UNIVERSIT`A DEGLI STUDI DI ROMA âTOR

` DEGLI STUDI DI ROMA UNIVERSITA “TOR VERGATA” ` DI SCIENZE MATEMATICHE, FISICHE E NATURALI FACOLTA Dipartimento di Fisica

Resistive Plate Chambers for the ATLAS level-1 muon trigger

Tesi di dottorato di ricerca in Fisica presentata da

Alessandro Paoloni

Relatore

Professor Rinaldo Santonico Coordinatore del dottorato

Professor Piergiorgio Picozza

Ciclo XII Anno Accademico 1998-1999

Contents Acknowledgments

iii

Introduction and Overview

1

1 The ATLAS detector at LHC: description and perspectives for Higgs boson research

3

1.1 The LHC project . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.2.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.2.2

The Inner Detector . . . . . . . . . . . . . . . . . . . . . . . .

5

1.2.3

The calorimeters . . . . . . . . . . . . . . . . . . . . . . . . .

8

1.2.4

The muon spectrometer . . . . . . . . . . . . . . . . . . . . .

10

1.2.5

Trigger and Data Acquisition . . . . . . . . . . . . . . . . . .

13

1.3 Higgs boson search: from LEP to LHC . . . . . . . . . . . . . . . . .

15

1.3.1

The Higgs boson in the MSM framework . . . . . . . . . . . .

15

1.3.2

Higgs boson search at LEP . . . . . . . . . . . . . . . . . . . .

18

1.3.3

The Higgs boson search with the ATLAS detector at LHC . .

19

1.3.4

The Higgs sector in the Minimal Supersymmetric Standard Model (MSSM) . . . . . . . . . . . . . . . . . . . . . . . . . .

22

2 Resistive Plate Chambers: working principles and implementation in the ATLAS muon trigger

23

2.1 Interactions of fast charged particles in gases . . . . . . . . . . . . . .

24

2.2 Description of a RPC and principles of operation . . . . . . . . . . .

27

i

ii

Table of contents

2.3 Signal formation

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

2.4 RPCs in the muon trigger of the ATLAS experiment at LHC . . . . .

33

2.5 Front-end electronics for the ATLAS RPCs . . . . . . . . . . . . . . .

38

3 Response uniformity of a large size RPC

43

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

3.2 Experimental lay-out . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

3.3 Description of the tracking algorithm . . . . . . . . . . . . . . . . . .

46

3.4 Response uniformity test . . . . . . . . . . . . . . . . . . . . . . . . .

48

3.5 Inefficiency distribution of a RPC chamber . . . . . . . . . . . . . . .

51

3.6 Studies on the intrinsic inefficiency and on the spacers inefficiency . .

55

3.7 Intrinsic inefficiency and primary ionization . . . . . . . . . . . . . .

58

3.8 Cluster size studies . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

3.9 Preliminary results with the ATLAS final Front-end electronics . . . .

62

4 The LVL1 muon trigger in the barrel

69

4.1 Hardware implementation . . . . . . . . . . . . . . . . . . . . . . . .

70

4.2 Trigger performance simulation . . . . . . . . . . . . . . . . . . . . .

76

4.2.1

Description . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

4.2.2

Trigger coincidence windows . . . . . . . . . . . . . . . . . . .

77

4.2.3

Trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . . .

86

Conclusions

95

Bibliography

97

Acknowledgements I wish to express my gratitude to Rinaldo Santonico, for having introduced me to the field of Resistive Plate Chambers and for his careful reading of this manuscript. I acknowledge also Anna Di Ciaccio and Roberto Cardarelli for their support in data acquisition systems and in data analysis techniques. I strongly benefited from the fruitful collaboration with Barbara Liberti during the three years of my Phd work. I am indebted to Luigi Di Stante for the assembling and the maintaining of the tested detectors. I thank also Paolo Camarri, Giulio Aielli, Enrico Pastori and Vincenzo Chiostri for their different contributions. Precious suggestions concerning the trigger simulation came also from Lamberto Luminari and Alessandro Di Mattia.

Introduction and Overview

1

The ATLAS collaboration proposed to build a general-purpose detector to exploit the full discovery potential of the Large Hadron Collider (LHC). The most prominent issue is the quest for the origin of the spontaneous symmetry-breaking mechanism in the electroweak sector of the Standard Model; however refined measurements regarding top and b-physics, as well as eventual new physics beyond the Minimal Standard Model (Supersymmetry, heavy W and Z-like objects, leptoquarks), are other important goals. In chapter 1 is given a general description of the collider and of the ATLAS detector; the potential contribution to the Higgs boson research is also shown. One of the distinctive features of the ATLAS detector is the quality of muon momentum measurement, obtained with a high resolution, large acceptance and standalone spectrometer. Precision momentum measurement and triggering are performed by different dedicated detectors. Resistive Plate Chambers (RPCs) will be used for the first-level muon trigger in the barrel part of the muon spectrometer, due to their excellent time-resolution, ease of operation and low construction cost. In chapter 2 the working principles of RPCs are described, together with the Research and Development activity carried out in view of their implementation on the ATLAS muon spectrometer. Chapter 3 presents the uniformity test of a large size RPC; the test was performed in the INFN laboratories of the university of Rome, “Tor Vergata”, using cosmic rays. Refined results about the detector intrinsic inefficiency are also reported. Finally in chapter 4, the barrel level 1 muon trigger logic is described, together with results of related Montecarlo simulations.

Chapter 1 The ATLAS detector at LHC: description and perspectives for Higgs boson research

3

4

Chapter 1. ATLAS detector: description and Higgs research

1.1

The LHC project

The Large Hadron Collider (LHC) will reach energies in the TeV range, offering a wide range of physics opportunities: research of the Higgs boson, refined measurements in the fields of top and beauty physics, exploration of new physics beyond the Minimal Standard Model (Supersymmetry and compositeness of leptons for instance). Proton bunches with an energy of 7 TeV will circulate and interact in the present LEP (Large Electron-Positron collider) ring, which has a circumference of about 27 Km. To reach such energies, in the bending regions of the accelerator 8.5 T dipolar magnetic fields are needed, obtained with superconductive magnets. The design luminosity is 1034 cm−2 s−1 (to be compared to 1031 cm−2 s−1 of the Tevatron), with about 1011 protons per bunch and a bunch-spacing of 25 ns. However LHC will start its operation with an initial luminosity of 1033 cm−2 s−1 for top and beauty-physics studies. Three detectors for p-p interactions are foreseen: ATLAS (A Toroidal LHC ApparatuS), CMS (Compact Muon Solenoid) and LHC-b (dedicated exclusively to bphysics). Being the total non-diffractive inelastic p-p cross-section of about 70 mbarn, at peak luminosity an average of 20 minimum-bias pile-up events per bunch crossing is expected. Interesting events (with the minimum-bias events superimposed) will be tagged with the presence of electrons, muons, photons, hadronic jets or missing energy at high-pt with respect to the beam axis. LHC environment requires for the detectors fine granularity, fast response with small dead-time and high tolerance to radiations. Heavy ions operation of LHC is also foreseen; a fourth experiment, ALICE (A Large Ion Collider Experiment), will be dedicated to related studies (quark-gluon plasma).

5

1.2

The ATLAS detector

1.2.1

Introduction

The ATLAS detector optimization has been guided by physics issues [1], such as sensitivity to the full mass range of the Standard Model Higgs boson (see 1.3.3). Starting from the interaction region, the detector, shown in figure 1.1, is composed by: • the Inner Detector for tracking and reconstruction of secondary vertexes (essential for the tagging of heavy quarks and τ leptons); • an electromagnetic calorimeter for identification of electrons, positrons and photons in a wide energy range (from 100 MeV up to 1.5 TeV); • the hadronic calorimeter for jets reconstruction and missing energy measurement; • a precision spectrometer for muons detection. In the interaction region, the beam pipe is made of beryllium with a diameter of 5 cm. Before any detailed description of each ATLAS subdetector, it is convenient to introduce a reference system in cylindrical coordinates (z, R, φ), with the origin located in the nominal interaction point: z is the coordinate along the beam axis, R is the distance from it and φ is the azimuthal angle in the transverse plane. The pseudorapidity η is defined to be: 1 1 − cosθ η = − ln 2 1 + cosθ

!

θ = − ln tg 2

!

,

(1.1)

with θ being the angle respect to the beam axis.

1.2.2

The Inner Detector

A longitudinal view of a quarter of the Inner Detector [4] is shown in figure 1.2.

6


Figure 1.1: Three-dimensional view of the ATLAS detector.

Figure 1.2: Layout of the ATLAS Inner Detector. It combines high-resolution detectors at inner radii with continuous tracking elements at outer radii, all contained in a solenoidal magnet [5] with a central field

7

of 2 T. SemiConductor Tracking detectors (SCT), using fine granularity silicon microstrips and pixels, offer high-precision momentum and vertex reconstruction in the very large track density expected at LHC. A large number of tracking points (typically 36 per track) is given by a straw tube tracker (TRT) which provides the possibility of continuous tracking with much less material per point and at lower cost. The outer radius of the tracker cavity is 115 cm, fixed by the inner dimension of the cryostat containing the liquid Argon e.m. calorimeter, while the total length is 7 m, limited by the endcap calorimeters. Mechanically, the Inner Detector consists of three units: a barrel part extending over ± 80 cm and two identical endcaps covering the rest of the cylindrical cavity. The precision tracking elements are contained within a radius of 56 cm, followed by the continuous tracking and finally by the general support and service area at the outermost radius. In the barrel, the high-precision detector layers are arranged on concentric cylinders around the beam axis in the region with |η| < 1, while the endcap detectors are mounted on disks perpendicular to the beam axis and extend the tracking coverage to |η| < 2.5. The pixel layers are segmented in Rφ and z, while the silicon strips use small angle (40 mrad) stereo to measure both coordinates. The barrel TRT straws are parallel to the beam direction. All the endcap tracking elements are located in planes perpendicular to the beam axis. The strip detectors have one set of strips running in radial directions, and a set of stereo strips at an angle of 40 mrad. The continuous tracking consists of radial straws arranged into wheels. During the initial low-luminosity running, the secondary vertex measurement performance will be enhanced using an innermost additional layer of pixels at a radius of 4 cm, the so-called b-physics layer, with lifetime limited by radiation damage. The momentum resolution obtained combining the informations from the discrete precision points and the large number of drift-time measurements of the TRT is shown in figure 1.3. The impact parameter resolution (with the dedicated b-physics layer) can be parametrized as follows :

8


60 √ µm pt sinθ

(1.2)

100 √ µm. pt sin3 θ

(1.3)

σ(d0 ) = 11 ⊕ for Rφ, and

σ(z0 ) = 70 ⊕

-1

σ(1/pT) (TeV )

for z. 1

0.75

0.5

0.25

0

0

0.5

1

1.5

2

2.5

|η|

Figure 1.3: The Inner Detector momentum resolution for tracks with pt = 500 GeV, for the real solenoidal field compared to a uniform 2 T field. Polyethylene moderators are placed between |z| = 340 cm and |z| = 345 cm to protect the Inner Detector from low-energy neutrons coming from the calorimeter endcaps.

1.2.3

The calorimeters

The calorimeters layout is shown in figure 1.4. A barrel cryostat around the Inner Detector cavity contains the barrel electromagnetic calorimeter and the solenoidal coil which supplies the magnetic field to the inner tracking volume. Two endcaps cryostats, with a length of 3.25 m, enclose the e.m. and hadronic endcap calorimeters as well as the integrated forward calorimeters, placed around the beam pipe. The barrel and the extended barrel hadronic calorimeters are contained in an outer support cylinder, having an external radius of 4.23 m, which acts also as main solenoid flux return.

9

Figure 1.4: Two-dimensional view of the ATLAS calorimeter system. The liquid Argon sampling calorimeter technique [2] with “accordion-shaped” electrodes is used for all electromagnetic calorimetry, covering the pseudorapidity interval |η| < 3.2. The liquid Argon technique is also used for hadronic calorimetry from |η| = 1.4 up to the acceptance limit |η| = 4.8, corresponding to detector radii less than 2.2 m. At larger radii, where the radiation levels are low, a less expensive iron-scintillator hadronic “Tile calorimeter” [3] is used. The expected energy resolutions are:

for the e.m. calorimeter,

σE 10% ⊕ 1% =q E E(GeV )

σE 50% =q ⊕ 3% E E(GeV )

(1.4)

(1.5)

for the barrel part of the hadronic calorimeter and σE 100% ⊕ 10% =q E E(GeV )

(1.6)

10


for the hadronic calorimeter endcaps. The active depth of the e.m. calorimeter ranges from 25 radiation lengths in the barrel to 28 in the endcaps; the combined thickness of the calorimeters from 11 nuclear interaction lengths to 14.

1.2.4

The muon spectrometer

The ATLAS muon spectrometer [6], shown in figures 1.5 and 1.6, is endowed with three large superconducting air-core toroid magnets [5], precision tracking detectors and a powerful dedicated trigger system. The air-core magnet, shown in figure 1.7, reduces systematic uncertainties on muon tracks reconstruction due to multiple Coulomb scattering. MDT chambers

12 m Resistive plate chambers 10 Barrel toroid coil 8

Thin gap chambers

6

4 End-cap toroid 2 Radiation shield

Cathode strip chambers 0

20

18

16

14

12

10

8

6

4

2m

Figure 1.5: Side view of the muon spectrometer. The Barrel Toroid (BT) extends over a length of 26 m, with an inner bore of 9.4 m and an outer diameter of 19,5 m. The two EndCaps Toroids (ECTs) are inserted in the barrel at each end. They have a length of 5.6 m and an inner bore of 1.26 m. Each toroid consists of eight flat coils assembled radially and symmetrically around the beam axis. ECT coils are rotated by an angle of π/8 rad with respect to the BT ones. BT coils are contained in individual cryostats, while the eight coils of each

11

Resistive plate chambers MDT chambers Barrel toroid coils End-cap toroid

Inner detector

Calorimeters

Figure 1.6: Transverse view of the ATLAS muon spectrometer. ECT are assembled in a single large cryostat. The barrel sector (|η| < 1.1) is divided into (η, φ) projective towers composed by three measurement stations : the inner, the middle and the outer stations. The chambers used are divided into large (between the coils) and small ones (covering the coils). In the transition region (1.1 < |η| < 1.4) muons are reconstructed using three vertical stations placed near and above the endcaps toroids. In the endcaps (|η| > 1.4) the muon reconstruction is done using three vertical stations: one before the endcaps toroids, another behind them and the last on the walls of the experimental hall. Being impossible to join the high spatial resolution of the tracking with the time resolution (< 25 ns) needed for triggering, dedicated trigger chambers are foreseen, whose informations are used together with the nominal interaction vertex. In the barrel region there are three trigger stations: two placed in the middle tracking station (one under the precision chambers and the second one above them) and the last located in the outer tracking station. The same trigger concept is used in the transition and endcap regions. Trigger detectors will also help muon tracking by

12


Figure 1.7: Superconducting air-core toroid magnet system. The left-hand end-cap toroid is shown retracted from its normal operating position.

identifying the bunch crossing and delimiting intervals for pattern recognition on the precision chambers. As precision chambers, Monitored Drift Tubes, MDTs, are used for |η| < 2.4, while for |η| > 2.4 Cathode Strip Chambers, CSCs, are needed because of their better granularity. MDTs are drift tubes having a radius of 3 cm and working with a non-flammable gas mixture at a pressure of 3 bar; their spacial resolution is 80 µm. CSCs are wire chambers having the distance anode wire-cathode equal to the wire spacing, which is 2.54 mm. The coordinate read-out is performed by cathode strips with a resolution of 60 µm. The wires of both kinds of detectors are oriented perpendicularly to the beam axis, measuring muon hits coordinates only on the bending plane. Non-bending plane coordinates are provided by the trigger chambers, with a resolution of 1 cm.

13

The overall resolution on the momentum of muons with pt =100 GeV is about 1%, allowing a good reconstruction of events H → ZZ ∗ → 4µ. For the trigger system, Resistive Plate Chambers, RPCs, are employed at |η| < 1.05 and Thin Gap Chambers, TGCs, elsewhere. RPCs are gaseous detectors with parallel resistive electrode plates, providing coordinate measurements both in the bending and in the non-bending planes with a time resolution of about 1 ns. TGCs are wire chambers with capacitive read-out having a time resolution < 5 ns.

1.2.5

Trigger and Data Acquisition

The ATLAS Trigger and DAQ system [1] is described in figure 1.8. The trigger is organized in three levels: LVL1, LVL2 and EF (Event Filter). Rate [Hz]

Latency CALO

MUON TRACKING

40 × 106

pipeline memories

LVL1 ~ 2 µs (fixed)

104-105 derandomizing buffers MUX

MUX

MUX

multiplex data digital buffer memories

LVL2 ~ 1-10 ms (variable)

102-103 Readout / Event Building

~1-10 GB/s Switch-farm interface

LVL3 processor farm

101-10 2 Data Storage ~10-100 MB/s

Figure 1.8: Block diagram of the Trigger/DAQ system. LVL1 [7] acts on reduced granularity (∆η×∆φ = 0.1×0.1) data from the calorimeters and the muon spectrometer; its decision is based on selection criteria of inclusive nature. Example menus are shown on tables 1.1 and 1.2 with the corresponding trigger rates expected at low and high luminosity. LVL1, whose block diagram is shown in figure 1.9, is divided into four blocks: the calorimeter trigger, the muon trigger, the central processor (CTP), which takes

14


Calorimeter Trigger

Muon Trigger

Front-end Preprocessor Endcap Muon Trigger (TGC based)

Cluster Processor (electron/photon and hadron/tau triggers)

Barrel Muon Trigger (RPC based)

Jet/Energy-sum Processor Muon Trigger / CTP Interface

Central Trigger Processor

TTC

Figure 1.9: Block diagram of the LVL1 Trigger system.

the final decision, and the TTC (Timing, Trigger and Control distribution system), which distributes it to the front-end. LVL1 accepts data at a frequency of about 40 MHz and its fundamental task is to correctly identify the bunch crossing of interest. This is not a trivial thing, in fact the dimensions of the muon spectrometer imply times of flight larger than 25 ns and the shape of calorimeter signals extends over many bunch crossings. The latency (time taken to form and distribute the decision) is about 2 µs, while the output rate is 75 KHz, increasable to 100 KHz (limit imposed by the design of front-end electronics). Events selected by LVL1 (with data from the whole ATLAS detector) are stored in apposite ROBs, Read-Out Buffers, waiting for LVL2 decision. In case of positive decision, events are fully reconstructed and stored for the final decision of the Event Filter.

15

Table 1.1: Example of LVL1 trigger menu (L = 10 33 cm −2 s −1 ). Trigger Single muon, pt >6 GeV Single isolated EM cluster, Et >20 GeV Pair of isolated EM clusters, Et >15 GeV Single jet, Et >180 GeV Three jets, Et >75 GeV Four jets, Et >55 GeV Jet, Et >50 GeV AND missing Et >50 GeV Tau, Et >20 GeV AND missing Et >30 GeV Other triggers Total

Rate(kHz) 23 11 2 0.2 0.2 0.2 0.4 2 5 '40

The second level reduces the trigger rate to 1 KHz, using also informations from the Inner Detector. LVL2 has access to the full data of one event, with full precision and granularity; however only data from a small fraction of the detector, corresponding to the ROIs, Road Of Interest, identified by LVL1, are needed for the decision. LVL2 latency is variable from 1 ms to 10 ms, depending on the event. The final trigger decision is taken by the Event Filter by means of off-line algorithms; the acquisition rate is required to be less of 100 Hz for events of about 1 Mbyte. The optimization of tasks division between LVL2 and the Event Filter is still under study.

1.3 1.3.1

Higgs boson search: from LEP to LHC The Higgs boson in the MSM framework

The Minimal Standard Model, MSM, describes the interactions among elementary particles by imposing the invariance of its lagrangian under local gauge transformations. The underlying symmetry of the MSM is: SUc (3) ⊗ SUL (2) ⊗ U (1).

(1.7)

16


Table 1.2: Example of LVL1 trigger menu (L = 10 34 cm −2 s −1 ). Trigger Single muon, pt >20 GeV Pair of muons, pt >6 GeV Single isolated EM cluster, Et >30 GeV Pair of isolated EM clusters, Et >20 GeV Single jet, Et >290 GeV Three jets, Et >130 GeV Four jets, Et >90 GeV Jet, Et >100 GeV AND missing Et >100 GeV Tau, Et >60 GeV AND missing Et >60 GeV Muon, pt >10 GeV AND isolated EM cluster, Et >15 GeV Other triggers Total

Rate(kHz) 4 1 22 5 0.2 0.2 0.2 0.5 1 0.4 5 '40

SUc (3) acts on quarks colour and describes the strong interaction, while SUL (2)⊗U (1) accounts for the electroweak sector. SUL (2) acts only on left-handed components of fermion fields: ψL =

1 − γ5 ψ. 2

(1.8)

Gauge invariance excludes in the MSM lagrangian the presence of mass terms both for gauge boson, mediating the interactions, and for fermions (leptons and quarks). The spontaneous symmetry-breaking mechanism makes the MSM consistent with the phenomenology. A charged scalar boson doublet, Φ, is introduced, described by the following lagrangian: LHiggs = (D µ Φ)+ (Dµ Φ) − V (Φ+ Φ),

(1.9)

with Φ = (φ+ , φ0 ). The kinetic term of (1.9), (D µ Φ)+ (Dµ Φ), accounts for Φ-coupling to electroweak gauge bosons, contained in the covariant derivatives. Theory renormalization and the existence of a ground state impose: V (Φ+ Φ) = µ2 (Φ+ Φ) + λ(Φ+ Φ)2 ,

(1.10)

with λ strictly positive. µ2 can be negative and on this case V (Φ+ Φ) has a non trivial

17

infinity of ground states for: Φ+ Φ = −

1 µ2 = φ20 > 0. 2λ 2

(1.11)

Gauge invariance allows to parametrize: !

1 Φ(x) = 0, φ0 + √ ρ(x) , 2 where ρ(x) is a field describing a neutral scalar boson with mass mH =

(1.12) √

−2µ2 (the

Higgs boson) and φ0 is the ground expectation value of the Φ-doublet. Substituting the parametrization (1.12) for Φ into (1.9), mass terms for W ± and Z 0 come from the kinetic term, as well as terms describing their interactions with the Higgs boson; auto-interaction terms for it come from V (Φ+ Φ). Fermion masses are also explained with the coupling to the Φ-doublet, which for each fermion must be like: LY ukawa = gf Φ ψ¯f ψf .

(1.13)

Substituting the parametrization for Φ, from (1.13) one obtains: gf LY ukawa = gf φ0 ψ¯f ψf + √ ρ ψ¯f ψf . 2

(1.14)

The mass of the fermion f is thus given by: mf = g f φ0 ,

(1.15)

and its coupling constant to the Higgs boson by: gf mf , gHf f¯ = √ = √ 2 2φ0

(1.16)

using (1.15). As can be seen from (1.16), the fermions coupling constants to the Higgs boson are proportional to their masses. The Minimal Standard Model doesn’t predict exact values both for particles masses and for their coupling constants, which are free parameters of the theory. The model loses consistency, however, for a Higgs mass greater than 1 TeV. The Higgs boson discovery is certainly the most important experimental verification of the MSM still missing and, consequently, one of the main goals at LEPII and, in the future, at LHC.

18


1.3.2

Higgs boson search at LEP

The tightest limits on the Higgs boson mass, mH , have been obtained by the four LEP experiments (ALEPH, DELPHI, L3 and OPAL), with direct research and with precision indirect measurements. The main Higgs production mechanism at LEP is the Higgs-strahlung, with H decaying preferably into a b¯b couple according to 1.16; the corresponding Feynman diagram is shown in figure 1.10a.

a)

b)

Figure 1.10: Feynman diagrams for the Higgs-strahlung process (a) and for WW and ZZ fusion process (b). At LEPI, with a centre-of-mass energy

√ s ' mZ 0 ' 91 GeV, the final Z 0 is not

on mass-shell. On the contrary, at LEPII, with the centre-of-mass energy that has been increased till to reach 200 GeV, the Z 0 in the final state is on mass-shell. A little contribution to the total Higgs boson production cross-section comes from W W and ZZ fusion process, whose Feynman graph is shown in figure 1.10b. At LEPII the direct search of the Higgs is sensible to mass values mH
120 GeV, a golden research channel is H → ZZ (∗) → l+ l− l+ l− , with

l+ l− = e+ e− or µ+ µ− . In case mH < 2mZ , only one Z 0 is on mass-shell. This Higgs decay mode combines together a high statistical significance and an excellent resolution on mH , expected to be of about 2 GeV with the performances of the electromagnetic calorimeter and of the muon spectrometer. Finally, for mH > 2mZ , two interesting channels for Higgs boson research could be H → W W → lνjj and H → ZZ → l+ l− jj, especially for their high branching ratios: BR(H → lνjj)/BR(H → l+ l− l+ l− ) ' 150

(1.18)

BR(H → l+ l− jj)/BR(H → lνjj) ' 1/7.

(1.19)

Distinctive features of these decay modes are: • a couple of high-energy jets with an invariant mass of mW , in the case of H → lνjj, or mZ in the case of H → l+ l− jj;

• an isolated high-pt lepton, in the case of H → lνjj, or a couple l + l− , with an invariant mass of mZ , in the case of H → l+ l− jj.

An improved background rejection can be obtained by requiring the presence of two additional tag jets produced at small angles with respect to the beam axis in W W , ZZ or gluon fusion processes.

22


1.3.4

The Higgs sector in the Minimal Supersymmetric Standard Model (MSSM)

In MSM extensions, the existence of more than one Higgs boson is generally foreseen. In the case of MSSM extension, two charged scalar Higgs doublets give origin to the gauge bosons masses and to five bosons: three neutral ones (h, H and A, with mh < mH ) and two charged ones (H ± ). At Born level, their masses can be expressed as a function of only two parameters, mA and tgβ, with the latter being the ratio between the ground expectation values of the two original doublets. √ The four LEP experiments combined, with the data taken at s < 183 GeV, have excluded [8] at 95% confidence level mh < 79.6 GeV, mA < 80.2 GeV and mH ± < 69.0 GeV. For mH + < mt , the quark top can decay into H + b final state, with branching ratio dependent on tgβ and on mH + . The main decay channels of H + are H + → τ + ντ and

H + → c¯ s, with the last favourite only in case tgβ < 1.5.

Assuming mt = 175 GeV, for great values of tgβ, CDF has excluded at 95% c.l. mH + < 147 (158) GeV with σ(p¯ p → tt¯) = 5.0 (7.5) pb [14]. Assuming mt = 175

GeV, σ(p¯ p → tt¯) = 5.5 pb and mH + = 60 GeV, D0 has excluded at 95% c.l. tgβ < 0.97 and tgβ > 40.9 [15]. With about ten years of data-taking at LHC, exploiting different decay modes of Higgs bosons, all the parameters space, (mA ,tgβ), should be explored, and the three neutral bosons observable in great part of it. The search strategy for the MSSM neutral Higgs bosons is similar to the MSM

one, with the addition of H → τ + τ − and A → τ + τ − channels, for which both good τ -identification capability and high resolution on the transverse missing energy are needed. At low-luminosity LHC operation, charged Higgs bosons produced in top decays, t → H + b, can be detected in the decay mode H + → τ + ντ ; good b and τ -identification capabilities are needed.

Chapter 2 Resistive Plate Chambers: working principles and implementation in the ATLAS muon trigger

23

24

Chapter 2. RPCs: principles of operation and implementation on ATLAS

2.1

Interactions of fast charged particles in gases

A fast charged particle traversing a gaseous medium interacts mainly by means of incoherent Coulomb scattering with its electrons, resulting in excitation and ionization of the atoms. In the framework of quantum mechanics, an expression for the average energy loss per unit length is given by the Bethe-Bloch formula: dE Z ρ 2mc2 β 2 Em − ln = k dx A β2 I 2 (1 − β 2 ) "

with k =

!

− 2β

2

#

,

(2.1)

2πN z 2 e4 . mc2

N is the Avogadro number, m and e are the electron mass and electric charge, Z, A, ρ and I are, respectively, the atomic number, mass, density of the medium and its effective ionization potential; z is the charge in units of e of the crossing particle and β its velocity in units of the speed of light. Em represents the maximum energy transfer allowed in each interaction and is given by: Em =

2mc2 β 2 . 1 − β2

(2.2)

As can be seen from (2.1), the differential energy loss doesn’t depend on the mass of the particle traversing the medium. It is customary to consider, instead of 1 dE , ρ dx

dE , dx

because it is weakly dependent on the crossed material.

After a fast decrease dominated by the β −2 term, the energy loss reaches a constant value around β ' 0.97 and eventually slowly increase for β → 1. This relativistic rise is mitigated by effects due to the density of the medium that are not described in (2.1). The region of constant loss is called “minimum ionizing region” and corresponds to the most frequent case in high-energy physics. The energy loss of a minimum ionizing particle, normalized to the density of the material, is about 1.2 MeV cm 2 g −1 . The ionization process happens in two steps: at first the incident particle creates positive ion-electron couples, called “primary ionization”, then primary electrons freed with sufficient high energy (above few KeVs), called “δ-rays”, can ionize themselves the medium, producing “secondary ionization”. The total number of positive

25

ion-electron couples is therefore 3-4 times greater than the primary ionization and it is proportional to the energy loss of the incident particle. Fluctuations on energy loss are dominated by the relatively small number of primary collisions at short range with great impulse transfer. The so-called Landau distribution for the energy loss is therefore asymmetric with a tail extending to energy values much greater than the average value. In presence of an electric field in the gas volume, freed electrons and positive ions drift along the field; the average velocity of this slow movement is called “drift velocity”. For positive ions it is linearly dependent on the intensity of the electric field: w + = µ+ E ;

(2.3)

µ+ is called “mobility”. On the contrary, the mobility of the electrons is a function of the electric field, because, having a much smaller mass, they can considerably increase their kinetic energy between two subsequent collisions. The electrons drift velocity is given by: w − = µ− (E) E ,

(2.4)

with µ− (E) =

e τ (E) . 2m

(2.5)

τ (E) is the average time interval between two collisions and depends on E (Ramsauer effect). Typical electron drift velocities are of the order of 50 µm/ns, while those of the ions are about three orders of magnitude lower. Drifting along the electric field, electrons acquire sufficient energy to ionize the gas, giving origin to an “avalanche” multiplication. If n is the number of electrons at a given space point, after a drift of dx their increase will be: dn = nα(E) dx,

(2.6)

where α is the first Townsend coefficient. In good approximation, P α(E) = Ae−B E , P

(2.7)

26


with P being the gas pressure; A and B are constants depending on the gas. Because of the great difference between the drift velocities of electrons and ions, the avalanche assumes the characteristic shape of a drop oriented along the electric field (see figure 2.1). Electrons are concentrated on the front of the drop, which has a tail of positive ions.

Figure 2.1: Drop-like shape of an avalanche. Integrating the (2.6) in the case of an uniform electric field, one obtains: n(d) = n0 eαd . M =

n(d) , n0

(2.8)

the charge multiplication factor, cannot be increased at will; a phe-

nomenological limit is M ' 108 , corresponding to αd ' 20 (Raether condition). In fact inside the avalanche, because of the attenuation of the electric field due to spacecharge effects, recombination of electrons with positive ions can take place, resulting in emission of ultra-violet photons. These can generate new avalanches by photoionization of the gas or of the cathode, giving origin to a “streamer”, the formation of an ionized gas channel between the electrodes with consequent discharge. Another important process that happens in the gas is the electron attachment to electronegative molecules. The decrease of a number n of electrons after a path dx is: dn = −

n dx , λa

(2.9)

27

where λa is the mean free path for electron capture.

2.2

Description of a RPC and principles of operation

Resistive Plate Chambers, RPCs, are gaseous ionization detectors with parallel resistive electrode plates; the sketch of a RPC is shown in figure 2.2.

Figure 2.2: Sketch of a resistive plate chamber. The electrode plates, made of bakelite (resistivity ρ = 1011±1 Ω cm), have a thickness of 2 mm and generate an uniform intense electric field (4-5 kV/mm) in a 2 mm gap filled with gas. The voltage is applied on a thin graphite layer, having a surface resistivity σ ' 100 kΩ. As a consequence of the passage of an ionizing particle in the gas, the signal is formed by induction on aluminium pick-up strips, separated from the electrodes by a film of insulating material. The strips behave like transmission lines with a signal propagation velocity of about 0.2 m/ns. Oriented perpendicularly on two read-out layers, the reconstruction of two coordinates is possible.

28


It is worth noticing that if, instead of graphite layers, perfect conducting electrodes were used, they would behave like a Faraday cup preventing the signal induction on the read-out strips. For a detector with intense electric fields produced by electrode plates, it is very important to have an uniform gap thickness. Polycarbonate spacers are therefore placed inside the gap on a lattice of 10 cm pace. The spacers, shown in figure 2.3, have a cylindrical shape with a radius of 0.4 cm and a height of (2.00 ± 0.01) mm; the central ring has a radius of 0.6 cm.

8 mm

2 mm

12 mm Figure 2.3: Detailed sketch of a spacer. The surface of bakelite electrodes is coated with a thin layer of linseed oil, which improves the surface smoothness on a microscopic scale. In absence of ionization in the gas, the RPC can be described as shown in figure 2.4.a. Cb and Rb accounts for the resistive electrodes, while Cg and Rg for the gas gap. Being Rg >> Rb , the voltage is entirely applied on the gas gap. When the gas is crossed by an ionizing particle, the electric discharge generated in the gas can be described by a current generator (see figure 2.4.b) which discharges the capacitor Cg [17]. The system goes back to the initial condition following an exponential law with time constant: τ = ρ0

2d r + g

!

,

(2.10)

29

where ρ is the bakelite volume resistivity, r ' 5 its relative dielectric constant, d the

thickness of the plates and g the gas gap. For ρ = 1010 Ω cm, τ is of the order of 10

ms, while the RPC characteristic discharge duration is about 10 ns 10

45

cm), disuniformity in the response is expected to be due mainly to the inhomogeneity of the spacers thickness; the production tolerance, 15 µm on 2 mm, corresponds to a 0.75% dispersion on the electric field intensity. At smaller scales, the response uniformity test consists in studies about the inefficiency, measured as a function of the distance from the spacers.

3.2

Experimental lay-out

The experimental lay-out used in the present experiment is described in figure 3.2, which shows the test chamber together with the four RPC stations used for tracking cosmic muons. The size of the chamber under test is 90 × 290 cm 2 . The tracking stations 1,2 and 3 have comparable sizes, but only 16 strips per view are read out, so that the sensitive area is 50 × 50 cm2 . The lowest tracking station is a single-gap

RPC, 50×50 cm2 wide, located under a 15 cm thick lead shielding. The test chamber is movable with respect to the monitor telescope for scanning the full area.

Figure 3.2: Layout of the test. The alignment has been performed using the plumb-line. In order to cure offline the remaining misalignment, hit positions have been biased with offsets estimated by centring the residuals distributions of each chamber (see next section). All the chambers work in avalanche regime with a gas mixture composed of

46

Chapter 3. Response uniformity test of a large size RPC

C2 H2 F4 , C4 H10 and SF6 in the volume ratios 96.65/3.00/0.35. Results with 0.5% SF6 are also reported. The readout strips of all RPCs are 2.9 cm wide and the pitch is 3.1 cm. The monitor chambers work at 9.6 kV ; their signals are amplified by a factor 10 and discriminated with a threshold of 15 mV. A scheme of the test chamber read-out is shown in figure 3.3: the RPC signals are amplified with a two-stage amplifier (gain=250, bandwidth=160 MHz), made of commercial components, and discriminated with threshold 60 mV.

Figure 3.3: Test chamber read-out scheme. The front-end electronics consists of a pre-amplifier with gain'10, which is located inside the chamber Faraday cage, and of a second stage amplifier with gain'25. Signals are discriminated with a threshold of 60 mV and coincidences with the trigger signal are registered with a latch. The trigger signal, is the threefold coincidence of the ORed short strips of the layers 2, 3 and 4. It is 60 nsec shaped and is used to latch the signals from the monitor and from the test chamber, which are 100 nsec shaped. Due to the lead shielding, the muons selected by the trigger system have energies above 200 MeV .

3.3

Description of the tracking algorithm

The tracks used in the analysis are selected according to the following criteria: • only one cluster in each layer of the monitor RPCs, with size ≤ 3 strips; • linear fit with

χ2 dof

< 1.1 in both projections.

47

monitor chamber 1

monitor chamber 3

monitor chamber 2

monitor chamber 4

Figure 3.4: Y-projection residuals distributions for the monitor chambers.

In figure 3.4 are shown the typical residuals distributions for the Y-projection of the monitor chambers, after having applied the software corrections for misalignment. The spikes present in the distributions are due to the discrete position of the hits; the great central peaks in stations 1 and 2 are due to the fact that in the fit their informations are strongly correlated. The residuals of the monitor chambers for the X-projection have similar shapes. The distributions of the chi-square per degree of freedom for the two projections are shown in figure 3.5 and 3.6. In figure 3.7 and 3.8 are shown the distributions of the impact point on the test chamber for both views. The resolution on the reconstructed impact point of the tracks on the test RPC is of the order of 1 cm, as can be seen from the distributions of the residuals in figure 3.9 and 3.10 for events having low cluster size hits in the chamber.

48


Figure 3.5: Tracking chi-square distribution for the Y-projection.

Figure 3.6: Tracking chi-square distribution for the X-projection.

Reconstructed impact point (cm)

Figure 3.7: Y-projection: reconstructed impact point on the test chamber.

3.4

Reconstructed impact point (cm)

Figure 3.8: X-projection: reconstructed impact point on the test chamber.

Response uniformity test

The chamber large scale uniformity has been investigated by subdividing it into 12 pads of area (50 × 50) cm2 , covering the whole detector surface with some overlap, as shown in figure 3.11. With the purpose to formulate a criterium for defining the maximum acceptable

49

Figure 3.9: Y-projection residuals distribution for events having cluster size ≤ 3 strips.

Figure 3.10: X-projection residuals distribution for events having cluster size ≤ 3 strips.

12

11

10

9

8

7

1

2

3

4

5

6

Figure 3.11: Pads subdivision of the tested chamber: overlap regions between neighbouring pads are coloured in grey.

residual for an efficient hit in the test chamber, the residuals are compared in figures 3.12 and 3.13 with the half-width of the clusters. The distributions suggest that possible systematic errors on the reconstructed impact point do not exceed one half of the read-out pitch. The RPC tested is therefore considered efficient if there is a cluster matching the reconstructed track with a tolerance of 1.6 cm. For each pad the efficiency has been measured at different operating voltages. In order to take into account the different atmospheric conditions during data-taking, operating voltages have been normalized according to the formula [22] [25]:

50


cm cm

Figure 3.12: Y-projection distribution of the difference between the absolute value of the residuals and the clusters half-width. The cut used in the analysis is indicated with an arrow.

HV = HVsper

Figure 3.13: X-projection distribution of the difference between the absolute value of the residuals and the clusters half-width. The cut used in the analysis is indicated with an arrow.

T P0 , T0 P

(3.1)

where HVsper ,P and T are the operating voltage, pressure and absolute temperature; HV is the voltage normalized at T0 = 293 K and P0 = 1010 mbar. This correction reflects the fact that the avalanche growth depends on the ratio between the electric field and the gas density, which is proportional to

P T

in the approximation

of ideal gases. In figure 3.14 and 3.15 are shown the efficiency plots related to longitudinal (Yprojection) and transversal strips (X-projection) for all the pads of the tested RPC. The operating voltages corresponding to 50 % detection efficiency are all contained within a range of ± 60 V around 9.1 kV. Interpreting this in terms of gap thickness disuniformity, it corresponds to a variation of ±13 µm on 2 mm , to be compared with the maximum spacers thickness tolerance, which is ± 15 µm.

51

Figure 3.14: Pads efficiency plots for longitudinal strips.

3.5

Inefficiency distribution of a RPC chamber

A detailed analysis of the detector inefficiency has been made using a sample of about 53000 muons collected all over the chamber sensitive area at a normalized voltage of about 9.7 kV. In order to study the intrinsic detector efficiency free from any effect due to the read-out electronics, the OR of longitudinal and transversal strips is considered for efficiency calculations. The overall efficiency on the sample is: = (98.560 ± .052) % . For each pad, the position of the spacers has been reconstructed using the scatter plot of the inefficiencies, as shown in figure 3.16. With the purpose of studying the short scale (≤10 cm) uniformity, the distribution of the inefficiency as a function of the distance, r, between the reconstructed track and the centre of the closest spacer, is reported in figure 3.17. The distribution exhibits a peak at r = 0, due to the spacer insensitive areas, extending till to r = rcut = 2.2 cm because of the coarse tracking

52


Y (cm)

Figure 3.15: Pads efficiency plots for transversal strips.

X (cm)

Figure 3.16: Example of spacers pattern reconstructed from the inefficiencies scatter plot for pad 1.

Inefficiency

53

Distance from closest spacer (cm)

Figure 3.17: RPC inefficiency distribution as a function of the distance between the reconstructed track and the centre of the closest spacer. resolution. For r > rcut the inefficiency is independent of r, and it is interpreted as the chamber intrinsic inefficiency: (1 − )intr = (0.584 ± 0.036) % . The azimuthal distribution of the intrinsic inefficiency for the events at r > rcut is uniform, as shown in figure 3.18. The contribution of the spacers to the inefficiency of the chamber can be schematized by describing them as an effective insensitive circle of radius ref f . In such a scheme the efficiency for r < rcut is given by:

cut =

2 2 πrcut − πref f int . 2 πrcut

(3.2)

From the considered sample, ref f and the spacers contribution to inefficiency, (1 − )sp , are therefore estimated using the following formulae:

54


Figure 3.18: Azimuthal distribution of the intrinsic inefficiency for r > rcut .

ref f = rcut

s

int − cut ; int

(1 − )sp =

2 πref f . 2 l

(3.3)

(3.4)

The effective spacer radius evaluated from the sample, ref f = (0.522 ± 0.013) cm, is included between the inner, ri = 0.4 cm, and the outer radius of the spacers, ro = 0.6 cm. Consequently, the spacers contribution to inefficiency, (1 − )sp = (0.856 ± 0.043) %, is below the total spacers area, which is about 1 % of the total detector surface. By comparing (1 − )sp with (1 − )intr at full efficiency, it can be concluded that spacers are the principal source of inefficiency for a RPC.

55

3.6

Studies on the intrinsic inefficiency and on the spacers inefficiency

Grouping together the remaining data collected at different operating voltages and already presented in section 3.4, the intrinsic inefficiency and the effective spacer radius dependence on the voltage have been studied. The effective radius of the spacers, shown in figure 3.19, is compatible with a constant. The result of the fit performed on the data is: ref f = (0.544 ± 0.013) cm

(χ2 /dof = .99) ,

consistent with the one evaluated from the large sample at 9.7 kV.

Figure 3.19: Effective spacer radius as a function of the operating voltage. The estimated spacers contribution to the inefficiency of the chamber is therefore: (1 − )sp = (0.929 ± 0.044) % .

56


The same studies have been done for a sample of data collected on the pad 1 with a gas mixture C2 H2 F4 /C4 H10 /SF6 = 96.5/3.0/0.5. Also for this mixture the effective radius of the spacers, shown in figure 3.20, is seen to be constant and compatible with the two values previously obtained: ref f = (0.527 ± 0.013) cm

(χ2 /dof = .57) .

Figure 3.20: Effective spacer radius as a function of the operating voltage with 0.5% SF6 . The estimated spacers contribution to the inefficiency is: (1 − )sp = (0.873 ± 0.043) % . In figure 3.21 are shown the intrinsic inefficiencies as a function of the operating voltage for the two gas mixtures. As a consequence of the different SF6 percentage, a shift of about 200 V is seen between the two plots. In both cases, increasing the operating voltage, the intrinsic inefficiency becomes less than 0.5%.

57

Figure 3.21: RPC intrinsic inefficiency for the two different SF6 percentages.

The singles counting rate, R, has been monitored during data-taking. It has been found to be less than 4 Hz/cm2 at the maximum operating voltage for transversal strips, and one order of magnitude greater for the longitudinal ones, presumably due to a worse electromagnetic shielding. Nevertheless, the contribution to the measured inefficiencies:

∆(1 − ) = 1 − e−GSR , 1−

(3.5)

where S is the read-out strip panel surface and G the signal time-shaping plus the trigger gate (G=160 nsec), turns out to be less than the statistical errors of the analysis.

58


3.7

Intrinsic inefficiency and primary ionization

The intrinsic inefficiency, interpreted as the “zero-probability” of a Poisson distribution, can be parametrized as:

(1 − )intr = e−n

,

(3.6)

where n is the average effective number of primary ionizations contributing to detector efficiency in the actual set-up.

Figure 3.22: Average effective primary ionizations for the two different gas mixtures. In figure 3.22, n = ln (1−)1 intr is shown as a function of the operating voltage for the two different gas mixtures. In both cases, for efficiencies above 70% (n=1.2), the data fit a straight line:

n = A + B HV (kV ) .

(3.7)

59

The values of A and B are reported on table 3.7, together with the voltage extrapolated at n=0, HV0 . Table 3.1: Values of A and B A B(kV −1 ) χ2 /dof dof HV0 (kV )

SF6 = 0.35% −59.23 ± 0.19 6.608 ± 0.021 0.7910 3 8.963 ± 0.040

SF6 = 0.5% −66.27 ± 0.38 7.204 ± 0.040 0.9549 6 9.199 ± 0.073

In figure 3.23 it is shown the angular distribution of the tracks used for the analysis, f (θ), θ being the angle with respect to the vertical direction.

theta (rad)

Figure 3.23: Angular distribution of the tracks from the large sample at 9.7 kV. The number of effective primary ionizations is expected to scale with

1 , cos(θ)

which

changes only of the 8.6% between the limits θ=0 and θ=0.4. Effects due to inclined tracks are therefore not observable in the present analysis. Making the further assumption that the effective primary ionizations must be produced in an “effective gap”, D, at sufficient distance from the anode, D can be evaluated by:

60


D=

n g ntot

,

(3.8)

where g is the gas gap and ntot is the total number of primary ionizations in the gap. For the considered gas mixtures, this number, estimated from the Argon value normalized for the atomic number of C2 H2 F4 [16], is ntot ' 17. In the plateau efficiency region the effective number of primary ionizations increases from 4 to 7 (see figure 3.22) and the “effective gap” from 0.5 mm up to 0.8 mm.

3.8

Cluster size studies

In figure 3.24 and 3.25 the correlations between the efficiency and the cluster size are reported for both projections of the 12 pads (see figure 3.11). A uniform correlation is observed, with the exception of pads 3,5,6 and 7. In the case of pads 6 and 7, this effect has been found to be due to a noisy pre-amplifier card in transversal strips read-out. Pads 3 and 5, which presented wide inefficiency regions probably due to spacers not well glued, have been compressed using lead bricks (pad 3) or a clamp (pad 5) in order to reach full efficiency during the response uniformity test. It is worth noticing that the correlation plots for the non-pathologic pads are more spread in the case of the longitudinal strips, for which the pads with greater cluster size are the ones more distant from the read-out side (pads 1,2,11 and 12). In figure 3.26 it is shown a comparison between the efficiency and the cluster size plots related to the data taken on pad 1 with 0.35% and 0.5% SF6 . A shift of about 200 V between the data taken with the two different mixtures is seen both for efficiency and for cluster size. From the corresponding correlation between efficiency and cluster size, shown in figure 3.27, however, a difference is seen between transversal and longitudinal strips, the latter having a greater average cluster size. The efficiency and cluster size plots with different thresholds are reported in figure 3.28 for data taken on pad 2. As expected the average cluster size decreases with increasing threshold. The two different projections are equalized with different

61

Figure 3.24: Efficiency vs cluster size correlation for longitudinal strips.

Figure 3.25: Efficiency vs cluster size correlation for transversal strips.

thresholds: 40 mV and 80 mV for transversal and longitudinal strips respectively. This shows that the different cluster size is due to the different gain of the front-end amplifiers. Indeed, one of them is inverting and the other non-inverting, because signals on opposite strip panels have different polarity (see figure 2.5). Typical cluster size distributions are shown in figures 3.29 and 3.30 for longitudinal and transversal strips at different operating voltages with 60 mV thresholds. The distribution peaks move from one to three strips for increasing voltage. The probabilities of cluster size greater than 3 for transversal and longitudinal strips is shown in figure 3.31 for the same gas mixture. The probabilities of having cluster size one and two strips as a function of the reconstructed impact point are shown in figure 3.32 at fixed voltage: events with cluster size one have peaks in the middle of the strips, while events with cluster size two have peaks in the interstices between them. Typical residual distributions are shown in figure 3.33: also for events of cluster size 3 strips, the residuals are contained in great part within ± 1 strip.

62


Figure 3.26: Efficiency and cluster size plots with 0.35% and 0.5% SF6 for longitudinal ((a) and (c)) and transversal strips ((b) and (d)).

3.9

Preliminary results with the ATLAS final Frontend electronics

For sake of completeness a few preliminary results concerning an 80 × 180 cm 2 RPC prototype equipped with the ATLAS final front-end electronics are reported. The experimental set-up is similar to the one already described in figure 3.2. The gas mixture used is composed by C2 H2 F4 , C4 H10 and SF6 in the volume ratios: 96.7/3.0/0.3. The chamber has been subdivided into 8 50 × 50 cm2 pads. Vth =-1.35 V and Vbias =-1.00 V, so that the threshold on the amplified analogic signal is 350 mV (see section 2.5). Discriminated signals from the test chamber are sent through 6 m long flat cables to a receiver, which shapes them in TTL logic, as required for the final ATLAS trigger electronics [7]. From the receiver the signals are then sent via 7 m long flat cables to a transducer, which changes the logic into differential ECL. Through 3.5 m long flat cables, the chamber hit patterns are finally registered with a commercial latch.

63

Figure 3.27: Efficiency vs cluster size correlation with different SF6 percentages.

Figure 3.28: X and Y-projection efficiency and cluster size plots for different thresholds. In figure 3.34 the efficiency plots are shown for transversal strips and in figure 3.35 the corresponding correlations between efficiency and cluster size are reported.

64


a)

b)

c)

d)

Figure 3.29: Cluster size distributions for longitudinal strips with 0.5% SF6 at H.V.=9.37 kV ( = 69.4%) (a), 9.80 kV ( = 97.7%) (b), 10.00 kV ( = 98.8%) (c) and 10.11 kV ( = 99.1%) (d). The distributions refer to data taken on pad 1.

a)

b)

c)

d)

Figure 3.30: Cluster size distributions for transversal strips with 0.5% SF6 at H.V.=9.37 kV ( = 51.4%) (a), 9.80 kV ( = 96.0%) (b), 10.00 kV ( = 98.3%) (c) and 10.11 kV ( = 98.8%) (d). The distributions refer to data taken on pad 1.

65

Figure 3.31: Cluster size > 3 probability as a function of the operating voltage with 0.5% SF6 for data taken on pad 1.

a)

b)

Figure 3.32: RPC hit probability vs reconstructed hit position for events of cluster size 1 (a) and 2 (b).

66


Figure 3.33: Typical residual distributions for all the events, for the events with cluster size=1, cluster size=2 and cluster size=3. A comparison with the commercial front-end is reported in figure 3.36.

Figure 3.34: Efficiency plots for transversal strips with the ATLAS final front-end electronics.

Figure 3.35: Efficiency vs cluster size correlation plot for transversal strips with the final front-end electronics.

67

Figure 3.36: Efficiency vs cluster size correlation plot for transversal strips, read out with the commercial front-end electronics and with the final ATLAS front-end.

Chapter 4 The LVL1 muon trigger in the barrel

69

70

Chapter 4. The LVL1 muon trigger in the barrel.

Figure 4.1: View of a standard barrel sector. The RPCs are represented by shaded boxes.

4.1

Hardware implementation

A general description of the Level 1 trigger and of the muon spectrometer has been already given in chapter 1. As specialized trigger detectors, RPCs are used in the barrel part (|η| < 1.05) of the muon spectrometer, and TGCs, Thin Gap wire Chambers, in the end-cap. RPCs are disposed in three stations, two of them (RPC1 and RPC2) cover the internal and external faces of the middle precision chamber and the third (RPC3) is located close to the external precision chamber, as shown in figure 4.1. Each station is composed of a RPC doublet with read-out in two orthogonal views, η and φ, referred as bending and non-bending projections respectively. The trigger logic is based on coincidences between different stations, one of the inner two stations being chosen as pivot (see figure 2.10). The two innermost stations

71

Large Barrel Sector

Small Barrel Sector

Figure 4.2: Azimuthal view of one half-barrel octant. Small units are placed in correspondence of magnet coils.

are used to trigger low-pT muons (mainly for b-physics studies), while the outermost is used to trigger high-pT muons. The barrel is divided in two half-barrels, symmetric with respect to η = 0, and azimuthally segmented in octants; each octant is further subdivided in two parts, referred as Large and Small sectors (see figure 4.2). RPC chambers are classified, according to their location, into BML (Large sectors of RPC1 and RPC2), BMS (Small sectors of RPC1 and RPC2), BOL (Large sectors of RPC3) and BOS (Small sectors of RPC3). Each sector is divided along the z direction into several units, which are mechanically and functionally independent detectors, as shown for example in figures 4.3 and 4.4. With the exception of BMS units, which are composed of two RPC layers with a single chamber, all units are composed of two RPC layers with two chambers. The trigger logic is implemented through Coincidence Matrices (CM), to which the RPC strips are connected so as to logically subdivide the pivot planes in η and φ, as shown in figure 4.5 and 4.6. Four CMs, two in η and two in φ, form a Pad. The intersection of one η-CM and one φ-CM within a Pad gives a ROI (Road Of Interest)

72


Figure 4.3: Units disposition on a Large sector of RPC1 station. The dimensions are indicated in mm. Each unit is composed of two RPC layers with two chambers.

Figure 4.4: Units disposition on a Small sector of RPC1 station. The dimensions are indicated in mm. Each unit is composed of two RPC layers with a single chamber.

of size ∆η × ∆φ ' 0.1 × 0.1. The trigger logic is reported in figure 4.7. The low-pT CM has in input the 32+32 strips of the first RPC doublet (the pivot plane) and the 48+48 strips of the second doublet. Coincidences are required within a programmable road depending on the wanted trigger pT -threshold, with a majority of three-out-of-four, in order to have some redundancy in the trigger system. The road width is defined this way: for each strip i in the pivot plane, a strip j is identified as the projection of i in the confirmation plane; then a set of strips around j is selected such that more than a given percentage of muons with pT equal to the threshold are triggered. The output is the 32-bits pattern of the coincidences, plus eight more bits for local flags and threshold information. The high-pT CM has in input the output pattern from the low-pT CM and the 48+48 strips of the outer (RPC3) doublet. A coincidence within the trigger window is required in at least one layer of the outer chamber. A possible option is to increase the CM size from 32 × 48 to 32 × 64 channels. In the non-bending projection a road of three strips is enough to account for the multiple Coulomb scattering of the muons in the calorimeters, triggering 100% of them. Given the steeply falling muon pT -distribution shown in figure 4.8, the trigger has to make a sharp cut on the true pT of the muon candidates, in order to keep the background from π’s and K’s decay as small as possible.

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It is also required that the rate of fake triggers, due to the high level of random hits from low energy background, shall be much less than the real muons rate. Space coincidences are therefore required both in the bending and in the non-bending view, with a time gate close to the bunch-crossing period (25 nsec). The programmable coincidence matrix allows to increase the pT threshold from 6 to 20 GeV for the low-pT trigger and from 20 to 35 GeV for the high-pT trigger. The trigger logic can operate simultaneously with various thresholds suitable for different physics processes: three thresholds for low-pT muons (presently 6, 8 and 10 GeV), and two for high-pT muons (20 and 30 GeV).

4.2 4.2.1

Trigger performance simulation Description

Two different trigger configurations have been considered so far: one with the pivot in RPC1 station, and the other with the pivot in RPC2. The present analysis deals with the second case. The different schemes are shown in figures 4.9 and 4.10; it is worth noticing that the displacements of a given particle hits in the confirming stations from the trajectory of an infinite-pT muon have the same sign if the pivot is in RPC1 station and opposite signs if the pivot is in RPC2 station. For measuring the trigger window sizes and the trigger efficiency, the muon samples described in table 4.1 have been generated using DICE (Detector Integration for a Collider Experiment), the ATLAS full simulation program. The DICE program consists of three parts: event generation, detector simulation (using GEANT 3.21) and digitization, in which the detector output is reproduced (in the case of the RPCs, the strips fired). The first level muon trigger logic has been simulated in the ATRIG framework, which is the standard for trigger simulations. The pT -range of the samples has been chosen to cover the main physics issues, considering also that muons with pT < 3 GeV are absorbed in the calorimeters. Because of the symmetry of the spectrometer, the study has been restricted to a φ-octant of a half-barrel. The octant is centred on a magnetic coil and the η-range

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Figure 4.9: Trigger scheme with the pivot in RPC1 station. The dashed line is the trajectory of a muon of infinite pT .

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Figure 4.10: Trigger scheme with the pivot in RPC2 station. The dashed line is the trajectory of a muon of infinite pT .

exceeds the half-barrel in order to consider in the analysis also border effects.

4.2.2

Trigger coincidence windows

In order to estimate the trigger coincidence windows in the bending projection, the sectors of the pivot plane have been divided into slices corresponding to the η-CM partitioning described in figures 4.5 and 4.6. Inside a single slice, the trigger windows are assumed to be constant. Each hit in the pivot station is projected to the confirming station (the inner for low-pT triggers and the outer for high-pT ); the windows are estimated from the distribution of the distance, ∆z, between the projected point and the centre of the fired strip. In presence of several fired strips, the minimum ∆z is taken among all possible combinations, corresponding to the highest pT . Some of the ∆z distributions for pT =6 GeV and pT =20 GeV muons are shown in figures 4.11 and 4.12. In figures 4.13 and 4.14 the ∆z distributions at η ∼ 0 and η ∼ 1 concerning the

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Figure 4.12: ∆z(cm) distributions on RPC3 for pT =20 GeV muons: on Large sectors, for η ∼ 0 (a), η ∼ 0.6 (c), η ∼ 1 (e), and on Small sectors, for η ∼ 0 (b), η ∼ 0.6 (d), η ∼ 1 (f).

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Table 4.1: Muon samples generated for trigger performance studies; each sample is composed of 10000 µ+ and 10000 µ− . pT (GeV) Number of events 4 20000 5.5 20000 6 20000 8 20000 10 20000 15 20000 20 20000 30 20000 40 20000

η range −0.15 ≤ η ≤ 1.15 −0.15 ≤ η ≤ 1.15 −0.15 ≤ η ≤ 1.15 −0.15 ≤ η ≤ 1.15 −0.15 ≤ η ≤ 1.15 −0.15 ≤ η ≤ 1.15 −0.05 ≤ η ≤ 1.1 −0.05 ≤ η ≤ 1.1 −0.05 ≤ η ≤ 1.1

φ range 0 ≤ φ ≤ π/4 0 ≤ φ ≤ π/4 0 ≤ φ ≤ π/4 0 ≤ φ ≤ π/4 0 ≤ φ ≤ π/4 0 ≤ φ ≤ π/4 0 ≤ φ ≤ π/4 0 ≤ φ ≤ π/4 0 ≤ φ ≤ π/4

low-pT trigger are reported for muons of different pT . The same is done in figures 4.15 and 4.16 for the high-pT trigger. The spread decreases with increasing pT . For pT ≥ 10 GeV in the case of the low-pT trigger, and for pT ≥ 30 GeV in the case of the high-pT trigger, the pT -discrimination becomes poor. The trigger windows tuned for selecting respectively 90% and 95% of the muons of given pT are shown in figures 4.17 for pT =6 GeV, 4.18 for pT =8 GeV, 4.19 for pT =10 GeV, 4.20 for pT =20 GeV and 4.21 for pT =30 GeV. The pitch of the η-strips is uniform in the simulated layout: 3.00 cm for RPC1 and RPC2 stations, 3.38 cm for RPC3 station. Also the pitch of the φ-strips is uniform: 3.070 cm for the BML chambers, 3.080 cm for the BMS chambers, 3.890 for the BOL chambers and 3.950 for the BOS chambers. Increasing |η| (and consequently p) at fixed pT , the muon curvature decreases. On the other hand, muons describe larger trajectories for greater |η|. The overall effect is that larger windows are needed for greater |η| values. The window size also depends on the width of the nominal p-p interaction region (σvtx ∼ 5.5 cm), the Coulomb scattering and the fluctuations on the energy loss in the calorimeters. The window asymmetry, due to the larger spread of the outwards bending muons with respect to the inwards bending ones, is effective especially for low-pT muons at η → 1. The asymmetry is even more pronounced for Small chambers, because of the

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Figure 4.13: ∆z(cm) distributions for muons of different pT on RPC1 station at η ∼ 0.




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Figure 4.17: 90% and 95% trigger windows for pT =6 GeV muons on RPC1 station. The window sizes are indicated both in cm and in strips.

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Figure 4.22: Comparison between the trigger windows on RPC1 station in the present analysis and on RPC2 station with the old trigger configuration, for threshold 6 GeV.

Figure 4.23: Comparison between the trigger windows on RPC3 station in the present analysis and with the old trigger configuration, for threshold 20 GeV.

inhomogeneities of the magnetic field close to the coils. In figures 4.22 and 4.23 the 90%-acceptance windows with the pivot in the RPC2 station (present analysis) and with the pivot in the RPC1 station are compared. In the latter case, for a better comparison, the sign of the low-pT windows has been changed to compensate for the change of ∆z sign, due to the different position of the pivot station. With the pivot in the RPC2 station, a reduction in the number of strips is seen both for the low-pT (12% for 6 GeV threshold) and for the high-pT (31% for 20 GeV threshold) trigger windows. This reduction allows to implement the 95%-acceptance trigger with the present CM size (32 × 48 channels).

4.2.3

Trigger efficiency

In the present analysis, concerning only the barrel, the trigger acceptance is defined as the fraction of generated muons with one or more strips fired in the pivot RPC

87

Figure 4.24: Trigger acceptance as a function of η at the generation point for p T =6 GeV µ+ (a) and µ− (b). doublet. The trigger efficiency is given by the fraction of the triggered muons with respect to the “accepted” ones. The trigger acceptance as a function of η at the generation point for muons with pT =6 GeV and pT =20 GeV is reported in figures 4.24 and 4.25. For pT =6 GeV, the observed difference between µ+ and µ− is due to the opposite bending; this difference is much smaller for pT =20 GeV. For pT =6 GeV µ− , the acceptance loss is already significant at η ' 0.9, to be compared with the limit of the barrel region, η ' 1. It must be considered however that muons with η ∼ 1 can be triggered also by the end-cap muon trigger. The combined performance of the LVL1 muon trigger is still under study. Acceptance losses are also visible at η=0, due to the spectrometer central gap, at η ' 0.4 and η ' 0.75, due to the ribs of the magnet coils in the Small chambers (see also figures 4.26 and 4.27). The overall acceptance in the range 0 ≤ η ≤ 1 is shown in figure 4.28. The efficiency as a function of η for the low-pT trigger with threshold 6 GeV is

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Figure 4.25: Trigger acceptance as a function of η at the generation point for p T =20 GeV µ+ (a) and µ− (b).

Figure 4.26: Distribution of the hits in the pivot station as a function of η for pT =6 GeV µ+ ((a) and (b)) and µ− ((c) and (d)).

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Figure 4.27: Distribution of the hits in the pivot station as a function of η for pT =20 GeV µ+ ((a) and (b)) and µ− ((c) and (d)).

Figure 4.28: Trigger acceptance as a function of the muon pT .

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Figure 4.29: Trigger efficiency as a function of η at the generation point for pT =6 GeV µ+ (a) and µ− (b). shown in figure 4.29, and the same is done in figure 4.30 for the high-pT trigger with threshold 20 GeV; muon samples with pT equal to the nominal trigger threshold are considered in both cases. The effects of the central gap and of the ribs in the Small chambers of the confirming stations are clearly visible. The trigger efficiency as a function of pT is reported in figure 4.31 for the low-pT thresholds (6, 8 and 10 GeV) and in figure 4.32 for the high-pT thresholds (20 and 30 GeV). The not negligible efficiency for muons of pT lower than the nominal threshold could give raise to significant effects on the trigger rates. It has been also considered the possibility to increase the low-pT trigger robustness against low energy charged particles (energy < 100 MeV) by requiring a confirmation in the outer trigger station. The “confirmed” low-pT trigger efficiency as a function of η is shown in figure 4.33 with threshold 6 GeV, for muons with pT equal to the nominal threshold. The inefficiency is more pronounced for η=0 with respect to the non “confirmed” trigger (see figure 4.29), and it increases more rapidly for η → 1 as a consequence of µ− bending outwards and missing the outer station.

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Figure 4.30: Trigger efficiency as a function of η at the generation point for pT =20 GeV µ+ (a) and µ− (b).

Figure 4.31: Low-pT trigger efficiency with threshold 6 GeV (a), 8 GeV (b) and 10 GeV (c).

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Figure 4.32: High-pT trigger efficiency with threshold 20 GeV (a) and 30 GeV (b).

Figure 4.33: “Confirmed” trigger efficiency as a function of η at the generation point for pT =6 GeV µ+ (a) and µ− (b).

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Figure 4.34: 6 GeV low-pT trigger efficiency without (a) and with the outer station confirmation (b). In figure 4.34 a comparison is made as a function of pT , and the overall efficiency is seen to be still good. In order to increase the trigger acceptance in the barrel, it is planned to insert special RPC chambers [27] covering the cracks in the Small sectors and in the feet regions of the spectrometer (whose effects haven’t been studied in the present analysis).

Conclusions

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Conclusions

The study presented here supports the validity of the RPCs, Resistive Plate Chambers, as dedicated muon trigger detectors in the ATLAS experiment at LHC. The response uniformity of an ATLAS realistic RPC has been tested using cosmic rays. The dispersion of the efficiency vs operating voltage plots corresponds to a gap thickness variation of the order of the maximum spacer thickness tolerance. The correlation between efficiency and cluster size results uniform on the chamber and characteristic of the front-end electronics. Spacers are seen to be the principal source of inefficiency at high operating voltages: their contribution to the overall inefficiency doesn’t exceed the ratio between their surface and the total detector area (which is ∼ 1%), while the intrinsic inefficiency becomes lower than 0.5% at sufficient high voltage. The intrinsic detector inefficiency has been interpreted as the zero-probability” of a Poisson distribution, and parametrized in terms of the average effective number of primary ionizations contributing to the detector efficiency (presumably those produced near the cathode, which have a greater charge amplification in the gas). The number of effective primary ionizations increases linearly with the operating voltage, starting from ∼ 70% efficiency. RPCs in the muon trigger of the ATLAS experiment are disposed in three stations. The trigger logic is implemented through coincidences between the different stations within a road depending on the threshold applied. One of the two innermost stations is used as a pivot. Montecarlo simulations have shown that moving the pivot from the innermost station (the standard trigger configuration) to the middle station, the width of the coincidence roads decreases, allowing to increase the acceptance of the trigger windows from 90% to 95%.

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UNIVERSIT`A DEGLI STUDI DI ROMA âTOR

UNIVERSIT`A DEGLI STUDI DI ROMA âTOR

UNIVERSIT`A DEGLI STUDI DI ROMA âTOR

UNIVERSIT`A DEGLI STUDI DI ROMA âTOR