seeds can optionally be checked for these shared clusters. If then seeds are found with shared clusters, these seeds are dismissed. If not tested, all seeds will be kept, including those with shared clusters. After the seed finding, the seeds can be propagated. Forward as well as backward propagation is possible. For backward propagation, the previous read out R sensor is found. Using extrapolation of the seed it is predicted in which R sector the R, but also the Φ cluster should be found. Within the boundaries of this R sector, R and Φ clusters are looked for within a certain tolerance. When successful in at least finding a (best) matching R or Φ cluster, they are added to the original seed and included in a new fit to obtain new extrapolation parameters. Again, the previous read out R sensor is looked for and this propagation process repeats itself until no previous sensors are found.

28 28 5 Pattern Recognition Techniques When a track satisfies all given constraints, the clusters of the track are marked used and will not be used anymore in further seed finding or seed propagation. The track is stored in the local track container. The program continues to the following upstream sensor and repeats the processes of seed finding, seed propagation and storing tracks. After the Generic PR is finished a different set of tracks will be obtained as after the running the for the same data. These differences are mainly due to only a few different features. These features, which cause the main differences, will be compared in the following section. 5.3 Feature Differences The and the Generic PR are developed for different purposes and the ways in which patterns of clusters are selected using these pattern recognition techniques are also different. Only a few features of the two pattern recognition techniques are the main cause of the significantly different results. This section is dedicated to the different features of the pattern recognition techniques which will be referred to when analysing the results in section Tolerances An important difference between and Generic PR is the different use of tolerance parameters. Tolerance is here defined as the maximal distance between a cluster and the predicted position of that cluster, in order for the cluster to be accepted in the pattern recognition. The tolerance area is also called the acceptance window. In the ACDC3 HP4 cable configuration some consecutive stations are not read out. This results in larger distances between read-out stations and larger extrapolation errors in the prediction of cluster positions. Choosing the correct tolerance parameters is thus important. Here the ways in which tolerances are used in the and the Generic PR will be discussed. In the five tolerance parameters are used: two tolerance parameters for finding R clusters and three tolerance parameters for finding Φ clusters. For the R clusters, this pattern recognition technique distinguishes between the tolerance for finding the second cluster of a seed (interpolation) and the tolerance used for finding clusters using extrapolation. Both these tolerances are in units of strip pitch. For finding Φ clusters, no seed of three clusters is created, but a list of Φ clusters is created. The first cluster has to lie within a tolerance which is dependent of the r coordinate of the selected R cluster in that module. The other clusters have to be found within a second tolerance, which is dependent on the distance between modules. There is also a Φ tolerance on the boundaries of the R sector in which the Φ cluster must be

29 5.3 Feature Differences 29 found. The five tolerances used are listed below, with their names as used in the algorithms and with their default values between brackets. rmatchtol (.9): the fraction of the pitch used as the tolerance for finding clusters on the middle sensor of a potential R sensor triplet. rextratol (3.5): the fraction of the pitch used as the tolerance for finding clusters on additional sensors after an R sensor triplet has been created. PhiAngularTol (.5): an small tolerance in φ angle on the boundaries of the R sector, in which Φ clusters are looked for to match the RZ track. PhiFirstTol (.5): the fraction of the r coordinate used to determine the r dependent tolerance to find the first Φ cluster matching the RZ track. PhiMatchTol (.15): the fraction of the interval between the Φ sensor on which the last added cluster was found and the current Φ sensor, which is used to determine the distance dependent tolerance for finding clusters on the current Φ sensor. Generic PR In the Generic PR three tolerance parameters are used: one tolerance parameter for finding R clusters, one for finding Φ clusters and one parameter for both R and Φ clusters, with which their tolerances are multiplied. The tolerances for finding R and Φ clusters are constant and do not depend on distance, neither is there a distinction between the tolerance for finding seed clusters and propagation clusters. RAliTol (.): the tolerance parameter added to the digital resolution to increase the total tolerance used for finding R clusters. PAliTol (.): the tolerance parameter added to the digital resolution to increase the total tolerance used for finding Φ clusters. SigmaTol (4.): a multiplication factor used for both the tolerances in R and Φ. Having the default values of RAliTol and PAliTol set to. and the default value of SigmaTol set to 4., means that a tolerance of 4 times the digital resolution - which is pitch/ 12 - is always used. Example In the Generic PR a smaller tolerance to find clusters through extrapolation is used than in the. The result of this is that, where only clusters in modules are found using Generic PR, additional clusters are often found in modules using. This effect is clearly visible in the hitmaps of sensors 25 and 39 using the in figure 16 and compare them with the same hitmaps using the Generic PR in

30 3 5 Pattern Recognition Techniques figure 12. Using the Generic PR, considerably more hits are found in module 39 than in module 25. Straight beam track data are used, which means that the same number of hits are expected in each module. Using the, the number of hits in each module is comparable, as expected. Fig. 16: XY track hitmaps for modules 25 (left) and 39 (right) made using the Standard PR technique. The horizontal axis represents the x position of the tracks in mm and the vertical axis the y position in mm Unique Seeds To create a seed in the three R clusters are needed. In the Generic PR three pairs of R/Φ clusters are needed to create a seed. Due to noise or spurious hits in an event, it may occur that a cluster can be used for more than one seed. For larger tolerances this will occur more often. The different ways in which and Generic PR deal with the multiple use of clusters, cause differences in tracks found and especially differences in the number of tracks found per event. looks at all clusters on a first R sensor and for each of these clusters it then looks at clusters of the third R sensor of the possible seed, increasing in strip number. As soon as a cluster on the second sensor is found which matches the requirements, the seed is stored and none of the three clusters used in this seed are considered anymore for a second seed. Thus, the always chooses one seed - the first, not necessarily the best - regardless of any other combinations that can be considered with the same clusters. Generic PR In the Generic PR for a given first sensor all possible combinations are made seeds. If the option CleanSeed is set to true, all seeds are compared to see if they share a common cluster. If a cluster is used in more than one seed, all seeds containing this cluster are not considered. This option was originally used to cope with large misalignments. For large misalignment, large tolerances are necessary and if different clusters on a sensor are found close enough to each

31 5.3 Feature Differences 31 other, many combinations of clusters can be made to create seeds. To select only the unique ones out of all these seeds is very useful to align the VELO with these high quality tracks. For the purpose of alignment efficiency is not so important. If CleanSeed is set to false, the seeds which are found for the same first sensor, are all considered. After this all clusters in these seeds are flagged as used. When looking for seeds using the next sensor (which will then be the first one of a seed), these used clusters will not be considered again. Increasing the tolerance in this case may cause many tracks to be created. Example To demonstrate the difference in unique seed treatment an event where the effect of the option CleanSeed and the effect of the increase of the tolerances are clearly visible is considered. Using the one track containing the following clusters is reconstructed, see figure 17. Fig. 17: R and Φ clusters of five modules (red curves) are shown in space with a track (blue line) found using the. One seed is found using the, in this case the R triplet If there could be any other seeds starting with strip 244 is not considered. Thus is chosen in stead of , simply because 441 is a lower strip number than 444. With CleanSeed set to true, no tracks are found using Generic PR. With CleanSeed set to false, 4 tracks are found, using 1 different clusters, see table 1. The alternating orientation of the sensors is visible in the cluster strip numbers of the tracks. Tab. 1: The different tracks found in the same event using and Generic PR, with the option CleanSeed set to true and false. The tracks are given using the cluster strip number of each sensor. Generic PR true Generic PR false sensor track 1 track 1 track 2 track 3 track

32 32 5 Pattern Recognition Techniques Enlarging the tolerance to RAliTol =.6 and PAliTol =.1, now results in 16 tracks, using only 14 clusters. Fig. 18: R and Φ clusters of two modules (red curves) are shown in space with several tracks (blue lines) found using the Generic PR, with the option CleanSeed set to false. These images are close ups of complete tracks going through five modules. (a) 4 tracks are found using 1 clusters on five modules. (b) A larger tolerance causes 16 tracks to be found using 14 clusters on five modules Cuts on tracks The is optimised for analysing tracks from the interaction region. A cut to select these kind of tracks improves the speed of the program, which is necessary for a fast trigger on secondary decay tracks. In the a cut is made on the radial position of the cluster in the third sensor of an R seed. Using the option ZVertexMin a minimal z-value of the vertex is specified. The minimal z-value of the vertex and the radial position of the first cluster in the seed, determine the maximal radial position of a third cluster of the seed. Because only tracks from the interaction region are of interest, it is assumed that tracks do not cross R sectors. is therefore unable to deal with angled beam track data. However, there is an option called AdjacentSectors which can be set to true for the open VELO mode. Tracks which cross from outer to inner R sectors are also considered in that case. Generic PR The goal of the Generic PR is to be able to deal with all kinds of tracks. Therefore there are no cuts on the direction of the tracks. The only constraint is that all clusters of a seed lie within the boundaries of the same R sector. The other clusters of the track are allowed to be found in other R sectors. This constraint keeps most of the expected tracks and reduces the number of seeds.

33 33 6 Data Analysis: Comparison of Pattern Recognition Techniques The two pattern recognition techniques compared are the standard pattern recognition () and the generic pattern recognition (generic PR), discussed in section 5. For this comparison three different data sets are used: straight beam track data, inner target data and outer target data. Straight beam track data (opposed to angled beam track data) consist of beam tracks perpendicular through all six modules of the detector. The inner and outer target data consist of straight tracks originating from the inner or outer target, traversing the detector at an angle. First the yield obtained using these pattern recognition techniques will be discussed using straight beam track data (section 6.1). The numbers of tracks found per event and the numbers of modules per track are compared. This comparison will show that using the Generic PR more sensors are missing in the reconstructed tracks. Adjustments in the Generic PR will show to improve the results and will lead to a better comparison. The Generic PR including these adjustments will be called the Adjusted Generic PR. The quality of the tracks found is compared using the unbiased track residuals. The residuals for both R and Φ sensors will be considered using the Generic, the Adjusted Generic and the. In addition the effect of alignment is demonstrated using the residuals of tracks which only contain hits in the downstream Φ sensors (section 6.2). The residuals for the R sensors show peak structures. This can be improved using the η-function, which depicts non linear charge charging (section 6.3). For the inner and outer target data the quality of the tracks will also be compared using the unbiased residuals of the tracks (section 6.4). Because the is optimised for inner target data, some adjustments in the options of the code have to be made. The with the adjusted options will be called the adjusted. In addition both pattern recognition techniques are compared by reconstructing targets to determine target edge resolution (section 6.5). 6.1 The Yield of Straight Beam Track Data using Original and Adjusted Pattern Recognition Techniques The first the Generic PR and the are tested using straight beam track data. Because the particles travel straight through the detector, it is expected that clusters are found in all 12 sensors of the setup. Looking at the hitmaps in figures 12 and 16, a similar number of entries is expected in the hitmaps of sensor 25 and 39, because straight beam tracks traverse all sensors. Using the indeed both hitmaps contain a similar number of entries, but using the Generic PR the hitmap of sensor 25 contains much less entries. To start the analysis the number of tracks found per event and the number of modules present in each track found using the and the Generic PR are looked at first. For this analysis 1, straight beam track events are run over. The results are depicted in figure 19.

34 34 6 Data Analysis: Comparison of Pattern Recognition Techniques (a) number of tracks per event (b) number of modules per track Fig. 19: (a) The number of tracks found per event using (blue crosses) and Generic PR (red circles). (b) The number of modules used to reconstruct a track using (blue crosses) and Generic PR (red circles). In 1, events a total of 64,61 tracks were reconstructed using and 73,977 using Generic PR. Using the Generic PR gives considerably more tracks in total than using the. The number of events in which no tracks are found is comparable for both PR techniques. The difference occurs in events where at least one track is found by both PR techniques. This can be explained by the difference in seed finding, as explained in section Using the more often 1 track is found in an event, because when searching for seeds the first unique seed found is selected. In the Generic PR the search for other seeds which may share clusters with other seeds found continues and therefore it is more likely that more tracks per event are found. Although with the Generic PR more tracks are found in total, less tracks with all 6 modules are reconstructed. To investigate this problem further the number of full tracks per event is looked at. Full tracks are tracks which have a measurement on all 12 sensors. In addition the number of times sensors are missing in a track reconstructed using the Generic code is considered. The results are depicted in figure 2. Figure 19b already showed that using the Generic code about 2% less tracks with 6 modules are reconstructed. Figure 2a shows that about 4 % of the 12 sensor tracks found using are also found using Generic PR. This means that often when a module is used in the reconstruction of a track, only one of the sensors in the module is used. In figure 2b, which depicts how often a sensor is missing in a track, most often the upstream three R sensors ( ) and the upstream three Φ sensors ( ) are missing. The reason that these sensors are missing is due to the fact that the reconstruction process starts with the most downstream module, working its way upstream, as explained in section 5.1. The extrapolation distance from module 35 to module 31 is 31 mm. Due to small misalignments, an extrapolation over a long distance can cause large errors and with the small tolerances of the Generic PR, hits on sensors

35 6.1 The Yield of Straight Beam Track Data using Original and Adjusted Pattern Recognition Techniques (a) number of full tracks per event (b) sensor number Fig. 2: (a) The number of tracks with measurements on all 12 sensors found per event using (blue crosses) and Generic PR (red circles). (b) The number of times a sensor is not used in the reconstruction of a track using Generic PR. In the 73,977 reconstructed tracks 26,947 sensors were not used in reconstruction. are easily missed. The difference between the tolerances of the and the Generic PR is described in section These differences in how seeds are selected in the PR methods and the way their tolerances differ are clear. When different seeds share a common cluster, only the first seed is selected in the, while in the Generic PR either all or none of these seeds are selected. And in the there are different tolerances for finding clusters in a seed and finding clusters through extrapolation. In contrast, increasing the tolerance used in Generic PR would increase both the tolerance for finding a seed cluster and the tolerance for finding clusters through extrapolation. However, there may be other less obvious differences. In order to make a better comparison between the Standard PR and the Generic PR the obvious differences are filtered out. This is done by making the two following small modifications to the Generic PR code: [1] Only the first seed is selected when common clusters in the seeds occur. All other seeds with shared clusters are dismissed. [2] A new distance dependent R and Φ tolerance, which distinguishes between seed clusters and others is added. The added parameters are called ExtraTolr, the extra tolerance for finding R clusters, and ExtraTolp, the extra tolerance for finding Φ clusters. The new tolerances are calculated from the original tolerances (OldTol) and the new parameters. The new R tolerances are: For finding the middle R cluster of a seed the new R tolerance is given by: ( OldTol 1 + z ) 2 z 6 ExtraTolr 6

36 36 6 Data Analysis: Comparison of Pattern Recognition Techniques For finding R clusters through extrapolation the new R tolerance is given by: ( OldTol 1 + z ) 1 z 3 ExtraTolr 3 The new Φ tolerances are calculated in a similar manner, substituting ExtraTolp for ExtraTolr. For finding the middle cluster of a seed, z and z 2 are the z-positions of the first and the third sensor of the potential seed. For finding other clusters z 1 z is the distance between the last added sensor to the track and the current sensor on which the next cluster is looked for. The values of 3 and 6 are chosen, because the most common distance between two consecutive sensors is 3 mm. In both cases the term OldTol stands for the original tolerance which was already used in the Generic code. In order to better match the new tolerance of finding the middle cluster of a seed to the tolerance used in the, the option SigmaTol is changed to a value of 3, in stead of its default value of 4 (see section 5.3.1). This Adjusted Generic PR will be compared with the. The number of tracks per event found using each algorithm and the number of modules used to reconstruct the tracks is shown in figure (a) number of tracks per event (b) number of modules per track Fig. 21: (a) The number of tracks found per event using (blue crosses) and Adjusted Generic PR (red circles). (b) The number of modules used to reconstruct a track using (blue crosses) and Adjusted Generic PR (red circles). In 1, events a total of 64,61 tracks were reconstructed using and 64,718 using Generic PR. A large change in the number of tracks found per event can be seen. It now occurs slightly more often with the Adjusted Generic PR more events with one track are found and with the slightly more events where two or three tracks are reconstructed are found. The total number of tracks found using the Adjusted Generic code has gone down from 73,977 to 64,718 which is in much better agreement with the 64,61 tracks found using the Standard code. There will always remain differences because the way the two PR techniques work remains essentially different. There is also a better agreement in the number of modules used to reconstruct tracks. Due to the increase in tolerance

37 6.2 Residuals of Straight Beam Track Data using Old and Improved Alignment 37 over larger distances for the Adjusted Generic code, clusters on all 6 modules are can be located and used to reconstruct tracks. That also many more 12 sensor tracks are reconstructed can be seen in figure (a) number of full tracks per event (b) sensor number Fig. 22: (a) The number of tracks with measurements on all 12 sensors found per event using (blue crosses) and Adjusted Generic PR (red circles). (b) The number of times a sensor is not used in the reconstruction of a track using Adjusted Generic PR. In the 64,718 reconstructed tracks 27,733 sensors were not used in reconstruction. As expected the numbers of full tracks found using the two pattern recognition techniques are in much better agreement now. The number of missing sensors for the Adjusted Generic PR has gone down from 26,947 to 27,733 missing clusters (figure 22), which is much closer to the 23,925 missing sensors for the. The two first Φ sensors still miss more hits than the other Φ sensors, this is the same case for the. Increasing the tolerance even further brings the number of these missing sensors down as well. 6.2 Residuals of Straight Beam Track Data using Old and Improved Alignment All sensors are mounted with high accuracy at their nominal positions. The misalignments that remain are corrected for in the software, using so called alignment files. The results for the residuals depend highly on which alignment file was used. During the course of this analysis the HP4 alignment file was improved. First the influence of this new alignment file is shown before continuing with the results for the residuals using the improved alignment file. The unbiased residuals for the downstream three Φ sensors are considered. The track reconstruction start with the most downstream sensor. Figures 23a,b,c show that the Generic and the select a comparable number of hits in these sensors to reconstruct their tracks.

38 38 6 Data Analysis: Comparison of Pattern Recognition Techniques (a) Φ-99 residual (µm) (d) Φ-99 residual (µm) (b) Φ-11 residual (µm) (e) Φ-11 residual (µm) (c) Φ-13 residual (µm) (f) Φ-13 residual (µm) Fig. 23: Number of unbiased track residuals of Φ clusters for (blue crosses) and Generic PR (red circles), including residuals in tracks without three upstream Φ sensors (3Φ Generic PR, green dots). Results using old (a,b,c) and improved (d,e,f) alignment parameters. Total number of entries, mean residual, and root-mean-square for the different sensors are: (a) sensor Φ-99 (b) sensor Φ-11 (c) sensor Φ-13 entries entries entries mean (µm) 9.91 mean (µm) mean (µm) 8.5 r.m.s. (µm) 16.9 r.m.s. (µm) 16. r.m.s. (µm) 18.9 Generic PR Generic PR Generic PR entries entries entries mean (µm) 2.71 mean (µm) mean (µm) r.m.s. (µm) 28.3 r.m.s. (µm) 19.8 r.m.s. (µm) 3.6 3Φ Generic PR 3Φ Generic PR 3Φ Generic PR entries entries entries 2443 (d) sensor Φ-99 entries 6292 mean (µm) r.m.s. (µm) 16.6 Generic PR entries mean (µm) r.m.s. (µm) Φ Generic PR entries (e) sensor Φ-11 entries mean (µm) 7.74 r.m.s. (µm) 15.8 Generic PR entries 6114 mean (µm) 7.44 r.m.s. (µm) Φ Generic PR entries (f) sensor Φ-13 entries mean (µm) r.m.s. (µm) 18.5 Generic PR entries 6996 mean (µm) r.m.s. (µm) Φ Generic PR entries 23217

39 6.2 Residuals of Straight Beam Track Data using Old and Improved Alignment 39 The residuals for sensors 99 and 13 look very different; in the Generic PR a large shoulder appears. The residuals plotted in green are the Generic PR residuals of the tracks which do not contain Φ hits on the three upstream Φ sensors. The shoulder shows a misalignment of the three Φ modules. When more Φ clusters are used to construct a track, a misaligned cluster contributes less to the fit parameters and therefore is its misalignment less visible in the residuals of the other clusters. Figures 23d,e,f show the results after a recent alignment improvement 4. The improvement can be seen in the generic residuals of the tracks reconstructed with only three Φ sensors, which are now better centred. This has reduced the size of the shoulder in the generic residuals with all tracks included. Although the alignment has been tuned, the number of tracks found containing only three Φ clusters has not gone down much. Better alignment alone does not significantly increase the number of tracks reconstructed with more than three Φ clusters. The residuals for the upstream three Φ sensors show that using the Generic PR less clusters are found in the upstream three Φ sensors, compared to the number of clusters found in the downstream three Φ sensors (figure 24). With a perfect alignment the tight tolerances of the Generic PR would suffice. The number of clusters found using the is similar for all Φ sensors (a) Φ-89 residual (µm) (b) Φ-93 residual (µm) (c) Φ-95 residual (µm) Fig. 24: Number of unbiased track residuals of Φ clusters for (blue crosses) and Generic PR (red circles). Total number of entries, mean residual, and root-mean-square for the different sensors are: (a) sensor Φ-89 entries mean (µm) 2.47 r.m.s. (µm) 18.1 Generic PR entries mean (µm) r.m.s. (µm) 28.7 (b) sensor Φ-91 entries mean (µm) 4.36 r.m.s. (µm) 16.4 Generic PR entries mean (µm) 3.73 r.m.s. (µm) 18.2 (c) sensor Φ-95 entries mean (µm) r.m.s. (µm) 18.5 Generic PR entries mean (µm) r.m.s. (µm) Alignment by Sebastian Viret, 18 June 27. The improved alignment file includes R/Φ misalignment and z position correction of the modules. It is optimised for inner target data.

40 4 6 Data Analysis: Comparison of Pattern Recognition Techniques The number of reconstructed tracks and the number of modules used to reconstruct a track for the Generic and the differ less after adding a distance dependent tolerance to the Generic code and letting it select only one seed if seeds with shared clusters were found. The residuals using the Adjusted Generic PR are shown in figure 25. The Φ residuals now are very similar. There are still differences between the results obtained using the Adjusted Generic and the, which is shown by the R residuals of sensors 35 and 37. For sensor 35 less entries are found at the positive edge of the residual distribution using the. The residuals for R sensor 37 obtained with the Adjusted Generic PR clearly show three peaks figure 26, while the residuals obtained with the only show two distinct peaks. As discussed in section the standard PR is optimised for analysing tracks which origin at the interaction region. For this test run analysis the value of ZVertexMin was set to -1, mm in order to include parallel tracks. This still means that the RZ tracking requires the radial position of the cluster in sensor 35 to be strictly lower than the radial position of the cluster in sensor 39 (the third and first cluster of a seed) without any tolerance. Adding a small tolerance to the acceptance of clusters of sensor 35, results into the residuals show in figure 27. The unbiased residual distributions of the tracks reconstructed using the Adjusted Generic PR and the Adjusted are similar. That the residual distributions now look the same for both pattern recognition techniques, does not explain why they look this way. For example, the peak structures of sensors 35 and 37 remain unexplained. In section 6.3 this phenomena will be discussed in further detail.

41 6.2 Residuals of Straight Beam Track Data using Old and Improved Alignment (a) Φ-89 residual (µm) (d) Φ-99 residual (µm) (b) Φ-93 residual (µm) (e) Φ-11 residual (µm) (c) Φ-95 residual (µm) (f) Φ-13 residual (µm) Fig. 25: Number of unbiased track residuals of Φ clusters for (blue crosses) and Adjusted Generic PR (red circles). Total number of entries, mean residual, and root-mean-square for the different sensors are: (a) sensor Φ-89 (b) sensor Φ-91 (c) sensor Φ-95 entries entries entries mean (µm) 2.47 mean (µm) 4.36 mean (µm) r.m.s. (µm) 18.1 r.m.s. (µm) 16.4 r.m.s. (µm) 18.5 Adjusted Generic PR Adjusted Generic PR Adjusted Generic PR entries 6366 entries 5789 entries mean (µm) 2.93 mean (µm) 3.63 mean (µm) r.m.s. (µm) 18.5 r.m.s. (µm) 16. r.m.s. (µm) 19.6 (d) sensor Φ-99 entries 6292 mean (µm) r.m.s. (µm) 16.6 Adjusted Generic PR entries mean (µm) r.m.s. (µm) 16.7 (e) sensor Φ-11 entries mean (µm) 7.74 r.m.s. (µm) 15.8 Adjusted Generic PR entries mean (µm) 7.74 r.m.s. (µm) 16.3 (f) sensor Φ-13 entries mean (µm) r.m.s. (µm) 18.5 Adjusted Generic PR entries mean (µm) r.m.s. (µm) 17.8

42 42 6 Data Analysis: Comparison of Pattern Recognition Techniques (a) R-35 residual (µm) (b) R-37 residual (µm) Fig. 26: Number of unbiased track residuals of R clusters for (blue crosses) and Adjusted Generic PR (red circles). Total number of entries, mean residual, and root-mean-square for the different sensors are: (a) sensor R-35 (b) sensor R-37 entries 5711 entries 6363 mean (µm) mean (µm) 6.2 r.m.s. (µm) 16. r.m.s. (µm) 21.7 Adjusted Generic PR Adjusted Generic PR entries entries mean (µm) mean (µm) 5.44 r.m.s. (µm) 16.6 r.m.s. (µm) (a) R-35 residual (µm) (b) R-37 residual (µm) Fig. 27: Number of unbiased track residuals of R clusters for Adjusted (blue crosses) and Adjusted Generic PR (red circles). Total number of entries, mean residual, and root-mean-square for the different sensors are: (a) sensor R-35 Adjusted entries mean (µm) r.m.s. (µm) 16.5 Adjusted Generic PR entries mean (µm) r.m.s. (µm) 16.6 (b) sensor R-37 Adjusted entries mean (µm) 5.38 r.m.s. (µm) 21.3 Adjusted Generic PR entries mean (µm) 5.44 r.m.s. (µm) 2.8

43 6.3 Resolution Improvement with η function for Straight Beam Track Data Resolution Improvement with η function for Straight Beam Track Data When a particle traverses a sensor in between two strips or at an angle, the induced charge can be deposited on more than one strip. This phenomena is called charge sharing and leads to clusters containing multiple strips. The position where the particle has intersected the sensor, x, is then derived from the multiple strip charges. This conversion can be described by the η function, with η the charge ratio. For 2 strip R clusters η is given by [24] η = C 2 C 1 + C 2 (4) where C 1 is the charge of the inner strip of the cluster and C 2 the charge of the outer strip. In standard LHCb reconstruction the cluster position is approximated by taking the charge weighted mean of the strips. This means a flat η distribution is assumed, thus the intersect position is calculated using the relation x = ηp, where p stands for the pitch. This causes a two peak structure in the unbiased track residuals. This approximation of cluster position can be improved by assuming a nonlinear η function. For different angled tracks Thijs Versloot [25] has determined non-linear η functions, improving sensor resolution. These functions do not yet contain an angle dependence and because the angle of inner and outer target data is not constant, the non-linear η function has only been implemented for straight beam track data. A 3 rd order η function fitted to zero degree data is given by x = (η.5) (η.5)3 p As shown in figure 28, the fitted offset is.52 and not exactly.5, but to avoid correcting for the misalignment using the η-function the offset is set to.5 in the implementation. Fig. 28: A 3 rd order η function fitted for zero degree straight tracks. Figure by T. Versloot. Using this new function to determine the cluster position of the 2-strip

44 44 6 Data Analysis: Comparison of Pattern Recognition Techniques clusters in the reconstruction the sensor resolution increases and the unbiased track residuals for R sensors 35 and 37 depicted in figure 29 are the result (a) R-35 residual (µm) (b) R-37 residual (µm) Fig. 29: Number of unbiased track residuals of R clusters for Adjusted Generic PR using a non-linear η function (green crosses) and Adjusted Generic PR using the standard weighted mean method (red circles). Total number of entries, mean residual, and root-mean-square for the different sensors are: (a) sensor R-35 η function (b) sensor R-37 η function entries entries mean (µm) mean (µm) 7.11 r.m.s. (µm) 16.4 r.m.s. (µm) 19.6 weighted mean method weighted mean method entries entries mean (µm) mean (µm) 5.44 r.m.s. (µm) 16.6 r.m.s. (µm) 2.8 Even though there is still an unexplained peak structure in the residuals, a clear improvement is visible. It is interesting to note that the remaining peak structure is mainly due to the residuals of 1-strip clusters. This is true for the residuals of both tracks reconstructed with the linear weighted mean and the non-linear η function. The implemented η function only influences the determination of the position of 2-strip clusters. But the new 2-strip cluster positions influence all residuals. To determine the exact cause of the remaining peak structure, more analysis is needed. 6.4 Residuals for Inner and Outer Target Data Inner Target Data The was developed especially for fast reconstruction of tracks coming from the interaction region with a closed VELO configuration. These tracks correspond to inner target tracks in the test run setup. The is therefore expected to deal more efficiently with tracks coming from the inner target. If the results are similar to the results of

45 6.4 Residuals for Inner and Outer Target Data 45 the slower Generic PR will be investigated. Fig. 3: From all found tracks, those which satisfy x 2 + y 2 < 3 mm at z = come from the inner target area and are selected for analysis. Here every point depicts the x and y coordinate of a track at z =. Using the only tracks from a given interaction region are selected, while using the Generic PR tracks from all origins are selected. To make a fair comparison tracks from a large interaction region using. For both pattern recognition techniques a tighter selection on the interaction region will be made afterwards in the VeloTrackDataMonitor. The inner target is located at the origin and has a radius of 1 mm. All tracks which at z = have an x and y coordinate, such that x 2 + y 2 < 3 mm are selected and compared. These tracks will be called the inner target tracks. The selection of inner target tracks is shown in figure 3. As for the straight beam track data, the unbiased track residuals are compared. The results for the R sensors are shown in figure 31. Using both Standard and Generic PR many tracks which only have hits in the last three modules are found. In contrast to the straight beam tracks, where often clusters were missed due to small tolerances, the inner target tracks often only traverse the three most downstream modules due to their small angles. This also results in a residual distribution without the peak structures seen in figure 27. The effect of the smaller tolerance used by the Generic PR can still be seen in the number of entries in modules 29 and 31. For the R sensors this can be seen in figure 31. The effect seen in these results is smaller than the effect of the small tolerances on the straight beam track data, because about 85% of the found tracks are three module tracks while only 2% are six module tracks for the inner target data.

46 46 6 Data Analysis: Comparison of Pattern Recognition Techniques The Φ residuals are comparable to the found R residuals. Using the Generic PR slightly more hits in sensor 89 are found, but less in sensors 93 and 95. The previous section showed that adding a distance dependent tolerance to the Generic code and letting it only select one seed from the seeds which share clusters improves the results. Making these same changes here results into the unbiased track residuals shown in figure 32. For sensors 29 and 31 the number of clusters used to reconstruct tracks has increased. Overall the numbers of tracks reconstructed by the Adjusted Generic PR is slightly less than number reconstructed by the. Generic s tolerance for seed finding is marginally smaller than Standard s, especially for the first three clusters (Their relative distance is smaller and this affects Generic s tolerance, but not Standard s tolerance). These differences are still responsible for different results.

47 6.4 Residuals for Inner and Outer Target Data (a) R-25 residual (µm) (a) R-35 residual (µm) (b) R-29 residual (µm) (b) R-37 residual (µm) (c) R-31 residual (µm) (c) R-39 residual (µm) Fig. 31: Number of unbiased track residuals of R clusters for (blue crosses) and Generic PR (red circles). Total number of entries, mean residual, and root-mean-square for the different sensors are: (a) sensor R-25 entries 647 mean (µm) r.m.s. (µm) 46.3 Generic PR entries 6714 mean (µm).6 r.m.s. (µm) 58.8 (a) sensor R-35 entries mean (µm) 3.97 r.m.s. (µm) 28.1 Generic PR entries mean (µm) 3.96 r.m.s. (µm) 31.6 (b) sensor R-29 entries 1765 mean (µm) -.83 r.m.s. (µm) 19.5 Generic PR entries 8817 mean (µm) r.m.s. (µm) 23.1 (b) sensor R-37 entries mean (µm) r.m.s. (µm) 17. Generic PR entries mean (µm) r.m.s. (µm) 17.6 (c) sensor R-31 entries mean (µm).21 r.m.s. (µm) 36.9 Generic PR entries 993 mean (µm).96 r.m.s. (µm) 32.5 (c) sensor R-39 entries mean (µm) 3.42 r.m.s. (µm) 26.7 Generic PR entries mean (µm) 3.36 r.m.s. (µm) 3.6

48 48 6 Data Analysis: Comparison of Pattern Recognition Techniques (a) R-25 residual (µm) (a) R-35 residual (µm) (b) R-29 residual (µm) (b) R-37 residual (µm) (c) R-31 residual (µm) (c) R-39 residual (µm) Fig. 32: Number of unbiased track residuals of R clusters for (blue crosses) and Adjusted Generic PR (red circles). Total number of entries, mean residual, and root-mean-square for the different sensors are: (a) sensor R-25 (b) sensor R-29 (c) sensor R-31 entries 647 entries 1765 entries mean (µm) mean (µm) -.83 mean (µm).21 r.m.s. (µm) 46.3 r.m.s. (µm) 19.5 r.m.s. (µm) 36.9 Adjusted Generic PR Adjusted Generic PR Adjusted Generic PR entries 581 entries 9682 entries 1234 mean (µm) -.52 mean (µm) mean (µm).76 r.m.s. (µm) 51.7 r.m.s. (µm) 19.6 r.m.s. (µm) 38.2 (a) sensor R-35 entries mean (µm) 3.97 r.m.s. (µm) 28.1 Adjusted Generic PR entries mean (µm) 3.79 r.m.s. (µm) 28.6 (b) sensor R-37 entries mean (µm) r.m.s. (µm) 17. Adjusted Generic PR entries mean (µm) r.m.s. (µm) 16.9 (c) sensor R-39 entries mean (µm) 3.42 r.m.s. (µm) 26.7 Adjusted Generic PR entries 4975 mean (µm) 3.46 r.m.s. (µm) 27.5

49 6.4 Residuals for Inner and Outer Target Data 49 Outer Target Data As explained in section 3 the VELO stations are closer to the beam than the distance required by LHC during injection. The stations are therefore retracted during injecting, such that their distance to the beam line is 3 mm. This is called the open VELO mode. The outer target has a radius of 2.5 mm and is positioned at x = 15 and y = mm. This means that this situation corresponds to a half open VELO mode in the real experiment. The was not developed to deal with tracks coming from this region and therefore two problems occur. For a closed detector the tracks coming from the interaction point are constant in Φ and linear in RZ. However from a track starting from the position of the outer target neither of these are necessarily true. Secondly, it is possible that tracks cross from the outer two R sectors to the inner two. The Generic PR should have no problems to deal with these tracks. For the same reason named in the previous section, the selection of tracks is done in the VeloTrackDataMonitor. All tracks with coordinates such that (x 15) 2 + y 2 < 4 at z = are selected and these will be called outer target tracks. The selection of outer target tracks is shown in figure 33. Fig. 33: From all found tracks, those which satisfy (x 15) 2 + y 2 < 4 mm at z = come from the outer target area and are selected for analysis. Here every point depicts the x and y coordinate of a track at z =. The unbiased track residuals for both PR techniques for the outer target data are considered. The results for the R residuals are shown in figure 34. As expected the residuals distributions look the same, but the finds much less tracks due to the problems has as mentioned earlier. To overcome this problem the tolerances have to increased a lot. This is because the RZ code is looking for straight lines in RZ and so it has tight windows to see if three points from a line that points to nearly

50 5 6 Data Analysis: Comparison of Pattern Recognition Techniques x = and y =. The tolerances need to be enlarged to grab tracks which fail this. The same applies to the Φ tracking where it assumes that the second Φ cluster is at nearly the φ coordinate of the first Φ cluster. Opening the search windows for the half-open and open VELO mode is OK. For inner target tracks the search windows cannot be opened because far too many wrong hits will be found, which creates ghost tracks. The best tolerance settings for this situation are [23]: rextratol = 28 rmatchtol = 7.2 PhiMatchTol =.9 PhiFirstTol =.3 Also, the has an option AdjacentSectors which allows the crossing from the outer R sectors to the inner ones when set to true. The results with AdjacentSectors set to true and the increased tolerances for the are shown in figure 35. The Adjusted now give very similar results to the Generic PR. For the straight track data and the inner target data there was a significant number of tracks going through six modules and therefore adjusting the Generic tolerances improved the results. For the outer target data the number of tracks passing through more than three modules is so small, that adjusting the Generic tolerances does not make a significant difference. For constructing three module tracks, only the tolerance for finding a middle cluster is used. The tolerance used for finding clusters through extrapolation is not used.

51 6.4 Residuals for Inner and Outer Target Data (a) R-25 residual (µm) (a) R-35 residual (µm) (b) R-29 residual (µm) (b) R-37 residual (µm) (c) R-31 residual (µm) (c) R-39 residual (µm) Fig. 34: Number of unbiased track residuals of R clusters for (blue crosses) and Generic PR (red circles). Total number of entries, mean residual, and root-mean-square for the different sensors are: (a) sensor R-25 entries 1426 mean (µm) -4.3 r.m.s. (µm) 51.5 Generic PR entries mean (µm) 2.74 r.m.s. (µm) 66.2 (a) sensor R-35 entries 2471 mean (µm) 7.76 r.m.s. (µm) 42.2 Generic PR entries mean (µm) 8.66 r.m.s. (µm) 47.6 (b) sensor R-29 entries 1732 mean (µm) -.1 r.m.s. (µm) 17.1 Generic PR entries mean (µm) r.m.s. (µm) 24.3 (b) sensor R-37 entries 2491 mean (µm) -4.3 r.m.s. (µm) 21.9 Generic PR entries mean (µm) r.m.s. (µm) 24.9 (c) sensor R-31 entries mean (µm) r.m.s. (µm) 36.5 Generic PR entries mean (µm) 2.67 r.m.s. (µm) 36.7 (c) sensor R-39 entries mean (µm) 8.21 r.m.s. (µm) 4.4 Generic PR entries mean (µm) 11.5 r.m.s. (µm) 42.6

52 52 6 Data Analysis: Comparison of Pattern Recognition Techniques (a) R-25 residual (µm) (a) R-35 residual (µm) (b) R-29 residual (µm) (b) R-37 residual (µm) (c) R-31 residual (µm) (c) R-39 residual (µm) Fig. 35: Number of unbiased track residuals of R clusters for Adjusted (blue crosses) and Generic PR (red circles). Total number of entries, mean residual, and root-mean-square for the different sensors are: (a) sensor R-25 Adjusted entries mean (µm) 2. r.m.s. (µm) 66.4 Generic PR entries mean (µm) 2.74 r.m.s. (µm) 66.2 (a) sensor R-35 Adjusted entries mean (µm) 8.22 r.m.s. (µm) 46.7 Generic PR entries mean (µm) 8.66 r.m.s. (µm) 47.6 (b) sensor R-29 Adjusted entries mean (µm) r.m.s. (µm) 27.9 Generic PR entries mean (µm) r.m.s. (µm) 24.3 (b) sensor R-37 Adjusted entries mean (µm) r.m.s. (µm) 27.1 Generic PR entries mean (µm) r.m.s. (µm) 24.9 (c) sensor R-31 Adjusted entries 3459 mean (µm) 2.2 r.m.s. (µm) 43.3 Generic PR entries mean (µm) 2.67 r.m.s. (µm) 36.7 (c) sensor R-39 Adjusted entries mean (µm) r.m.s. (µm) 42.8 Generic PR entries mean (µm) 11.5 r.m.s. (µm) 42.6

53 6.5 Target Reconstruction for Inner and Outer Target Data Target Reconstruction for Inner and Outer Target Data One of the goals of the VELO is to reconstruct vertices with high resolution. In this section a vertex resolution comparison between the two pattern recognition techniques will be performed. This comparison is performed to show if there are differences between the Generic PR and the in terms of vertex resolution, which would show an uncertainty in vertex resolution caused by the pattern recognition. Inner Target Data Vertices reconstructed with a minimum of two tracks are considered to obtain as much statistics as possible. In order to say something about the resolution with which these vertices are reconstructed, the resolution with which the edge of the target can be measured will be considered. In the middle of the target a slice of vertices is selected, small enough that the curvature of the target does not influence the results. Figure 36 depicts the vertices found near the target and the vertical slice (x slice) of vertices which will be used to perform the analysis. Fig. 36: Selecting an x-slice of vertices. ues are shown in table 2. To determine the edge resolution, the x distribution of the vertices in the x slice is fitted. To do this each vertex measurement is assumed to be Gaussian. The distribution is fitted with the sum of two Gaussian error functions [26, 27, 28]. The deviations of the fits can be interpreted as the resolution with which the position of the target edges can be determined. The results for the Generic, Standard and Adjusted Generic PR are shown in figure 37 5 The number of entries and the fitted resolution val- Tab. 2: The number of entries and the fitted resolution values of the inner target x slice for the Generic, Standard and Adjusted Generic PR. Adjusted Generic PR Generic PR number of entries bottom edge resolution (µm) 157 ± ± ± 23 top edge resolution (µm) 272 ± ± ± 27 All three resolutions found for the bottom edge are within the error margins of the resolutions obtained by the other two pattern recognition techniques. 5 These plots are created using the vertex analysis by A. Papadelis.