University of Ferrara
[0.9ex] Physics and Earth Sciences Department
[0.9ex] Degree of Doctor of Philosophy in subject of Physics
[1.2cm] Research and development in cylindrical triple-GEM detector with TPC readout for the BESIII experiment
Dr. Gianluigi Cibinetto
Dr. Erika De Lucia
[0.4ex] Prof. Theodoros Alexopoulos
[1.4ex] PhD Coordinator:
Prof. Vincenzo Guidi
Academic years 2015-2018
XXXI course - FIS/04
The third generation of the Beijing Electron Spectrometer, BESIII, is an apparatus for high energy physics research. The hunting of new particles and the measurement of their properties or the research of rare processes are sought to understand if the measurements confirm the Standard Model and to look for physics beyond it. The detectors ensure the reconstruction of events belonging to the sub-atomic domain. The operation and the efficiency of the BESIII inner tracker is compromised due to the the radiation level of the apparatus. A new detector is needed to guarantee better performance and to improve the physics research. A cylindrical triple-GEM detector (CGEM) is an answer to this need: it will maintain the excellent performance of the inner tracker while improving the spatial resolution in the beam direction allowing a better reconstruction of secondary vertices. The technological challenge of the CGEM is related in its spatial limitation and the needed cylindrical shape. At the same time the detector has to ensure an efficiency close to 1 and a stable spatial resolution better than , independently from the track incident angle and the presence of magnetic field.
In the years 2014-2018 the CGEM-IT has been designed and built. Through several test beam and simulations the optimal configuration from the geometrical and electrical points of view has been found. A new electronics has been developed to readout charge amplitude and time information from the detector signal. This allows to measure the position of the charged particle interacting with the CGEM-IT. Two algorithms have been used for this purpose, the charge centroid and the TPC, a new technique introduced by ATLAS in MicroMegas and developed here for the first time for triple-GEM detector.
A complete triple-GEM simulation software has been developed to improve the knowledge of the detection processes. The software reproduces the CGEM-IT behavior in the BESIII offline software. The simulation of the CGEM-IT in the BESIII apparatus validates the improvements of the detector thought the study of some physics analysis.
1 The Beijing Electron Positron Collider II and the Beijing Spectrometer III
- 1.1 BEPCII
- 1.2 The BESIII detector
- 1.3 The BESIII physics
- 1.4 The needs of a new inner tracker for BESIII
- 2 CGEM-IT
- 3 The GEM technology
4 Characterization and reconstruction of a triple-GEM signal
- 4.1 Experimental setup
- 4.2 The offline software: GRAAL
- 4.3 Analysis results
- 4.4 Performance at high rate
- 4.5 Test of Cylindrical GEM
- 4.6 TIGER with triple-GEM performance
- 5 Triple-GEM simulation
- 6 Impact of the CGEM-IT on physics analysis
- 7 Conclusion and outlook
A Review on the gaseous detectors
- A.1 Ionization in gaseous detectors
- A.2 Drift of electrons and ions in gases
- A.3 Amplification of ionization
- A.4 Gas choice
- A.5 Creation of signal
- A.6 Brief history of the gaseous detectors
- A.7 Micro pattern gaseous detectors
- B Diffusion and capacitive corrections in TPC
List of Figures
- 1.1 BEPCII.
- 1.2 BESIII detector
- 1.3 MDC performance
- 1.4 TOF performance
- 1.5 RPC internal structure
- 1.6 MDC aging effect in hit efficiency
- 2.1 Jagged anode layout
- 2.2 TIGER calibration curves
- 3.1 Gem Holes
- 3.2 Gem electric field
- 3.3 Induction field in a GEM
- 3.4 Drift field in a GEM
- 3.5 Triple-GEM representations
- 3.6 Gain and discharge probability in GEM
- 4.1 Test beam setup
- 4.2 Gas gain in a triple-GEM
- 4.3 Offline software block diagram
- 4.4 Fermi-Dirac and linear fit in time measurement
- 4.5 Time distribution with TIGER
- 4.6 TPC reconstruction
- 4.7 Time distribution with APV25
- 4.8 Alignment plots
- 4.9 Efficiency and CC resolution results
- 4.10 Cluster size and charge results
- 4.11 CC and TPC in magnetic field
- 4.12 Cluster size and charge results
- 4.13 Cluster charge distribution
- 4.14 Cluster time distribution
- 4.15 CC, TPC and merge resolution with sloped tracks
- 4.16 Simulated and measured drift velocity
- 4.17 CC weighting functions
- 4.18 Spatial resolution for different incident angle with magnetic field
- 4.19 Cluster charge dependency on beam rate in triple-GEM
- 4.20 Drift velocity dependency on beam rate in triple-GEM
- 4.21 GEM and CGEM signal comparison
- 4.22 CC resolution in CGEM
- 4.23 TIGER with triple-GEM results
- 5.1 Ionization distributions from Garfield++ and GTS
- 5.2 Electron drift distributions from Garfield++
- 5.3 GEM gain in Garfield++ and GTS
- 5.4 Induced current and readout charge in GTS
- 5.5 Experimental measurement of capacitive effects
- 5.6 GTS and real data comparison
- 5.7 Drift velocity and time resolution comparison
- 6.1 BOSS and CGEMBOSS comparison
- A.1 Electron diffusion and drift velocity.
- A.2 HV regime in proportional counter
- A.3 Single wire electric field
- A.4 Space charge effect in proportional chamber
- A.5 MWPC electric field.
- A.6 Time projection chamber representation
- A.7 Resistive plate chamber
- A.8 Micro Strip Gas Chamber electric field.
- A.9 MicroMegas.
- A.10 -RWELL.
- B.1 The TPC points residual
- B.2 First diffusion and capacitive correction
- B.3 First diffusion and capacitive corrections parameters
- B.4 Second diffusion and capacitive correction and its parameters
- B.5 Third diffusion and capacitive corrections
- B.6 TPC resolution with and without corrections
List of Tables
- 1.1 Main parameters of the BEPCII storage ring
- 1.2 Main parameters of the BESIII
- 1.3 TOF time resolution
- 1.4 Geometrical parameters of EMC
- 1.5 QCD theories and energy scale
- 1.6 Inner tracker requirements
- 2.1 CGEM-IT geometrical details
- 5.1 Drift parameters from Garfield++
- 6.1 Summary cuts on the benchmark channel
- A.1 Physical constants and approximated values of energy loss and ion pair production
Chapter 1 The Beijing Electron Positron Collider II and the Beijing Spectrometer III
High energy collisions between particles create new states of matter as ruled by the nature and described by the physics laws. As the number of collisions increases then it is possible to perform more precise measurements of the particle properties or the transitions from a state to another. Around the world there are several experiments and scientists that approach the knowledge of the physics laws looking at the collision results of high energy particles, one of those experiments is the BEijing Spectrometer (BESIII) at the Institute of High Energy Physics (IHEP) in People’s Republic of China (PRC): an apparatus composed of several sub-detectors that measure the properties of the particles such as momentum, energy, mass and path. The leptons are provided by the Beijing Electron Positron Collider (BEPCII). They are injected by a linear accelerator in two accumulation rings where electrons and positrons are disposed in bunches. The collision happens in the interaction point (IP). The center of mass energy range varies from to in order to explore the -charm region to continue the research about light hadrons, charmonium, exotics and other topics explained in Sect. 1.3
In this Chap. a review about the experimental layout will be reported and the physics research of the BESIII experiment in order to understand the scenario and the background needed by the new particle detector that has been studied in this work.
BEPCII is the upgrade of the pre-existing BEPC machine and it is a double ring electron positron collider that acts also as a synchrotron radiation (SR) source [1, 2]. The beam energy ranges from 1 to with a design luminosity of at that has been reached in 2016 data taking on April 14. The facility is exploited in high energy physics experiment and synchrotron radiation. The acceleration of is performed by an injector consisting in a electron linac with 16 Radio-Frequency (RF) power sources and 56 S-band RF structures. Then two super-conducting cavities are used with one cavity in each ring to provide the RF voltage. BEPCII requires 363 magnets of different types: bending magnets, quadrupole and sextupole. The details of BEPCII are shown in the Tab. 1.1. The luminosity of an electron-positron collider is expressed as:
where r is the beam aspect ratio at the IP, the vertical beam-beam parameter, the vertical envelope function at IP, the bunch number in each beam and the bunch current. A double accumulation ring scheme allows to reach a higher bunch number than an single one. The inner and outer rings (represented in Fig. 1.1 ) cross each other in the northern and the southern IP. In order to have sufficient separation between the rings without a significant degradation of the luminosity, the horizontal crossing angle between the two beams is 11 mrad 2 in the southern IP, where the BESIII experiment is placed. In the northern IP a vertical bump is used to separate the beams. The layout of BEPCII minimizes the machine errors such as misalignment or problems in the multipole field of magnets. This tunes the beta function and reduces the background due to Touschek effect. The mean beam lifetime is around three hours and its limits are due to beam-beam bremsstrahlung, Touschek effect and beam-gas interaction.
|SR loss per turn||121|
|Energy spread||-||5.16 10|
|function at IP||1/0.015|
|Crossing angle||11 2|
1.2 The BESIII detector
BESIII measures trajectories and momenta of charged and neutral particles except , produced in collisions in the energy region between 2 and 4.6 GeV by means of a set of detectors and a solenoid producing a 1 T magnetic field . A schematic drawing of BESIII is shown in Fig. 1.2. Around the beryllium beam pipe the Multi-layer Drift Chamber (MDC) is placed and around its conical shape in the end-cap regions there are two superconducting quadrupoles (SCQs). The time-of-flight (TOF) system is located outside the MDC: it is composed by two layers of plastic scintillator counters in the barrel and a multigap resistive plate chamber in the end-caps. The CsI(Tl) ElectroMagnetic Calorimeter (EMC) is placed between the TOF system and the Superconducting Solenoid Magnet (SSM). The MUon Counter (MUC) is built up by several layers of resistive plate chambers (RPCs) placed in the gaps between steel plates of the flux return yoke. The coil of the superconducting magnet is placed outside the electromagnetic calorimeter. It has a mean radius of and length of 3.52 m. The covered solid angle is = 0.93, where the azimutal angle is totally covered while the polar angle is limited between 21 and 159. The main parameters of BESIII sub-detectors are summarized in Tab. 1.2.
|EMC||Position resolution ()|
|Muon||N layers barrel||9|
|Muon||N layers end-cap||8|
|Solenoid magnet||Magnetic field|
1.2.1 The multi-layer drift chamber
The design of the MDC has been optimized to detect low momentum particles with performance shown in Tab. 1.2.
Moreover the MDC provides the level 1 (L1) trigger as described in Sect. 1.2.5 to select good events and to reject the background.
The radius of the MDC varies from 59 mm to 810 mm and the entire detector is composed by 43 sense wire layers. The first 8 define the inner MDC (IDC) and the others the outerMDC (ODC). The gas mixture is He-CH (60:40) to minimize the multiple scattering effect.
The measured position in the r-111 and are defined in Fig. 1.2. plane is given by each single wire while the measurement along the beam direction is performed by layers with different stereo angles (-3.4 and + 3.9). The average gas gain of the
MDC is about at the reference operating
high voltage of about .
Each layer is divided in several cells with an almost square section. The cell size varies from to . The cells have a trapezoidal shape with eight field wire on the perimeter and the sense wire in the middle. Each cell of a layer has the same shape and length. The resolution of a single wire is dominated by the electron diffusion and a proper balance is needed between the cell size, the readout channels and the multiple scattering given by the wires . The wires are made of gold-plated tungsten with 3% rhenium. The 43 layers of the MDC are divided in 11 superlayers and the field wires within a superlayer are shared between neighboring cells. Track segments reconstructed in superlayers are linked and used in the L1 trigger.
The momentum resolution of the MDC is determined by the resolution of a single wire and the multiple scattering.
The single wire resolution is a function of the drift distance and includes contribution from primary ionization statistic, longitudinal electron diffusion and the jitter in the time measurement. The distribution has been fitted to two Gaussian functions and the has been calculated by:
where and are the amplitudes and and are the standard deviations of the two Gaussian functions. The average spatial resolution of drift cell with a pion beams at 12 GeV/c is shows in Fig. 1.3.
The performance is determined mainly by the fluctuation in the number of primary ionizations along the track. A minimum ionizing particle (MIP) track in helium creates about 8 ion pair per centimeter. Monte-Carlo simulation shows that the is about 6% and the corresponding momentum resolution is better than , where the first term is related to the trajectory measurement and the second one to the multiple scattering. It allows to separate and within 3 up to momenta of .
The signals from the sense wired are first amplified by fast trans-impedance preamplifiers located close to the wire then output signal is sent outside BESIII thought 18 m cables. Then it is further amplified and split in three branches for timing, charge measurements and the L1 trigger. The wire spatial resolution of corresponds to a time resolution of and the charge produced by a MIP on a sense wire after the amplification is about .
1.2.2 The time of flight
The time-of-flight system is segmented in a barrel and two end-caps. The barrel is built up by two layers of 88 scintillating bars with a thickness of about and a trapezoidal cross section. The signal is collected by two photomultiplier tubes (PMT) attached to the bars. The end-caps have been recently upgraded with Multi-gap Resistive Plate Chambers (MRPC) and each end-cap station has 36 trapezoidal shaped modules arranged in a circular double layers .
The PMTs chosen to readout the TOF counters in the barrel are Hamamatsu R5924-70 and they match the size of the scintillator bars. The average quantum efficiency is about 23%, the rise time is and the signal transition time is with rms spread. A fast preamplifier with a gain factor of 10 is used to boost the signals and to extend the lifetime of the PMT. The signal is received by the front-end electronics that splits the signals into two branches for time and charge measurements. The required dynamic range is and the time resolution of the electronics is less than 25 ps. The charge amplitude signal measured ranges from 200 mV to 4 V.
A different technology is used in the end-cap where the time measurement is performed by MRPC. Each module is divided into 12 readout strips and their length changes from to and the width is . The strips are readout from both ends. The internal structure is composed by 14 pieces of thin glass sheet, arranged into two stacks. The stacks are sandwiched in between two layers of readout strips. The time measurement is given by 12 active gas gaps of thick. The MRPC module is placed in a gas-tight aluminum box with a gas mixture of Freon-SF-iCH 90:5:5.
The time resolution is about 100 ps in the barrel and 65 ps in the end-caps and it allows to separate within 3 up to at 90. The precise time resolution of the TOF is also used in the trigger logic for charged particles. The solid angle coverage of the barrel is while in the end-caps is . The dead gaps are needed for the mechanical support of the MDC and service line. The inner radius of the first barrel TOF layer is and the second , while in the end-caps the flight path is about .
The time resolution of the TOF is given by several contribution as shown in Tab. 1.3, while the intrinsic time resolution is determine by the rise time of the scintillation light, the fluctuation of the photon arrival time at the PMT and the transition time spread of the PMT.
|Counter intrinsic time resolution||80-90|
|Uncertainty from bunch length||25|
|Uncertainty from clock system||20|
|Uncertainty from angle||25|
|Uncertainty from electronics||25|
|Uncertainty in expected flight time||30|
|Uncertainty from time walk||10|
|Total time resolution, one layer barrel||100|
|Total time resolution, two layers barrel||80|
The separation capability depends on the polar angles of the tracks and its limit is reached at momenta of about 0.7 GeV/c at 90 where the particle flight is the shortest in the barrel, the limit moves to about 1.0 GeV/c in the end-cap systems. The particle identification is calculated by a likelihood analysis. The probability to identify a kaon or to misidentify it as a function of the kaon momentum is shown in Fig. 1.4. A separation efficiency of 95% is reached up to 0.9 GeV/c.
1.2.3 The electromagnetic calorimeter
The electromagnetic calorimeter measures the energy of photons above and provides a trigger signal. It is mandatory to measure precisely invariant mass of particles with radiative decay, , , , etc. In radiative decay the photon has to be distinguished from and decays. The minimum detectable opening angle between two photons is about 10 and for momenta higher than it can discriminate .
The EMC consists of 6240 CsI(Tl) crystal with a length of , about 15 radiation length (X), and a surface of . The crystals are arranged as 56 rings and each one covers an angle of about 3 in both polar and azimuthal directions. The calorimeter is divided in three parts: the barrel and two end-caps. The total weight of the EMC is about 24 tons. The design energy resolution is = 2.5% and the position resolution is = at . The angular coverage is while in the end-caps is . Details of the EMC are shown in Table 1.4.
|Number of sectors||120|
|Barrel number of rings||44|
|Barrel number of crystals||5280|
|Barrel inner radius|
|Barrel total weight|
|end-caps number of rings||6|
|end-caps number of crystals||960|
|end-caps distance to IP|
|end-caps total weight|
The energy resolution of EMC depends by the crystal quality, dead material between the IP and the crystal, photodiode and amplifier noise, fluctuation of shower energy, etc.
The signal readout is performed by two photodiodes of 1 cm 2 cm and a light guide of thick glued directly at the center of the crystal surface. Only 10% of the surface is covered but a larger fraction of light is collected thanks to the light reflection performed by reflective material covering the crystal surface. The signal is readout by the electronics that measures the energy deposited and provides a fast energy trigger.
1.2.4 The muon counter
Resistive plate counters are active detector used within the gaps of the flux return steel to identify the muons surviving the EMC with respect other charged particles such as pions. It is divided in three pieces: a barrel and two end-caps. The system is composed by nine layers of steel plates with a total thickness of and nine layers of RPCs in the barrel. The end-caps have eight layers of counters. The minimum muon momentum at which the RPC starts to become effective is about 0.4 GeV/c due to the energy loss in the EMC and the bending in the magnetic field. The hits reconstructed in the RPC are associated to the tracks reconstructed in the MDC and the energy measured in the EMC. The readout of the RPC is performed by strip of about in both direction and . The space resolution is modest because of the multiple scattering of low momentum muons in the EMC.
The RPC are constructed by two plates of high resistivity material, the Bakelite, of thickness around a gas gap of . Figure 1.5 shows the cross-sectional view of the detector. The RPCs work in streamer mode and the signal is collected on the strips outside the gas gap. The gas mixture is Ar-CFH-CH 50:42:8 and the working voltage is of 8 kV. This provide a single gap efficiency of about 96%. In order to improve the detection efficiency a double-gap layout has been used with the readout sandwiched in between the two. Each layer can measure only one coordinate and the orientation of the strips changes layer by layer. Due to the size of the detector, the number of readout channel is about 10000.
1.2.5 The trigger system
The trigger, data acquisition and online computing system are designed to sustain an acquisition with multi-beam bunches separated by 8 ns. The trigger system has two levels: a hardware level (L1) and a software level (L3). The L1 trigger signal is generated by the TOF, MDC and EMC. Conditions on the number of minimum tracks are required on the MDC, TOF and EMC. The clock of the trigger system is , it is synchronized with the accelerator RF and it is distributed to the readout electronics crate to synchronize every operation in the BESIII data acquisition. The maximum L1 rate expected is about at . The data in the front-end buffers is read once L1 trigger is validated, after the collision. Then the event reconstruction takes place and the background events are suppressed by the L3 trigger.
1.3 The BESIII physics
The BESIII physics plan is to accumulate a significant data sample in the center of mass energy between 2 and 4.6 GeV: energy point at the mass of charmonium states, above threshold, energy points at the mass of new resonances and in the continuum region. Up to now it has collected , , . The aim is to be sensitive to the observation of new physics concerning hot topics like mixing, the charmonium-like states and CP violation in charmed-quark and sectors. The high precision measurements at BESIII are compared with QCD calculations. The huge data sample allows to search for rare decays like lepton-number violating or flavour violating processes.
1.3.1 Hadron Spectroscopy
BESIII investigates the structure of matter and the nature of the interactions between its constituent components . To access a small object it is needed to increase the energy scale but increasing the energy the theoretical description of the phenomena changes. At momentum transfers around the MeV scale, below , the fundamental scale of Quantum Chromodynamics (QCD), the chiral symmetry theory can provide solutions to study the low-energy dynamics as QCD becomes non-perturbative . Increasing the energy in a range that is greater than , the partonic and gluonic behavior is shown in the deep inelastic scattering. In this energy region it is allowed to study QCD processes through perturbative expansion . Between these two energy regions there is no theory that can describe the phenomena so meson and baryon resonances are studied to know the constituent behavior. The QCD calculations in this region are described with a naive quark model [8, 9]:
spontaneous breaking of chiral symmetry leads to the presence of massive constituent quarks within a hadron as effective degrees of freedom;
hadrons can be viewed as a quark system in which the gluon fields generate effective potentials that depend on the relative positions and spins of the massive quarks.
These pieces compose the QCD puzzle and the hadron spectroscopy plays an important role in its interpretation. In the light quark sector () the mass differences are relatively small ( , and ) then the strong interaction can be approximated with a global SU(3) flavour symmetry. This approach allows to predict the masses of mesons and baryons composed by the quarks of the symmetry. Different theories and their validity ranges are summarized in Tab. 1.5.
A non-relativistic approach can be used with the naive method for quarks that have constituent masses comparable or greater than the . For quarks with an excitation energy of the excited hadron states comparable to their masses this approach is meaningless but it works in a wide range of empirical tests . Several theories can be found in literature: the semi-relativistic flux-tube model [11, 12], the instanton model , the Goldstone boson exchange model , the diquark model , etc.
The ultimate goal of the study of the hadron spectroscopy is to understand the dynamics of the constituent interactions. Conventional meson can be constructed in the quark model and their spectrum is studied to be described in an empirically efficient way. QCD also does not forbid the existence of other bound states that are made completely of gluons ( so-called “glueball”), multiquark mesons, such as and so-called “hybrid” mesons which contain both and gluon. Glueballs are bound states of at least 2 or 3 gluons in a color singlet. Gluons inside glueballs could be massive. The abundance of isoscalar scalars in the 1-2 GeV, mass region, (1370), (1500), (1710), (1790) and (1810) should be confirmed in further experiments. They are the natural scalar glueball candidates and they are studied at BESIII as decay products. Hybrid mesons are hypothesized to be formed by a pair plus one explicit gluon field. Evidence for the existence of hybrid mesons would be direct proof of the existence of the gluonic degree of freedom and the validity of QCD. In addition, the lightest hybrid multiplet includes at least one J exotic state. Multiquark are states with a number of quark-antiquark greater than three. They are always colourless. An example of a recent discovery of states is the (4260) . Hybrid states are a wide topic and they are connected to Charmonium and Charm physics, further description will be given in next sections.
1.3.2 Charmonium physics
Charmonia are charm-anticharm () bound states, like the resonance or its excitation. Due to their heavy mass ( quark mass is 1.29 GeV) they probe the QCD at different energy scales: from the hard region, where the coupling constant is small and can be expanded, to the soft region, where non-perturbative effects dominate.
To predict the properties of the charmonia states in these regions, a Non-Relativistic QCD (NRQCD) expansion can be used because is large and the motion velocity of the c quark is smaller than the speed of light ( 0.3 by potential model and Lattice simulation ). This method allows to expand the theory in power of and describe the mesons annihilation decays. It is named as perturbative NRQCD (pNRQCD) if . The system is weakly coupled and the potential of the meson is calculated. The next challenge is to interpret the newly discovered charmonia states. The spectrum of the charmonium states has been measured and the narrow resonances below the open-charm threshold are experimentally clear. On the other hand above the threshold many charmonia states have been theorized but only few of them have been observed. The spectrum of the charmonium states can be described by a potential model that combines a Coulomb-like term and a linear one for the confinement: the Cornell potential.
A spin dependent term is added to better describe the scalar nature of the potential:
Precision measurements are needed to answer some questions related to the low-mass charmonium spectrum and BESIII is playing its role to determine the masses and the widths of all charmonium states.
Some charmonium-like mesons not fitting in the previous discussed model were observed, while others, which are foreseen by the theory, like charmonium hybrids, have not been observed. Particles of interest are called < mesons: multiquarks candidates. On April 26, 2013 BESIII announces a new mystery particle: (3900) the first observation of a tetra-quark or a charm molecule confirmed later by other experiments. Later on several decays of the state has been observed in decay channels with charmonium or open charm state [17, 18, 19, 20]. states are well investigated by BESIII thanks to the high precision measurement. are connected to the states and their nature is still puzzling. An abundance of those states have been observed such as (4220) and (4360) in several charmonium decays and open charm mesons [21, 22].
Charmonium spectroscopy is studied with the hadronic and radiative transitions. Hadronic transitions are decay modes of heavy quarkonia to lighter state and a light hadrons. The typical mass difference between the initial and final meson is around a few MeV, so that the typical momentum of the emitted hadron is low. The light hadron is produced from gluons and it is emitted in S,D and P-Wave mode. Information about the wave-function of the charmonium states is accessible from the leptonic partial widths. In the non-relativistic limit of an S-wave and D-wave quarkonium system the coupling through a virtual photon involves the wave function and the partial width is given by :
Radiative decay can be used to extract the coupling constant from:
where stands for light hadrons and is a photon produced by the . At BESIII huge data samples of vector charmonium states as , and are produced and it allowed to understand the light hadron spectroscopy and charmonium decay dynamics. Hadronics decays are the 85-98% in charmonia mesons, the basic process is the annihilation of the inside the charmonium to light quarks, gluons or leptons. The energy released in the process is 2m and the space-time distance is . , ’, and decays to light hadrons are used to test theories as NPQCD and extract the variables of these or to access the gluonic behavior.
1.3.3 Charm physics
mesons are the lightest particle containing charm quark and due to Standard Model (SM) prediction the system is a good environment to test the theory, such as CKM matrix and mixing to the CP asymmetries, through their leptonic and semi-leptonic decay. The QCD potential used for meson system needs precise theoretical control to describe branching ratios, spectrum and quantum numbers. Meanwhile SM predicts small CP-violating asymmetries in charmed particle decay because the mode is Cabibbo suppressed and a large data sample is required with a complex final states to be analyzed. A resonance above the threshold has to be created to produce mesons pairs via . There are four broad resonance states that decay into pair of charmed meson final states: the initial meson decays via the production of light pair and forms - system that separate in two charmed mesons. These states are the (3770), (4040), (4160) and (4415). They are easily produced at collider because their quantum number J 1. To study this mechanism the charmed cross section is measured
where is the integrated luminosity and is the number of charmed meson obtained using tagging technique. The cross section of the states above the open-charm threshold can be understood as the successive onset of the charmed meson channels: ,,,, etc. Each charm decay of these charmonium state is studied to determinate amplitude and width and to compare with the theory that describe these decays . Pure leptonic decays are the cleanest decay modes of meson: the and quarks annihilate into a virtual boson with a decay width given by the SM:
where is the mass, is the lepton mass, is the CKM matrix element and is the decay constant that contains the information about the dynamics of the quarks inside the meson. Studying this kind of decay it determines . In the literature, has been extensively studied in a variety of theoretical approaches [24, 25]. In similar way mode is used to access to and . BESIII physics program include high precision measurement of and mesons. Semileptonic decays occur when a charm meson decay via weak interaction by emitting a lepton pair: , where =,. The quark is bound to the initial light quark of the charm meson by strong interaction ( meson in Eq. 1.11). In semileptonic decay the leptons do not interfere with the strong interaction then they can factored out the hadronic process. The process amplitude is:
The process depends on the quark-mixing parameter so the semileptonic decay is a good system to access to the CKM matrix and test the technique that calculate the hadronic matrix element developed by several method [26, 27, 28, 29, 30, 31]. These decay are sensitive to and by the determination of the absolute branching fractions, for in , , , , , , etc. These parameters are used together with the other CKM element to measure the mixing and the CP violating parameters, to test the self-consistency of the CKM picture and to search possible new physics beyond the CKM mechanism.
Meson-antimeson oscillation is another topic accessible at BESIII experiment. In these oscillation weak interaction effect build up over macroscopic distance and makes tiny mass differences measurable. It is mandatory to probe oscillation as sensitively as possible to provide proof of New Physics and CP violation.
physics is another branch of interest in charm studies. The lightest charmed baryon () decays only through the c weak decay, ,, at the leading order and it is the simpler theoretical environment to describe with non-perturbative models. This particle allows to measure the absolute branching fraction of and 12 Cabibbo-favored decays, studies of singly-Cabibbo-suppressed decays and the observation of the modes with a neutron in the final state.
1.4 The needs of a new inner tracker for BESIII
BESIII started to operate in 2009. In about the past 10 years the detectors suffered of aging due to radiation effect. The integrated charge on the innermost layer is about . The drift chamber is the system closest to the beam pipe. After several years of operation the performance of the drift chamber decreased due to the integrated charge. The aging in the anode is given by gas polymers that condense on the sense wire surface as thin films, whiskers and powder due to the high electric field. Those accumulation could be conductive or insulating; both contaminations cause a gain loss due to the increase of the effective diameter of the sense wire. Reduction of the gain is due also to the reduction of the electric field caused by the accumulation of charges in the insulating layer. The cathode suffers the aging too. A polymer deposits on the cathode surface and insulate it. This effect prevents the neutralization of the positive charge that modifies the detector electric field around the cathode up to a value that extracts electrons from the electrode. Those electrons can drift to the sense wire and create avalanches. The avalanche positive ions come back to the cathode, enhance the electric field around the cathode and thus feeds continuously this self-sustaining local discharge. This effect is called the Malter effect  and some water vapor has been added to the MDC gas mixture to slow down this issue. In order to reduce the dark currents of the sense wires and to use the detector in a safe configuration the voltage of the first four layers has been decreased with respect to the normal values, which result in the decrease of the performance of the detector. The gain with respect to 2009 status has been reduced up to 60% and this affects the event reconstruction worsening the detection efficiency up to 50% . The gain of the cells closer to the IP shows a sizable decrease, as shown in Fig. 1.6. This worsening does not allow the MDC to maintain the required performance in the next years. The BESIII collaboration decided to replace the inner part of the MDC with a new and more performing inner tracker with required performance described in Tab. 1.6.
A three layers cylindrical triple-GEM inner tracker has been proposed to replace the first eight layers of the MDC. A GEM (Gas Electron Multiplier) is a Micro-Pattern Gas Detector, a particular class of gas detectors that profits from modern photolitography and deposition of polyamide thin-layer. This allows to reach unprecedented performance with gas detectors as it will be shown in Chap. 4.
|Material budget||1.5 X|
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Chapter 2 Cgem-It
Despite various improvements, the detection technique based on wire structures suffers by limitation due to diffusion processes, space charge effects and aging of the anode and cathode electrodes. Modern construction technique allows to solve many of those problems, by using pitch size of a few hundred of to increase the granularity, or by photolithographic processes and the polyamide depositions of a layers of few to define new amplification geometries and detection techniques as reported in App. A.7. The GEM technology is the one chosen to replace the inner MDC: thanks to a thin pierced foil of copper-insulator-copper can magnify the primary ionization and measure the particle position within approximately of gas volume. The resolution achieved depends on gas mixture, gain and front-end electronics. In literature spatial resolution below hundred are reported  for orthogonal tracks without magnetic field. The GEM foils can be shaped to the needed surface and thanks to their thickness and formability are suitable to be used as inner trackers with cylindrical surface. In this Chap. a general overview about the components, the construction technique and the electronics of CGEM-IT will be provided. The details of GEM technology will be explained in detail in Chap. 3.
2.1 The KLOE-2 IT
The KLOE-2 inner tracker is an innovative detector built up by four coaxial layers of cylindrical triple-GEM: each layer exploits three GEM foils to amplify the signal from the particles that interact with it and it is shaped around the beam pipe. The inner radius of the layers ranges from 130 to and the length is about . Each layer is made by five foils: three GEMs, a cathode and a segmented anode. The layers provide a bi-dimensional measurement due to longitudinal and stereo strips of pitch.
GEM foils of the needed dimension can not be produced then they have been obtained through a gluing process with vacuum bag technique of two or three GEM foils together by means of epoxy glue on a peripheral region of kapton, the insulator material between the copper foils of the GEM. Then the large GEM foils are wrapped on an aluminum mould coated with Teflon film and glued in a overlap region. During the curing of the epoxy, a vacuum bag system is used to constrain the foil to the cylindrical shape given by the mould . Anode and cathode electrodes are shaped with the same technique then on a Honeycomb structure and, together with two permaglass rings glued at the edges of those two electrodes provide the structural support to the detector. The five electrodes are inserted one onto each other through a precise machine named Vertical Insertion System.
The front-end electronics used by KLOE-2 IT is GASTONE-ASIC : an analogue preamplifier integrates the signal that it is filtered from noise and then discriminated with a threshold range from 0 to . A digital output from each strip is sent out for the position measurement.
2.2 Innovation of the BESIII CGEM-IT
The BESIII IT starts from the KLOE-2 experience to develop a new tracker with GEM technology and cylindrical shape. The configuration used by KLOE-2 could not match the BESIII requirements due to its dimension, its total material budget and its spatial resolution (see Sect. 1.4) then a series of improvement have been introduced. Due to the dimension of the inner MDC in BESIII, the volume left free from its removal permits to insert three cylindrical layers instead of four. To keep reasonable the cost of the IT and for mechanical constrains, a pitch of has been chosen despite it would not reach the needed resolution if the digital readout was kept. It was mandatory to develop a new ASIC to measure charge and time information needed in the reconstruction algorithms described in Sect. 4.2. More details about the new ASIC will be discussed in Sect. 2.3. This is one of the most important innovation with respect to KLOE-2.
A new anode design has been implemented to reduce the inter-strip capacitance: longitudinal and stereo strips cross each other many times in the anode and each overlap of the two surfaces introduce a capacitance between the two strips that increases the noise in the readout channel. A jagged layout has been used in the BESIII IT to reduce the overlapping area. Simulations  show that it allows to reduce the inter-strip capacitance of about 30% with respect to the regular layout used by KLOE-2. Figure 2.1 shows the differences between the two design.
The sensitive volume in a triple-GEM detector has about of thickness. A signal bigger than 1 fC is collected mostly from a fraction of this sensitive volume: the region between the cathode and the first GEM because only the primary electrons generated in this region cross three timesthe GEM foils. In KLOE-2 this region, named , has thickness while in the BESIII IT has been increased to to increase the number of primary ionizations and to improves the reconstruction performances that will be explained in Sect. 4.3: larger gap correspond to better spatial resolution for the TPC technique.
The mechanical structure of the CGEM-IT in the KLOE-2 experiment is given by a Honeycomb foil on the anode and the cathode electrodes and the permaglass ring at the edges of the detector. BESIII uses a different material: the Rohacell that it allows to reduce the thickness of the structure, keeping the same mechanical properties. This reduces the material budged of the detector then its interaction length . The last design innovation is in the reduction of the copper thickness on the faces of the GEM foil from 5 to . This reduces the radiation length of the entire detector. The entire CGEM-IT will have a total material budget below 1.5% of .
In Tab. 2.1 are reported the values of the inner radius of each CGEM-IT layer, the active area length and the number of strips and the angle between longitudinal and stereo strips.
|Inner radius||Length||Stereo angle||N strips||N strips|
2.3 The new ASIC for the BESIII CGEM-IT
TIGER (Torino Integrated Gem Electronics for Readout) electronics, is a mixed-signal 64-channel ASIC developed to readout the CGEM detector of the BESIII Experiment . The ASIC is installed on a Front-End Board (FEB) with two chips to measure the signals from 128 strips. The ASIC measures time and charge of the signal. The chip uses two threshold, a first one to measure the rise up edge of the signal and a second one to discriminate signal from noise. The second threshold depends on the strip capacitance and chip temperature. Due to the variable length of the stereo strips, different threshold are used for each channel. A chiller stabilizes the chip temperature to avoid threshold variation. The time is measured with a lower threshold that send out the time information when the signal overstep the discrimination one. The charge can be measured with two methods: sampling and hold (S/H) mode and time-over-threshold (ToT) mode. S/H measures the signal amplitude in a dynamic range from 0 to . The ToT measures the leading edge of the signal and it convert the time length of the signal into charge information. Both methods need a calibration that has to be performed for each channel of the TIGER. Figure 2.2 shows the calibration curve of a TIGER for S/H and ToT methods . The output of the chip is fully digital. The advantage of S/H is the linearity between the charge and the output but the operating range is limited while ToT has an unlimited range but the output is not linear and it needs calibrations.
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Chapter 3 The GEM technology
Modern physics experiments use gaseous detector to reveal and measure particles properties and as the power of the accelerating machine increases a more sensitive and precise detectors are needed.
Gas detector exploits the physical processes between the particles, gas mixture and the high electric field. Charged particles interact with the gas and ionize it. As a function of the cross section, some gases can create more primary electrons with respect to others, then they have a larger amplitude in the collected signal on the readout. The probability to have a certain number of primary electrons is ruled by the Poisson distribution and the energy loss is described by the Bethe-Block formula. The electric field can drift the electrons: transverse and longitudinal diffusion contribute the time and spatial resolution of the detector. The electrons can trigger an avalanche if the electric field is higher and the electrons excite new gas molecule. Several working regimes are defined: if the electric field is too low the electrons and ions recombine; increasing the electric field the electrons generate an avalanche proportionally to the electric field; increasing more the electric field the electron can generate sparks. Once the avalanche is generated, it can induce a signal on the readout plane such as pads or strips and it is described by the Ramo theorem. More details are reported in the App. A.7 and in the bibliography there in.
A gas detector with a large diffusion is the Multi-Wire Proportional Chamber (MWPC) and its evolution: this is suitable detectors from different application but it suffers limitation such as the creation of a large amount of positive ions and the electric field distortion due to their back-flow, large drift volume that introduces limitations in rate capability higher than , low multi-track resolution due to the wire granularity limited at and its operability limitation for aging problems. Modern photolitography and thin-layer polymide deposition introduced by the Micro Strip Gas Chamber (MSGC)  overcome several limitation of the previous technology but it resulted too fragile in case of sparks. The new MPGD focused their design to increase the gain up to the Raether limit  of 10-10 electrons in the avalanche, in order to avoid the rupture of the gas dielectric rigidity and discharges.
In this Chap. a detailed description of the detector working setting, the mechanical design and the operability configuration will be reported. The modern application profits of the goals achieved step by step by this technology. A description of the advantages and weakness will be shown.
3.1 Gaseous electron multiplier
The Gaseous Electron Multipliers (GEM) is an electron amplification technique invented by F.Sauli in 1996 . It consist of a kapton foil with copper coated on the two faces and a high density holes. The foil is placed between two electrodes defining two regions: the drift gap where the primary electrons are generated collected to the GEM foil; the induction gap where the electron avalanche generated in the holes is driven from the GEM to the readout plane. The GEM operates with a high voltage difference between the two coppered electrodes on the two sides of the GEM: this creates an electric field up to inside each holes that accelerates the upcoming electrons and generates a cascade in a localized position given by the hole dimension. The GEM thickness is less than and this lets high gain regime without exceeds the critical Raether limit between the two GEM foil faces.
3.2 Design and construction
The shape, dimension and pitch of the holes are topics extensively studied by S. Bachamann and collaborators  in 1999 to optimize the GEM design. The typical GEM foil is composed by kapton and copper on both sides. The holes are produced with the photolitography on the metal and a specific solvent for the kapton. A bi-conical shape of the holes is produced applying the solvent on both sides: this technique is named process. In 2009 a new process, , has been developed to overcome the alignment needed by the two mask. The holes are equidistant and circular as shows Fig. 3.1. The study  ranged hole size from to and pitch between and . The optimal values have been found to be a diameter in the basis of the cone of and a diameter in the internal region of . The pitch chosen is . This configuration gives an optical transparency of 46%.
3.3 Electrical configuration
In a GEM detector three electric fields are needed:
between the cathode above the GEM foil and the electrode on top the GEM to generate the drift field ;
inside the GEM holes to multiply the electron number with a gain related to the high voltage difference ;
between the bottom electrode of the GEM and the anode below the GEM to generate the induction field .
The gain in a single GEM detector depends on those three components: , and . The is related to the gain with an exponential relationship. Figure 3.6 shows the exponential dependency of the gain from the . The dependencies on the and have been studied measuring the currents on the electrodes varying those fields. As the induction field increases then the total gain increases: a larger number of electrons are extracted from the holes and the current on the bottom face of the GEM decreases. See Fig. 3.3. The current as a function of the drift field has a different behavior as shown in Fig. 3.4. The total gain is maximum if . If is increased then a higher is needed to maximize the total gain.
3.4 Multistage multiplication
Several GEM amplification foils can be used to reach higher values of gain such as bi-GEM or even quadruple-GEM structures reducing the discharge probability. An example is shown in Fig. 3.5. Configuration with two foils of GEM has extensively studied in test beam by [5, 7], triple-GEM by [8, 9] and quadruple-GEM by [10, 11]. Those configuration needs another field, named transfer field , that has to extract the electron from the GEM above and transport them to the next GEM. Optimization of is needed to improve the gain of the multiple-GEM detectors. The most significant improvement of multiple amplification stages is to reduce then the discharge probability while the gain is even higher. This grants higher electrical stability and long living detector. Figure 3.6 shows the differences between single-, double- and triple-GEM.
3.5 Innovations and performance of triple-GEM detectors
In the past 20 years triple-GEM detectors have been extensively studied and several applications have been developed. The usual configuration in reported in Fig. 3.5. Best performance report a spatial resolution of tens of and time resolution below ; it has been used in low and high pressure environments ; gain up to 10 and discharge probability below 10 at a gain lower than 20000 . It can be shaped to to non-planar geometry such as cylindrical  or spherical  shapes. Moreover the application of the triple-GEM varies from high precision tracking detector, large TPC, single photon or single electron detection and even neutron detection .
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Chapter 4 Characterization and reconstruction of a triple-GEM signal
A full characterization of the triple-GEM signal is needed to optimize the geometrical and electrical configurations of the detector in order to fulfill the BESIII requirements defined in Sect. 1.6. The challenge is to achieve this requirement with a limited number of electronic channels, around 10000, over the whole detector and to build a system that fits the geometrical space left from the removal of the current Inner Drift Chamber. These details have been discussed in Sect. 2.2. The detector under study has a bi-dimensional readout with axial and stereo strips. The strip pitch chosen is in order to limit the number of channels in the final design. A smaller pitch would have led to a better measurement of the time and charge profile of the signal but it would be impossible to instrument and readout the signal from the detector.
Between 2014 and 2018 different triple-GEM detectors have been studied with test beam to measure their performance as a function of the gas mixture, the drift gap thickness, the geometry, the dimension and the readout electronics. In detail Ar+30%CO and Ar+10%iCH gas mixtures has been used, drift gaps of and thickness, planar and cylindrical shape. Transfer and induction gaps have thickness. The tested planar triple-GEM detectors have 10 active area and bi-dimensional readout while the cylindrical triple-GEM chambers have the dimensions of the first two layers of the CGEM-IT.
The bi-dimensional readout differs from chamber to chamber. Some chambers have readout with orthogonal strips for the two views, others have readout with an angle of 60 between the strips of different views, while the CGEM have readout with cylindrical shape and a stereo angle of 43.3 and 31.1.
As starting point the used high voltage settings are the ones used by KLOE-2  (, and ) and then an optimization is performed. The electric fields define the transport properties of the electrons in the triple-GEM geometry. The gain dependency on the is shown in Fig. 4.2.
The information on the used electronics, the offline software and a selection of results will be provided in this Chap. Offline software includes reconstruction of the data, its alignment and the analysis. Results of interest will show the configuration that fulfills the BESIII requirements.
4.1 Experimental setup
4.1.1 The facilities
The various detectors have been characterized at two test beam facilities:
CERN - H4 beam line in North-Area in Prevessin with muon and pion beams up to 150 GeV/c momentum;
MAMI - MAinz MIcrotron facility in Mainz with electron beam up to momentum.
The CERN facility allows to test the chambers in magnetic field thanks to Goliath , the largest ferromagnetic dipole magnet in the world providing a magnetic field up to 1.5 T in both polarities that can recreate an environment similar to BESIII. Let’s define the axis the one along the beam direction, axis the one perpendicular to and axis parallel to . The beam direction is orthogonal to the GEM detector plane and the magnetic field is perpendicular to the electric field direction and parallel to the GEM plane. Figure 4.1 represents the setup. Some measurements have been performed with a rotation of the chambers around the vertical axis in order to characterize the chamber with inclined tracks. A trigger system composed of two scintillator bars readout by photomultiplier tubes has been placed outside the magnet.
A similar setup has been used in the MAMI facility, where the magnet was not present and the setup was more compact.
4.1.2 Readout electronics
The design of the TIGER chip has been carried out from 2014 to 2018, therefore all the detector characterization has been performed using available commercial electronics, the APV25 developed by CMS collaboration. Only in 2017-2018 the test and integration of TIGER and triple-GEM started.
Some details about the APV25 [2, 4] and TIGER [5, 6] can be found in the references but some details has to be provided to understand the reconstruction technique. The APV25 chip has 128 channels connected to strips with a maximum capacitance of and it samples the charge up to each for 27 times after the trigger signal. The time is referred to the trigger time. The charge amplitude is digitized in 1800 bins. A conversion factor of counts per fC is used . The acquisition is performed with SRS  technology and mmDAQ software has been used to acquire the data from the Front-End Card (FEC). This allowed to record the information with an online pedestal subtraction.
The TIGER chip has 64 channels and it is mounted on a Front-End Board (FEB). Each FEB hosts two chips in order to measure the information of 128 channels. It has two threshold levels: the first one used to measure the time once the signal overstep it; the second to discriminate the signal from the noise. The chip has an analogue readout and it can measure the charge in two different modes: sampling and hold (S/H) mode and time-over-threshold (ToT) mode. The output is sent out digitally and decoded in 10 bits. Other details have been reported in Sect. 2.3.
4.2 The offline software: GRAAL00footnotetext: Gem Reconstruction And Analysis Libraries
The test beam data have been reconstructed and analyzed through a software developed for this purpose. A scheme of the offline software is shown in Fig. 4.3. Each trigger signal defines an event, for each event the signal on a strip is recorded. This signal is labelled hit. Hit information is reconstructed in order to obtain the time and charge information. The hit digitization depends on the front-end electronics.
Hits with charge greater than have been used in the analysis. Contiguous hits in the same detector and same view have been used to define a cluster of strips. If dead strips are present the clusterization algorithm takes them into account and it clusterizes the hits even if there is an empty strip between strips with signal. The charge of the cluster is defined by the sum of the charges of the hits and the information of each hit is used to evaluate the position measurement as described in Sect. 4.2.3.
4.2.1 Hit digitization with APV25
The APV25 chip acquires the signal shape sampling every . The total charge induced on the strip is the maximum charge measured in the 27 time-bins, , while the time needs to be extracted from the time profile of the charge through a fit with a Fermi-Dirac (FD) function on the rising edge of the signal, as described in Eq. 4.1.
First a pre-analysis in needed to measure the noise level and the time-bin where the signal is recorded: this is necessary to initialize the FD fit that otherwise would not converge. is initialized to the charge mean value of the first three time-bins, to the time mean value between the time-bin associated to and the time-bin with 10% of , to . The time related to the signal is assumed to be the the inflexion point, the value in the middle of the signal rise: . If the FD fit fails or if converge to anomalous values then a linear fit is used to extract the time information. The hit time is evaluated with the fit in the middle of the rising edge. Examples of those two fit are shown in Fig. 4.4.
The time-bin amplitude of introduces uncertainties in the time measurement. In the standard APV25 setup the trigger signal is used to start the data acquisition of each event. The setup has been upgraded to measure with higher precision the trigger time through the injection of this signal into an APV25 channel with a proper circuit 111Using an attenuator (10:1) in series with a 1 pF capacitance.. Then the trigger signal has been reconstructed in the same way as the standard hits and it has been used as reference for the hit time.
4.2.2 Hit digitization with TIGER
TIGER chip is a technology that can provide the hit information with and without an external trigger signal, named and modes respectively. Every time that a signal oversteps the threshold the TIGER measures the charge and time informations. In trigger-match mode an external trigger is used as signal for the front-end board to collect in a packet the information from each channel, in trigger-less mode a continuous stream of data is sent out from the TIGER to the front-end board and then to the acquisition computer. At the time of the test beam the trigger-match mode was not ready yet then the data acquisition was performed in trigger-less mode. To reconstruct the event was mandatory to inject the trigger inside a channel of the TIGER. Offline reconstruction has been performed to build each event with respect to the trigger time. The time window around the trigger time spans . Figure 4.5 shows the hit time distribution with respect to the trigger time.
The APV25 can not be used in BESIII because it is an IBM technology and it can not be exported to China but the custom design of TIGER grants additional features: it reduces the capacitance between the detector and the ASIC and moreover it has been designed with the needed minimal dimension.
4.2.3 Hit clusterization
The strip position is defined as the coordinate in the middle of the strip, orthogonal to the strip length direction. To measure the incident particle position two different algorithms have been deployed, the charge centroid (CC), also known as center of gravity, that uses the strip charge and position information and the micro-Time Projection Chamber (TPC), that uses also the time information.
184.108.40.206 The charge centroid
The CC method measures the position of the particles with a weighted average as described in the Eq. 4.2.
where is the number of hits in the cluster, referred as cluster size, and the hit position and charge.
220.127.116.11 The micro-Time Projection Chamber
The time information is used to reconstruct the particle path since the invention of drift chambers but in the last decade the ATLAS collaboration introduced the idea of using the same technique in MPGD technology, the MicroMegas detector. The few millimeters of drift gap are used to reconstruct the particle path. Very important contributions in this field come from [11, 12] that define the state of the art. A detailed study has been performed in this thesis work to develop a similar technique for triple-GEM detectors that shares some features with MicroMegas.
The TPC algorithm reconstructs the particle path inside the drift gap of the triple-GEM: strips are associated to points in x:z plane, named , where is the strip position and is the product of the hit time times the electron drift velocity. The drift velocity is computed by from Garfield++  simulation222Magboltz program is the one related to the simulation of motion of the electron in gas sensitive in Garfield++.. It is a quantity that depends on the electro-magnetic field in the drift gap and on the gas mixture. If the cluster size is at least two, a linear fit is performed with the TPC points and the value at the middle of the gap is chosen as the position measured by the TPC algorithm.
where is the drift gap thickness, and b the linear fit parameters as shown in Fig. 4.6.
To improve the TPC reconstruction it is important to assign to the TPC points proper uncertainty. Along the direction the fit uncertainty on the measurement has been considered. In the direction the pitch over is considered as uncertainty because the primary ionization that generates the main signal could start in any position within the strip pitch. Studies from ATLAS  show that the position distribution of the primary electrons in not flat but this will be discussed in App. B. Moreover, strips with lower have a higher probability to have a cross-talk contribution from the neighboring strips with higher charge. As it will be described in Sect. 4.3.3 and discussed in App. B, the signal generated from a primary electron is mainly collected on the strip below its position (if no magnetic field is present) but a certain fraction of the signal is collected on the neighboring strips: the higher is the fraction of charge carried by a strip, the smaller is the error associated on the coordinate. Due to this behavior an charge-dependent error is used on . Eq. 4.4 describes the errors associated to each TPC point.
4.2.4 Time reference for TPC reconstruction
As it will described in Sect. 4.2.3, the TPC algorithm reconstructs the particles path in the drift volume. The larger signal in a triple-GEM comes from the electrons amplified three times, bi-GEM effects are less than 2% . The hit time is the interval between the primary ionization and the signal induction on the anode. The time distribution of the hits is studied to evaluate the drift time needed from the first GEM to the anode. Figure 4.7 shows the time distribution of the hits in a run. The histogram is fitted with two FD function to describe the rising and falling edges. The time in the middle of the rise is associated to the fastest electrons: the closest to the first GEM. This is chosen as . The time in the middle of the falling edge corresponds to the slowest electron generated close the cathode. The time distribution shows peaks on the top due to capacitive effects. This will be discussed in App. B. The measurement is performed with a sub-sample of the run entries, 10% of the total number of events, to avoid bias.
4.2.5 Residual measurement
The test beam setup is composed by several triple-GEM detectors and they are divided in two groups: the trackers used to measure the particle path along the setup and the test detectors that are used to determine the performance of this technology. From three to seven triple-GEM detectors have been used in the tests beam. The outer detectors are usually used as trackers, the more trackers are used the more precise is the track position measurement. A linear fit is performed from the tracker position measurement, even if the magnetic field is present and the particle path is bent. Once the track is defined, the expected position at the test detector plane is evaluated and it is used to measure the residual as shown in Eq. 4.5.
The residual distribution has a Gaussian shape and a Gaussian fit is used to describe it. The of the Gaussian is related to the spatial resolution of the detector but distribution is not used for this purpose because it contains the contributions of the tracking system. is used in the alignment procedures. Another technique has also been used to characterize and extract the detector performance.
The residual distribution of the two detectors in the middle of the setup is used to measure their spatial resolution and efficiency as shown in Eq. 4.8:
This technique allows to remove in a easier way the systematic error due to tracking system on the spatial resolution thought the assumption that the two detectors are equal and they have the same performance. Then the spatial resolution of the two detectors can be evaluated with a Gaussian fit of the distribution and the is divided by as shown in Eq. 4.7:
4.2.6 The alignment procedures
Alignment procedures are needed to remove the translations and rotations of the real detector position with respect to the one reconstructed by the software. The detectors are installed perpendicular to the beam line (or rotated with respect this position in certain runs) with a precision within the millimeter. This can affect the resolution measurements. A sub-sample of the event corresponding to the 10% of the total event number is used in the alignment procedures. Three iteration cycle are needed to the alignment procedures before the analysis of the entire run. The quantities under study are the shifts along the and coordinate, tilts in the plane and rotation in the plane.
The shift alignments are the easiest to be performed: once the residual distribution is evaluated and the Gaussian fit is performed then the central value of the Gaussian is used to shift the detector reference frame and remove the difference between the real position of the detector and the reconstructed one. The tracking system itself needs an alignment, the angular coefficient of the track with the entire setup has to be perfectly orthogonal and being the resolution of the tracking system below the mrad then it is possible to rotate the entire setup in order to reconstruct precisely the track incident angle. The tracking system needs also an alignment: each detector is referred to the first tracker that has been fixed in (0,0,0) reference frame.
Those three are the macroscopic alignment. Now fine alignments, the ones related to the detector rotations, are needed. The first one is the evaluation of the tilt in the plane. A bi-dimensional plot is performed to do this alignment where is the position measurement333 measurement is performed in the same way as the measurement.. A linear fit of the bi-dimensional distribution is performed and the angular coefficient of the line is used to rotate the detector in the plane. Similarly, it is evaluated the tilt of the x coordinate of the tested detector with respect to the x coordinate of the first tracker. Similarly to the the previous measurement, a bi-dimensional plot is drawn for and a linear fit is used to measure the rotation between the two detectors.
4.3 Analysis results
A wide range of configurations have been studied for this PhD. Several hundreds of runs have been collected in order to measure the behavior of triple-GEMs in different conditions and to perform calibrations of the reconstruction algorithms to cross-check the results. The main goal is to find the optimal parameters to fulfill the BESIII requirements with a triple-GEM operated in magnetic field. A selection of the obtained results will be shown in the next sections: the detector efficiency at different gain; signal information ( cluster charge and size) as a function of the gain, the beam incident angle and particle rate; spatial resolution in different conditions ( gain, beam incident angle and magnetic field).
4.3.1 Detector efficiency and signal characterization
It is important that a detector used in high energy physics has an efficiency higher as possible to detect almost every particle. In Argon gas the number of electrons per millimeter is about 8, if CO or iCH are mixed in the Argon this quantities increases. The probability to have at least one ionizing interaction is almost 100% from Eq. A.3. Once the ionization occurs the signal has to be amplified depending by many factors. Those detail will be discussed in Sect. 5.
To evaluate the efficiency the distribution is fitted with a Gaussian: the number of events within 5 from the mean value is the number of times with a successful reconstruction in the two test detectors. This number is related to the number of event where the tracking system has a good event and each tracker has an inclusive residual distribution within 5. If the two detectors have the same behavior then the detector efficiency can be evaluated from Eq. 4.8:
where N and D are:
= N of events with a good tracking system and the tracker events are within 5 in their inclusive residual distribution ;
= N of event with a good tracking system and within 5 where is measured with both test detectors working properly.
Figure 4.9 shows the efficiency and the resolution of the CC algorithm as a function of the gain for both the studied gas mixtures. As expected from A.3, the highest efficiency is reached almost immediately at a gain of 2000 while the CC spatial resolution achieves at a gain of 10000. No TPC spatial resolution is shown right now because the algorithm does not work properly with orthogonal tracks and no magnetic field.
Figure 4.10 shows the behavior of the cluster size and charge as a function of the gain. The charge has linear dependency on the gain, with a slope different between the two gas mixtures since the number of electrons generated in the ionization is about 55.1 in Ar+10%iCH and 38.4 in Ar+30%CO, evaluated from Eq. A.5. The cluster size, the number of fired strip, is related to the diffusion properties of the electrons in the gas. The higher the transverse diffusion the larger the cluster size. Both gas mixtures increase the cluster size with the gain but the Ar+10%iCH is larger because its transverse diffusion in around in a cm while Ar+30%CO .
The results in Fig. 4.10 have been measured with orthogonal tracks and no magnetic field: if the primary electrons are generated on the same line when they drift to the first GEM they reach it in the same point, within diffusion effects. If the detector is set at high voltage value around 10000 then the electrons starting the avalanche in the same point of the first GEM generate their signal on three strips. This behavior has to be underlined to understand the further results.
Smaller cluster size and charge values have been obtained with drift gap detectors since the number of primary electrons and the path to diffuse are smaller.
4.3.2 Performance of a triple-GEM in magnetic field
The triple-GEM detector has been proposed as inner tracker for the BESIII experiment and it has to operate in 1 T magnetic field. A characterization as a function of the magnetic field has been performed. If the magnetic field is present then the Lorentz force acts on the electrons and it bends their path. The reconstruction algorithms has to take this effect into account because the magnetic field changes the diffusion properties of the electron and, more important, their path. The () is the angle between the electric field and the electrons path in the gas and it is used to determine the reconstruction properties as shown below.
In the orthogonal track configuration, the spatial distribution of the signal is larger if the magnetic field is present because the primary electrons position reaching the first GEM is spread. Similarly the case without magnetic field and non orthogonal tracks, the position width where the electrons arrive on the first GEM is . This effect explains the behavior of the CC and TPC shown in Fig. 4.11.
where depends on the magnetic field direction.
4.3.3 Performance of a triple-GEM with sloped tracks
At BESIII low momenta particles interact with the detector with an angle different from zero. It is important to guarantee an efficient reconstruction in this case. A characterization of the triple-GEM detector as a function of the incident angle has been performed to determine the signal shape ( and as shown in Fig. 4.12.
Let’s consider the angle between the track and the normal to the detector surface. As this angle increases then the path length of the particle in the drift gap is defined by . The number of primary electron and the cluster charge are proportional to the path . If then the projection on the first GEM plane of the path is not point-like such as in the case = 0 but it is equal to . Each electron reaching the first GEM generates an avalanche that induces a signal on the three strips below. On average the total signal generated by a particle in this configuration has a broaden shape given by a convolution of a box of a width and a Gaussian function similar to the charge distribution in the = 0 configuration. The single event is very different from the average: the charge distribution is not flat due to the large spread in the number of amplified electrons from each primary. This quantity can vary up to the 50% between each amplification. Charge distributions with and are shown in Fig. 4.13. This is the reason why the cluster size increases with and the charge distribution is no more Gaussian.
The CC algorithm is no more efficient as soon as the charge distribution is not Gaussian but TPC does because cluster size and the time difference between nigh strips are larger as shown in Fig. 4.14. Spatial resolution of the algorithms is shown in Fig. 4.15.
The TPC spatial distribution shows a Gaussian-like behavior with broad tails and its shape is fitter with a double-Gaussian fit and the resolution is measured with a weighted average of the two Gaussian like in Eq. 1.3. The events in the wider Gaussian are related to pathological TPC event and the cluster properties are not optimal, the cluster size is too small or too large. The position measurement through a fit make this algorithm less stable with respect to the CC. It is sufficient one bad TPC point to worsen the TPC-linear fit. Moreover, the shape of the reconstructed path is not properly a line due to the presence of diffusion and capacitive effects. Further studies are needed to improve more the TPC. Some of those study are present in App. B.
4.3.4 Temporal studies with sloped tracks
In Sect. 4.2.4 it has been shown how to measure the time needed to an electron to drift from the first GEM to the anode from the time distribution of the hits, named . See Fig. 4.7. Similarly is defined as the inflexion point of the FD used to describe the leading edge of the time distribution. The time value is associated to the time need by an electron to drift from the cathode to the anode. If the gap is know, then it is possible to measure the drift velocity of the electrons in the drift gap from the Eq.:
The measurement accuracy of the drift velocity improves with larger incident angle, then this measure can not be performed if = 0 where the time distribution is squeezed to , see Fig. 4.14. The drift velocity depends on the electric field and it can be computed with programs such as Garfield++ . A comparison of the simulated and measured value of the drift velocity has been performed and the results, as shown in Fig. 4.16 agree within 10%.
Similarly to the drift velocity, the time resolution of the detector is a measurement that improves with larger angles. The time difference between the trigger time and the faster hit of the cluster is the time distribution used to evaluate the detector time resolution. The distribution is fitted with Gaussian function and a of has been measured. The contribution of the electronics is about then the time resolution of the detector with both gas mixtures is about .
4.3.5 Merging algorithm
The CC and TPC are two algorithms anti-correlated: if the first performs properly then the second is not efficient and vice-versa. Once the detector will be installed in BESIII it has to provide a single measurement. Another algorithm to weight properly the two is needed. To achieve this purpose two methods have been developed: the first one uses the cluster size information , and the other one uses the track incident angle information . Both methods use the Eq. 4.11: