Experimental Particle Physics

Pekka K. Sinervo

Department of Physics, University of Toronto Toronto, ON M5S 1A7 Canada

Abstract

The accelerators and particle detectors that are used to study high energy particle interactions are reviewed. The parameters of the accelerators that are currently in use and those that will be shortly commissioned are summarized. The basic particle detection and identification techniques used in modern high energy physics experiments are discussed.

1 Introduction

These lectures are directed towards an audience seeking a basic introduction to experimental high energy physics. The task of covering this field in its entirety is an impossible one. To circumvent this difficulty, I have focused on an overview of accelerator facilities, and on a discussion of the principles and techniques of particle detection. I will therefore be discussing little “real” physics.

I have tried to be as general as possible, but space will limit me to discussing what I view as being the most salient issues. In addition, most of the discussion will be centered on experimental techniques at colliding beam facilities, as much of the current experimental work is being performed using such machines.

There is a great deal of literature on the subjects I will be discussing. In particular, “Experimental Techniques in High Energy Physics” by T. Ferbel [1] is a valuable reference for many of the discussions on detector technology.

2 Accelerator Facilities

A particle physics experimentalist is faced with the task of first bringing the necessary initial state particles together at the appropriate center of mass energy \sqrt{s}, and then identifying the specific final state one wishes to study. This all has to take place at a rate sufficient to make the desired measurement in a reasonable amount of time.

2.1 Fixed Target Machines

Historically, experimental particle physics relied heavily on fixed-target facilities such as

• the Brookhaven AGS (30 GeV protons),

• the Argonne ZGS (10 GeV protons),

• the CERN PS and SPS (30 and 130 GeV protons),

• the SLAC linac (30 GeV electrons),

• the Fermilab synchotron (400 GeV protons), and

• the Serpukhov proton synchotron.

These machines were almost all constructed after the invention of “strong-focusing,” which allows one to build rather large accelerators using strings of alternating focusing and defocusing magnetic lens. They have been used as sources of intense beams of high-energy protons and electrons, which are directed onto a target. A detector, located near or around the target measures the properties of some or all of the final state constituents, depending on the measurement being performed.

These facilities also provide “secondary” beams consisting of more exotic particles such as mesons (π’s and K’s), baryons (\overline{p}’s and hyperons like the Σ^{±}) and leptons (μ’s and neutrinos). The primary beam is directed onto a target, thereby producing a variety of elementary particles. A particle separator placed behind this target selects and collimates the desired secondary particles, which are then transported to an experiment and directed into a target.

Such fixed target facilities have several attractions: they can deliver very intense primary beams (10^{12} protons per second is a typical rate for the Fermilab Tevatron) and they provide the only means of making exotic particle beams. The two fundamental figures of merit for such machines are their maximum beam energy and the intensity of the beam. The rate R of a process with cross section σ in a target with particle density ρ_{t} and length l is

R = σ(F A)ρ_{t}l,  (1)

where F is the flux of beam particles and A is the cross sectional area of the beam. The quantity F A, the number of beam particles/second, is one of the crucial parameters in an experiment. For example, if we have a Cu target with ρ_{t} ∼ 5×10^{24} protons/cm^{3} and length 1 m, and F_{i}A ∼ 10^{10} particles/s, then

R = 5 × 10^{36}σ (σ in cm^{2})
= 5000 σ (σ in nb).

Although the only stable targets are nucleons, one can study more than just beam-nucleon interactions in such an environment. For example, one can study K − π elastic scattering through the process

K^{−}p → K^{−}π^{+}n.  (2)

This is because the charge-exchange production process is empirically known to be governed primarily by π-exchange in the t-channel. One first studies the behaviour of the K^{−}π^{+} system as a function of K^{−}π^{+} mass and the four-momentum transfer t between the incoming K^{−} and proton. This behaviour is then extrapolated back to the unphysical region where t = −m_{π}^{2} to extract the behaviour of the process K^{−}π^{+} → K^{−}π^{+}. A whole generation of spectroscopists performed such types of experiments, which have provided us with some of the richest data on light quark spectroscopy [2].

Fixed target physics does have limitations, with the most severe being that the center of mass energy \sqrt{s} is proportional to \sqrt{E_{beam}}, an unfortunately slow scaling behaviour. In addition, one is always performing an experiment involving a specific probe and a nuclear target. This implies that strong interaction effects enter into any description of the scattering process, making theoretical comparisons with data more problematic. Many of these problems were overcome with the advent of electron storage rings.

2.2 e^{+}e^{−} Storage Rings

The development of electron storage rings in the late 1960’s and early 1970’s provided a new way of studying particle interactions. For the first time, we could study e^{+}e^{−} interactions in as much detail as we wished. Many diagrams contribute to e^{+}e^{−} scattering but the most interesting involve the s-channel production of a virtual photon (γ), with the subsequent coupling of the γ to a fermion-antifermion pair. This provides us with a very clean, J^{P C} = 1^{−−} initial state, avoiding any complications from the strong interaction. These machines also hold out the hope for even higher \sqrt{s} in these collisions, as \sqrt{s} scales linearly with the beam energy. The beam energy, on the other hand, is limited by the RF power required to overcome the electrons’ energy loss via bremsstrahlung, which is proportional to γ^{4} (γ is the Lorentz factor for the accelerated electron). Thus the size of these machines has to increase dramatically as\sqrt{s} increases.

2.2.1 The Early Colliders

The SPEAR ring, built at SLAC and commissioned in 1971, produced the first significant results with the discovery of the charmonium resonances (which were simultaneously being observed in μμ final states in a fixed-target experiment at Brookhaven) [3]. This ring was filled with one bunch of electrons and one bunch of positrons from the SLAC linac, providing two interaction regions in the ring. The maximum \sqrt{s} of this collider was 6 GeV but it ran primarily at one of the J/Ψ resonance peaks.

The rate of events at SPEAR was low enough in any one specific channel that a new experimental philosophy and detector was required. It now become more efficient to operate a general purpose detector that could simultaneously study as many final states as possible. Even then, data rates were relatively low and a typical detector would take data for one or more years.

The two figures of merit for an e^{+}e^{−} collider are the maximum\sqrt{s} (to allow exploration of the energy frontier) and the luminosity of the machine, L. For example, suppose we have two bunches of particles and anti-particles with N_{1} and N_{2} particles in each bunch crossing through each other. Let d_{x} and d_{y} be the lateral dimensions of the bunch (actually the width of the Gaussian profile) and let ν be the crossing frequency of the bunches. Then the rate of a process with cross section σ is

R = σ (\frac{νN_{1}N_{2}}{4πd_{x}d_{y}} )
= σL,

where L is the luminosity of the machine in units of cm^{−2}s^{−1}. For example, at SPEAR where L could be ∼ 5×10^{30} cm^{−2}s^{−1}, the point cross section (e^{+}e^{−} → μ^{+}μ^{−}) is ∼ 10 nb, corresponding to a rate of

R = 10 nb × 5 × 10^{30} cm^{−2}s^{−1}
= 0.05 Hz.

SPEAR was initially instrumented with the Mark I detector that codiscovered charm. That detector was followed by the Mark II, a general-purpose detector designed to study charged leptons and photons resulting from the decay of charmonium states. A more specialized detector known as the Crystal Ball was subsequently installed in the other interaction region. It was designed to detect the γ’s resulting from the radiative decay of charmonium states.

Several other storage machines came online during the 1970’s. SPEAR was followed by DORIS, a similar storage ring located at the DESY facility in Hamburg, Germany. The PETRA storage ring at DESY began operation in 1978, providing collisions with \sqrt{s} as large as 46 GeV at luminosities of ∼ 10 × 10^{30} cm^{−2}s^{−1}. The ring accelerated a pair of electron and a pair of positron bunches, providing four interaction regions that were instrumented with (i) the PLUTO detector, which was moved from DORIS, and which was later replaced by CELLO, (ii) the JADE detector, (iii) the MARK J detector, and (iv) the TASSO detector. Several of these were specialized to investigate particular physics topics (e.g. two photon final states). The physics program at PETRA continued till 1986, and it has been reviewed by Marshall [4].

The PEP storage ring at SLAC was commissioned in 1979 as a high-luminosity e^{+}e^{−} collider with \sqrt{s} ∼ 30 GeV and L∼ 50×10^{30} cm^{−2}s^{−1}. The ring collided three bunches of electrons on three bunches of positrons, which provided for six interaction regions. These regions were instrumented with (i) the Mark II detector from SPEAR, (ii) the DELCO detector, (iii) the High Resolution Spectrometer (HRS), (iv) the MAC (Magnetic Calorimeter) detector, (v) the TPC detector (Time Projection Chamber), and (vi) the ASP experiment (ASP is an acronym for Anomolous Single Photon). Most of these experiments used general-purpose detectors capable of studying a broad range of physics processes. These were all prolific experiments, with several of them are still analysing data.

The most recent general-purpose e^{+}e^{−} colliders have been TRISTAN, which produces e^{+}e^{−} collisions with a maximum \sqrt{s} of ∼ 60 GeV and a maximum luminosity of ∼ 10 × 10^{30} cm^{−2}s^{−1}, and BEPC, a high-luminosity collider optimized to be a charmonium factory. The TRISTAN facility has four interaction regions that are instrumented with (i) the AMY detector, (ii) the VENUS detector, (iii) the TOPAZ detector, and (iv) the SHIP detector. The first three detectors have been extending the studies performed at PEP and PETRA, while SHIP is a specialized device designed to search for heavily ionizing particles (such as monopoles).

BEPC, located in Beijing, is an e^{+}e^{−} storage facility designed for charmonium studies, and is the first such accelerator project in China. It provides collisions up to \sqrt{s} ∼ 6 GeV at a design luminosity of ∼ 10 × 10^{30} cm^{−2}s^{−1}, well in excess of the maximum luminosity of the SPEAR ring [5].

2.2.2 e^{+}e^{−} Colliders for B Physics

Motivated by the discovery of the Υ in 1977 [7], the CESR storage ring at Cornell and the DORIS storage ring at DESY were upgraded to produce e^{+}e^{−} collisions at \sqrt{s} ∼ 10 GeV and have since been dedicated to the study of bottom hadrons.

The CESR ring can operate at a \sqrt{s} of ∼ 12 GeV with a maximum luminosity of ∼ 90 × 10^{30} cm^{−2}s^{−1}. The facility has two interaction regions, one being instrumented by CLEO, a general-purpose magnetic spectrometer, and the other being instrumented with CUSB, a γ detector designed to study radiative Υ decays. This ring is still operational with an upgraded version of the CLEO detector.

The DORIS storage ring at DESY began life as a low-energy e^{+}e^{−} storage ring in the early 1970’s. It was upgraded a decade later to produce collisions at a \sqrt{s} of ∼ 11 GeV with a maximum luminosity of ∼ 30 × 10^{30} cm^{−2}s^{−1}. The ring has two interaction regions, one instrumented by ARGUS, a general-purpose detector, and the other by the Crystal Ball, the γ detector initially installed at SPEAR. The ring is still operational, although it is overshadowed by recent increases in the CESR luminosity and the commissioning of HERA.

There are now several groups studying the possibility of building a very highluminosity asymmetric e^{+}e^{−} collider that would be devoted to high-rate B physics. Such a B factory could be built as an enhancement to the CESR or PEP facilities in the next decade [6].

2.2.3 Z^{∘} Factories

The latest generation of electron colliders have been built to produce e^{+}e^{−} collisions with \sqrt{s} equal to the mass of the Z^{∘} boson. These are

• the SLC, a linear collider that produces e^{+}e^{−} collisions up to \sqrt{s} ∼ 100 GeV by colliding very intense bunches of electrons and positrons that have been accelerated in the SLAC linac, and

• LEP (Large Electron Project), which in its first phase is producing collisions at \sqrt{s} up to 100 GeV and a luminosity of ∼ 3 × 10^{30} cm^{−2}s^{−1}.

SLC is the first generation of machines using the linear collider concept (see Fig. 1). Large bunches of electrons and positrons are accelerated in the SLAC linear accelerator. The e^{+} and e^{−} bunches are transported through separate “arcs” that come together at the final focus region. After the collision, the bunches are extracted and directed into a beam dump. This scheme avoids the cost of accelerating the electrons and positrons in a synchotron, where the power radiated by bremsstrahlung radiaton is much higher. However, one must now accelerate large bunches of electrons and positrons and focus them into a small beam spot in order to obtain a reasonable luminosity. At the SLC, the transverse size of the bunches are only a few microns, which is achieved by paying careful attention to the beam optics in the linac and collider.

SLC had a design luminosity of ∼ 1 × 10^{30} cm^{−2}s^{−1}. Unfortunately, it has experienced various technical problems and has not been able to attain this luminosity, due in part to persistent alignment problems, but it has the unique feature of being able to produce polarized beams. The machine has one interaction region, which until recently has accomodated the Mark II detector from PEP. An entirely new detector called SLD has been constructed and will continue the physics program at the SLC.

LEP is a conventional e^{+}e^{−} storage ring with a circumference of 28 km. It can store beams with energies in excess of 50 GeV in order to produce Z^{∘}’s, and a subsequent phase (LEP II) of the project will see the beam energy doubled in order to produce W^{+}W^{−} events. Phase I of the LEP collider was completed in fall of 1989, along with four general-purpose detectors, known as ALEPH, DELPHI, L3 and OPAL. Each detector has been optimized to study Z^{∘} decays, but they employ different philosophies and technology. For example, the OPAL (Omni-Purpose Apparatus for LEP) detector is perhaps most conventional in design, and has been viewed as the “conservative” detector, while the DELPHI detector incorporates several new technologies that have the potential for providing better performance, but are also unproven and pose certain risks. Together, these collaborations have collectively recorded 10^{6} Z^{∘} decays by fall 1990, and are expected to continue their studies over the next several years.

LEP II, which will have stored beams with twice the energy of LEP I, is scheduled to be completed by 1994, at which time the collaborations will begin a detailed study of W^{+}W^{−} production.

Figure 1: A schematic of the SLAC linear collider and the Large Electron Project at CERN. The two figures differ in scale by a factor of 5.

2.3 Hadron Colliders

Although e^{+}e^{−} colliders produce very clean initial states, they cannot compete on the energy frontier with hadron colliders. Whereas the \sqrt{s} of an e^{+}e^{−} machine is severely limited by the rapid rise in beam energy loss due to synchotron radiation, this effect is negligible at a hadron collider (because of the difference in mass of the accelerated particle). The \sqrt{s} at a hadron collider is limited by the strengths of the magnetic fields required to contain the hadron beams (alternatively, they are limited by the radius of the machine). The price paid for this increase in available \sqrt{s} is that one no longer is colliding elementary fermions, but two systems that consist of several strongly-interacting partons.

A consequence of this is that a high energy collision between two of the partons is accompanied by the “underlying event” that results from the disassociation of the hadrons during the collision process. The experience at hadron colliders in the past decade have shown that one can take the effects of the underlying event into account, but the resulting physics analyses are nevertheless complicated by its presence.

Another consequence is that the interaction cross section at a hadon collider is dominated by “soft” collisions, so that the more interesting high-P_{T} events occur at rates that are many orders of magnitude smaller. For example, the total cross section at a hadron collider is of order 50 mb, while a typical electroweak production cross section (such as W or Z^{∘} production) is on the order of 10 nb, constituting only 10^{−6} of all events. To study these relatively rare interactions, an experimentalist must actively reject these backgrounds by using a sophisticated detector trigger.

2.3.1 The CERN ISR and Sp\overline{p}S

The idea of a hadron collider was first pursued with the construction of the CERN ISR (Intersecting Storage Ring), a proton-proton collider with \sqrt{s} ∼ 50 GeV. In retrospect, most of the experiments at this machine ended up studying the relatively murky physics processes underlying the “softer” hadron-hadron collisions. The relatively low \sqrt{s} available for high-P_{T} collisions made them quite rare compared with the rate of “minimum-bias” interactions resulting from the disassociation of the hadrons. A major step in overcoming these problems was taken with the development of the Sp\overline{p}S, a proton-antiproton collider constructed in the tunnel originally used to house the SPS proton synchotron.

The primary obstacle to the development of a \overline{p} p collider was the difficulty of generating and accelerating a large bunch of anti-protons. This was solved by the technique of ”stochastic cooling.” Small bunches of \overline{p}’s are placed in a storage ring (the “accumulator”) and collected for several hours. The average position of the \overline{p} bunch at one point in the ring is used to apply a small correction to the bunch orbit on the other side of the ring when the \overline{p} bunch passes. This correction reduces the phase space of the \overline{p} bunch. When enough \overline{p}’s have been accumulated and their bunch reduced to the appropriate size, they are extracted from the accumulator and injected into the proton storage ring and accelerated to collision energy.

The CERN Sp\overline{p}S collider was the first machine to employ this technique. The collider was able to produce collisions with a \sqrt{s} of 630 GeV at an eventual luminosity of ∼ 3 × 10^{30} cm^{−2}s^{−1} in two interaction regions. One region was instrumented with the UA1 detector, a general purpose device consisting of a large charged particle tracking volume immersed in a dipole field and almost completely surrounded by a calorimeter [8]. The other region was instrumented with the UA2 detector, which consisted of a non-magnetic tracking system partially contained within a calorimeter [9]. Perhaps the most revolutionary aspect of the UA1 experiment was the focus on having almost complete (in the jargon, “hermetic”) calorimetry coverage in order to be able to detect neutrinos by the momentum imbalance observed in the calorimeter. This aspect gave the experiment the necessary tools to disover the W boson, and subsequently its neutral current partner the Z^{∘} [10].

The experimental program at the Sp\overline{p}S is now almost complete. The UA2 detector will be completing a final data run during winter, 1991, and no future runs are currently planned.

Process  Rate (nb)
Minimum Bias  50,000,000
Inclusive b quark production  ∼ 30, 000
Inclusive e^{±} (P_{T} > 12 GeV/c)  10
W^{±} → e^{±}ν_{e}  2
Z^{∘}→ e^{+}e^{−}  0.2

Table 1: Cross sections for several processes at the Fermilab Tevatron collider.

2.3.2 The Second Generation of Hadron Colliders

By the time the Sp\overline{p}S collider was nearing completion, the Isabelle proton collider at Brookhaven National Laboratory was under construction in the US. It was designed to collide protons together with \sqrt{s} = 300 GeV, but the development of the superconducting dipole magnets fell so far behind schedule that the project was cancelled in the mid-1980’s.

By this time, construction of the Fermilab Tevatron Collider was well underway. This device was designed around the Fermilab synchotron and had the ability to produce collisions with \sqrt{s} = 1800 GeV. The design luminosity of ∼ 1 × 10^{30} cm^{−2}s^{−1} was somewhat lower than that achieved at the Sp\overline{p}S, but the increased production cross sections for high-P_{T} processes more than compensated for the luminosity differences.

The collider has six interactions regions, with two being instrumented with large, general-purpose detectors. One of them is CDF, which had its first major physics run in 1988 [11]. It consists of a cylindrical tracking volume immersed in a solenoidal magnetic field and almost completely surrounded by calorimetry, except for 3^{∘} holes around the beamline. The other detector, D0, takes its name from the location of its interaction region [12]. It is also a general purpose detector, with the emphasis being placed on good calorimetry. In order to avoid compromising the hermeticity of the calorimeter, D0 does not contain a magnet for momentum analysis. The P_{T} of muons are measured using a set of toroidal magnets located outside the calorimeter. The CDF detector is currently completing the analysis of a successful data run performed in 1988-89, and both detectors and the Tevatron collider are being prepared for the next run that is currently scheduled to start in fall 1991.

The rate of interactions involving electroweak processes at a hadron machine are higher than at a comparable e^{+}e^{−} collider. However, they are mixed together with a very large interaction rate from “minimum bias” processes and from hard QCD interactions. For example, I have listed in Tab. 1 the approximate Tevatron cross sections for a variety of physics processes. The challenge to the experimentalists is to separate what one is calling interesting physics from the uninteresting rates.

Both UA1, UA2 and CDF have shown that this is possible. As the energy of the collider increases, the problems in some sense become easier as the relative rate of “interesting” physics grows with \sqrt{s}.

2.4 ep Colliders

High-energy ep collisions are a unique way of studying phenomena such as proton structure, the electroweak interaction, and the possible production of new particles (leptoquarks, supersymmetry, etc.). The earliest studies were done with high energy electrons interacting on a fixed nuclear target at SLAC. The HERA facility at DESY will be the first true electron-proton colliding beam machine. It is designed to collide 30 GeV e^{−}’s with 820 GeV protons with a design luminosity of 15 × 10^{30}cm^{−2}s^{−1}. HERA has four interaction regions, with two being instrumented with the ZEUS and H1 detectors [13]. Both of these are state-of-the-art devices with particular emphasis being placed on precision calorimetry. This focus comes from the desire to make precision measurements of the charge current interaction that produces final states consisting of high energy jets and neutrinos.

2.5 Summary of Existing Colliders

I summarize in Tab. 2 the parameters of existing colliders. One can see reflected in this table the quest for colliders with both higher energies and higher luminosities.

Looking somewhat into the future, the next generation of machines will be the new hadron colliders that will take a giant step forward in both center of mass energy and luminosity. The SSC, being constructed in Texas, will collide protons together at \sqrt{s} of 40 TeV with a luminosity of 10^{33} cm^{−2}s^{−1}. The LHC, a proton collider that is under consideration at CERN, will yield collisions with \sqrt{s} of 17 TeV at a luminosity of 10^{34} cm^{−2}s^{−1}. Both of these machines will stretch the capabilities of the physicists responsible for designing the accelerator and the detectors.

3 An Overview of Particle Detection Techniques

The task in most particle experiments is to detect and make the needed measurements of the interactions that one is interested in. In most cases, we identify the events by requiring that they have some number of “objects” and that they satisfy certain conditions (such as kinematic cuts). This means that we would like our detector to identify in each interaction all the leptons (e^{±}’s, μ^{±}’s and τ’s as well as their neutrinos) and quarks (or hadrons that result from the fragmentation of the quark). One would also like to identify any gluons, photons and W and Z^{∘} bosons that are also produced.

In practice, these requirements are met by identifying the constituents in the interactions by the different ways in which they interact in various media. We can identify electrons using a combination of

Facility  Beams  \sqrt{s} (GeV)  L(10^{30} cm^{−2}s^{−1})
SPEAR  e^{+}e^{−}  6  5
BEPC  e^{+}e^{−}  6  10
CESR  e^{+}e^{−}  12  90
DORIS  e^{+}e^{−}  11  30
PEP  e^{+}e^{−}  30  50
TRISTAN  e^{+}e^{−}  60  10
SLC  e^{+}e^{−}  100  1
LEP  e^{+}e^{−}  120  10
S\overline{p} pS  \overline{p} p  630  3
Tevatron  \overline{p} p  1800  2
HERA  ep  220  15

Table 2: A summary of the existing particle accelerators and colliders.

• a measurement of the momentum of the electron candidate with a charged particle tracking detector,

• a measurement of the Lorentz contraction factor γ using a transition radiation detector (TRD), the amount of ionization deposited by the electron or the angle of its Cerenkov radiation, or

• a measurement of the transverse and longitudinal profiles of the shower resulting from the electron interacting in an absorber such as lead or uranium.

Muon candidates are usually identified by taking advantage of the fact that a muon interacts with matter primarily through ionization energy loss and therefore can penetrate through a large amount of material (i.e. has a long range). One therefore utilizes a detector that measures the range of the charged particle. Typical implementations employ several meters of iron absorber with charged particle detectors interleaved with the absorber material. Candidate μ’s are those charged particles that manage to pass through the absorber without interacting.

Tau leptons are more difficult to identify as they decay into several particle final states, one of which is a ν_{τ} that can only be indirectly detected. In many detectors, the charged daughters from the τ decay can be reconstructed, but the resulting candidate sample often has significant background contributions from other types of events (e.g., light quark jets in a collider experiment). Secondary vertex detectors are commonly employed to measure the vertex position of the candidate τ decay and thereby reduce the background rates to acceptable levels.

Neutrinos have traditionally been detected indirectly using missing energy techniques. These rely on the detector being able to measure the “energy flow”^{∗} associated with all other particles (charged leptons and charged and neutral hadrons) in the interaction. Such energy flow measurements are normally performed with a finely segmented, hermetic calorimeter (i.e. one that subtends as much of the solid angle around the interaction as possible) in association with a muon detector to measure the momentum of the muons whose energies do not register in the calorimeter system.

Quarks produced with low energies (less than order 5 GeV) manifest themselves as one or a few individual hadrons. More energetic quarks result in well-defined “jets” of charged and neutral particles, with the energy and direction of the jet reflecting the momentum of the initial state quark. These jets are most often detected and measured using a calorimeter, although some experiments rely on the incomplete information available from a charged particle tracking system. The fragmentation process generates a complex final state that usually obscures the flavour of the parent quark. In the case of charm (c) and bottom (b) quark jets, it is often possible to perform some form of “flavour” tagging. The lifetimes of these quarks are long enough that the decay vertex of the heavy quark can be identified using a charged particle detector with sufficient spatial resolution [14].

It is often necessary to identify the species of one or more of the particles in the final state (for example when one is measuring the rate of various exclusive decay modes of heavy quarks). The classic method involves measuring the particle’s mass by determining its momentum and its velocity. The latter is measured using either (i) a time-of-flight (TOF) measurement, (ii) the rate of ionization energy loss (dE/dx) that can be related to the particle’s velocity, or (iii) the Cerenkov or transition radiation emitted by the particle.

We can see that the tools necessary to identify and measure the final states resulting from a high-energy interaction are

• charged particle detectors, providing the direction (and in most cases the momentum) of each charged hadron and lepton,

• vertex detectors that can measure with high precision the position of the particles near the interaction point,

• finely segmented calorimeters that measure the energy and direction of jets,

• hermetic calorimeters that indirectly detect neutrinos using the missing energy technique, and

• devices that identify particles, such as electromagnetic shower counters, muon detectors, and TOF systems.

We will discuss in more detail the principles involved in these detection techniques and outline how they are implemented in modern day particle detectors.

∗By energy flow, we mean the direction and energy of the particles produced in the interaction.

Figure 2: The avalanche processs that takes place in a proportional wire chamber. The primary ionization liberated by a particle traversing the gas volume drifts to the wire anode and “avalanches,” generating a detectable voltage signal. The positive ions move slowly away from the anode.

4 Charged Particle Detectors

Most modern-day charged particle detectors are electronic devices that have fast response times (< ∼ 1 μs), rate capability > 1 MHz, and that provide information in a form that is easy to digitize and readout. Most of these devices detect the primary ionization deposited by the charged particle in a medium and have their roots in the work done by Charpak et al. on proportional wire counters [15].

To understand these devices, consider the case of a cylindrical tube of radius b filled with a gas with a thin wire (radius a) running down the axis. A positive potential is placed on the wire so that the outer wall forms the cathode. A charged particle creates a number of electron-ion pairs as it traverses the gas volume, and the electrons drift with increasing velocity towards the anode because of the increasing electric field gradient. Within a few microns of the anode, the kinetic energy of the electrons is large enough that collisions with gas molecules create more electron-ion pairs. The original signal is thus amplified by a multiplicative gain that typically could be 10^{4} to 10^{5}. This is shown schematically in Fig. 2.

The voltage signal v^{−} generated by the electrons is given by

v^{−} = −\frac{Q}{2πϵ_{0}l} ln (\frac{a + λ}{a})  (3)

and the signal generated by the positive ion cloud drifting away from the anode, v^{+}, is given by

v^{+} = −\frac{Q}{2πϵ_{0}l} ln (\frac{b}{a + λ}) ,  (4)

where λ is the distance the avalanche electrons drift and l is the length of the wire. The latter signal is much larger since the ions drift over a further distance. The total signal is given by

v^{+} + v^{−} = \frac{Q}{2πϵ_{0}l} ln (\frac{b}{a}) = \frac{Q}{lC} ,  (5)

Figure 3: A schematic of a multi-wire proportional counter showing the anode sense wire plane and the two cathode planes.

where C is the capacitance/unit length of the tube and Q is the total charge. The dielectric constant ϵ_{0} is ∼ 8.85 pF/m for typical gaseous media. Although the signal from the electrons is much smaller, it is also much faster. Thus, most devices are designed to be sensitive to only the fast component of the total signal.

One of the features of this system is that it can be operated in several modes, depending on the voltage between the anode wire and cathode. In the “proportional” region, the observed signal is proportional to the primary ionization and the avalanche remains a local effect. Charpak et al. realized that a large detector could be conveniently manufactured by the use of many anode wires arranged in a plane with typical wire spacings on the order of 1-2 mm, as shown in Fig. 3. Such devices, which are known as multi-wire proportional chambers (MWPC), have become one of the most popular large-scale electronic detectors. They are ideal for applications requiring precision particle detection over large areas. The resulting anode signals can be detected and read out within ∼ 50 ns, with the detailed performance depending largely on the choices one makes for electronics and signal processing. They also have good rate capability (> 1 MHz) with high efficiency over a large instrumented area.

The choice of gas mixture for these chambers has received a great deal of attention. One usually requires a gas with large ion mobility in order to obtain the best rate capability and response time, but this has to tempered with the need to include a “quenching” gas that prevents the avalanches from propogating along the wire. A typical gas mixture consists of a noble gas (usually Ar) that provides a large multiplicative signal gain with high ion mobility, a quencher such as CH_{4} that absorbs the photons generated by the recombination of excited ions at the cathode before they generate photoelectrons, and trace amounts of some form of alcohol to prevent the accumulation of polymers on the cathode that otherwise would degrade the lifetime of the chamber.

Chambers in which the cathode planes are segmented into strips or pads are also quite common. The induced charges on the cathode can be measured and used to determine the position of the avalanche along the anode when the strips are aligned at an angle to the anode wires. However, MWPC’s have several limitations. The size of the chambers are limited by the electrostatic instabilities of the large wire

Figure 4: A schematic drawing of a conventional drift chamber cell.

planes help at high voltage. Practical chambers cannot be larger than ∼0.5-1.0 m without requiring additional support structures that compromise the efficiency and uniformity of the chambers. They require large numbers of readout channels for large scale applications. Finally, they are susceptible to aging effects after long exposures to charged particles and other radiation. Anode wires begin to show significant performance degradation when they accumulate more than ∼ 1 C/cm of total charge over their lifetime.

4.1 Drift Chambers

The combination of a proportional counter, a long drift region for the electrons released by the ionizing particle, and a drift time measurement for the electrons can be used to measure the position of the charged particle. In such “drift chambers,” an electric field in the drift region is made as uniform as possible so that the drift time is proportional to the distance the electrons drift to reach the anode wire. This is shown conceptually in Fig. 4.

Typical electron drift speeds of ∼ 40 μ/ns imply that an accuracy of a few nanoseconds in measuring the time of arrival yields position resolutions of order 100 μ. To attain this accuracy, the time-to-distance relationship in the drift region must be well understood (this is usually only approximately linear). One also must have some means of resolving the two-fold ambiguity in the position of each particle coordinate since one a priori does not know which side of the wire the particle passed. This ambiguity is usually resolved by using hit information in several nearby wires to define a track segment, which can be done uniquely provided that the nearby wires are not radially aligned (for example, the Mark II drift chamber built for the SLC uses staggered wire positions, while the CDF drift chamber uses tilted wire cells). Original drift chamber systems were planar devices with drift cells of order 5 cm. Drift chambers present a considerable savings in instrumentation cost compared to MWPC’s with comparable resolution since the drift region can be large compared with the MWPC wire spacing.

With the advent of storage rings, drift chambers constructed in a solenoidal geometry with anode wires coaxial with the solenoid have become ubiquitous. This geometry raises several complications to the design. The B field is now perpendicular to the E field so that the drift electrons experience an E × B Lorentz force that must be taken into account. A position measurement along the direction of the anode wire requires the use of an additional technology. In some cases, charge-

Figure 5: A schematic drawing of a time projection chamber. Electrons drift to the closest end plate of the device and are detected there using a MWPC. The time of arrival provides a measurement of the charge particle’s axial position. The other two coordinate positions are inferred from the segmentation of the end plate MWPC.

division readout is employed, in which the hit signal is read out on both ends of the wire and the amount of charge detected at each end is used to determine the relative position of the hit along the wire. Another technique involves the use of sets of “stereo” wires that are strung at a small angle (∼ 4^{∘} is typical) relative to the axial sense wires. In all of these schemes, the position resolution along the wire tends to be significantly worse than the azimuthal position resolution.

The size of drift chamber systems have steadily increased, with typical systems in use today consisting of a total of ∼ 5 × 10^{4} wires and 10^{4} sense wires. Such systems are matched to the dense particle environments typical in high-energy collisions. One of the consequences of this evolution is that the computer resources required to process the data from these chambers is prodigious. For example, it takes approximately 10^{8} computer instructions to execute the CDF tracking algorithm on a typical interaction at the Tevatron collider.

4.2 Time Projection Chambers

A specialized form of drift chamber known as the Time Projection Chamber (TPC) was developed in the late 1970’s, with the first full implementation being built for the TPC detector at PEP. Shown in Fig. 5, such a device consists of a cylindrical drift volume with the electric field oriented along the axis of the cylinder. Electrons resulting from the ionization caused by a charged track drift over a large distance (of order 1 m) to one end of the chamber.

The drift electrons are detected using a MWPC with an active area that subtends the entire endcap of the TPC. The time of arrival of the signal provides an accurate measurement of the z position of the particle. In most applications, the MWPC cathode is segmented into small pads. The position of the pad provides a measure of the radial and azimuthal coordinate of the particle. In many TPC’s, the amount of induced charge on the cathode pads is used to provide a measure of the particle’s ionization, which can be used to identify the particle type (see Sec. 8.4). Position resolutions of order 200-300 μ have been achieved [16].

The long drift is not well suited for high-rate experiments, but is well-matched with the low duty cycle required at current e^{+}e^{−} colliders. For example, the Aleph detector at LEP employs a TPC chamber to detect charged particles produced in the central region of the detector. By using shorter drift regions, the good pattern resolving ability of these chambers can still be used in a high rate environment. UA1 uses a TPC consisting of 10^{4} wires and a 20 cm drift region in their central detector, which is located inside a dipole magnetic field. CDF uses 8 small (22 cm radii) TPC modules, each with a drift of 20 cm for charged particle tracking close to the interaction region.

4.3 Vertex Detectors

With the discovery of the c quark, τ lepton and b quark, that decay weakly and have relatively long lifetimes, there has been a great deal of interest in detectors that can seperate the decay vertex of these particles from their point of production. The cτ of these particles is of order 100 to 500 μ, so that charged particle detectors with resolutions better than 100 μ are required.

These vertex detectors must not only be capable of precision charged particle position measurement, they must also have good two-track separation in order to be able to resolve tracks at short distances (< 100 μ). There are at least three different technologies currently being used for this purpose: (i) high resolution drift chambers and MWPC’s, (ii) Si strip detectors and Si diode detectors, and (iii) pixel detectors (CCD’s and Si pixel systems).

4.3.1 High Precision Drift Chambers

The resolution of a drift chamber system is limited by the longitudinal and transverse diffusion of the electrons as they drift to the anode, fluctuations in the time-to-distance relationship due to such effects as inhomogenous drift fields, and irregularities in mechanical structure and wire localization. One can reduce the contribution from diffusion by going to a pressurized system or by using exotic gases that have low diffusion coefficients. A higher pressure gas also yields an increase in the primary ionization yield, which reduces the fluctuations arising from the variations in the size of ionization signal. However, one is still left with second-order effects (such as δ-ray emission) that tend to create non-Gaussian resolution functions for these devices.

The ARGUS collaboration at DORIS has recently implemented this type of vertex detector for measurements of b quark lifetimes. They have demonstrated position resolutions better than ∼ 50 microns with this device [17].

Figure 6: The resolution of a cathode strip system. Each peak corresponds to the location of an anode.

4.3.2 High Resolution MWPC’s

The anode spacing d is the fundamental limitation on the position resolution of a proportional wire system (the position uncertainty is ∼ d/\sqrt{12}). However, the induced charge seen on the cathode can be used to localize the position of the avalanche provided that the cathode segmentation is fine enough and that one measures the size of the induced signal on each cathode pad or strip. In this case, the dominant source of uncertainty comes from the charge measurement—a typical channel-to-channel charge measurement uncertainty of 10% results in a position uncertainty of ∼ 2% of the strip width. An example of the performance of such a system is shown in Fig. 6, where the peak widths reflect the position uncertainty for a MWPC with an 8 mm anode-cathode gap and 3 mm wide cathode strips. The resolution is ∼ 35 μ [18].

However, these devices are limited by the the large number of channels required for even a modest system consisting of only a few planes of readout, and the relatively poor two-track separation (tracks within approximately 2-3 strip widths are difficult to resolve).

4.3.3 Si Strip Detectors

One of the most promising vertex detectors have been developed from Si crystals, taking advantage of the intrinsic properties of the n-p junction formed by enlarging the depletion region^{†} in the crystal by placing a voltage across the top and bottom surfaces, as shown in Fig. 7. A minimum-ionizing particle will deposit ∼ 80 ions/μ in the depletion region of the Si crystal. These charges drift to conducting strips located on the surface of the crystal and generate a detectable voltage signal. For a

†The depletion region is that part of the crystal that is depleted in charge carriers.

Figure 7: A schematic of a silicon micro-strip detector. The device shown has a strip pitch of 20 microns.

Si wafer with 300 μ thickness, 300 Volts across the junction is sufficient to completely deplete the Si, resulting in a signal of ∼25 000 electrons. The inherent noise in the detector comes from fluctuations in the number of available charge carriers, which can be kept to ∼1000 electrons in size. Micro-strip detectors with 50 micron strip pitch have demonstrated position resolutions on the order of 5 μ. This has been achieved by employing “capacitive charge division”, i.e. using the relative size of the signal observed on each strip to interpolate the position of the ionizing particle.

A potential drawback of these detectors is the amount of material they introduce into the tracking environment. A 300 μ thick wafer contributes 0.3% of a radiation length of material to the tracking system, which in itself is normally tolerable. Multi-layer systems, however, present many times this amount of material, which introduces large multiple scattering uncertainties in the charge track positions. In addition, the material may convert a significant number of the photons coming from the interaction, thereby increasing the number of charged particles and highenergy electrons in the detector. Radiation exposure can also be a limiting factor as the crystal damage induced by large exposures (> 10^{5} − 10^{6} Rads) increases the electronic noise in these devices and degrades their performance.

4.3.4 Charge Coupled Devices

The silicon micro-strip detectors only provide coordinate information perpendicular to the strips. Pixel tracking detectors offer the benefit of providing high-precision, three-dimensional coordinate position for charge tracks. Typical systems provide resolutions of ∼10 microns with two-track separations of ∼40 microns. The obvious disadvantage with these technologies is that they require each pixel to be instrumented, increasing the cost of an entire system.

In Fig. 8, I show an example of a charged-coupled device (CCD) that solves the instrumentation problem by adding to the Si detector the necessary circuitry to read out each pixel in a serial fashion. The CCD consists of a grid of pixels

Figure 8: A schematic of a typical charged-coupled device, showing the p-channel stops that define each row of pixels and the circuitry that make up the imaging gates. The pixel sizes are 22μ × 22μ.

formed by p-channel stops imbedded in the substrate, which prevent any lateral charge migration, and a set of imaging gates that divide up each channel into a set of discrete pixels. The imaging gates can be manipulated so that the charges residing in each pixel can be shifted over by one pixel simultaneously.

A typical CCD has a depletion region ∼ 1 μ thick, so that on average approximately 80 electron-hole pairs are liberated by a minimum-ionizing particle. This signal can be detected above the thermal noise in the Si if the detector is operated at low temperatures (Li N^{2} temperatures usually suffice). These devices have ∼ 10^{5} pixels in a single detector, which are read out in serial order by shifting the contents of each row of pixels one pixel over, with the contents of the last row of pixels being loaded into the output registers located at one end of the CCD. The contents of the output registers are then clocked out serially at rates that typically are several MHz. This implies an overall readout speed of ∼70 ms, which is poorly matched to high-rate applications. Thus, their role in particle physics experiments have been confined to low-rate experiments such as the SLD detector at SLAC.

There are many other high-precision charged particle detectors under development. These devices have been reviewed by Damerell [19].

5 Calorimetry

5.1 The Role of a Calorimeter

A calorimeter is a device designed to measure the energy of a particle. In many detectors calorimeters are the primary means by which the energy and direction of jets, electrons and photons are determined. Because of their inherent bulk and mechanical complexity, these devices have also begun to be one of the largest detector costs. There are several different types of calorimeters in use in high energy experiments:

(i) devices optimized to measure electromagnetic energy (EM calorimeters), and (ii) detectors designed for the measurement of hadronic energy (hadronic calorimeters).

In order to understand the differences between these types of devices, it is necessary to understand how high-energy particles interact in a material. The relevant interactions are

• energy loss (dE/dx) from low-energy collisions with nuclei,

• bremsstrahlung radiation given off by relativistic particles (primarily e^{±}’s),

• pair production γ → e^{+}e^{−}, and

• nuclear interactions.

Interacting particles experience many or all of these energy-loss processes, and in showers initiated by a high-energy hadron (what we will refer to as hadronic showers) the interplay between these effects is particularly complex.

It is worth pointing out that calorimeters in current day detectors not only are used to measure the energy and position of showers, but are also used to indirectly measure the momentum of non-interacting particles such as neutrinos or more exotic objects such as supersymmetric particles that do not interact in material. This is done using the missing energy techniques described earlier, and requires both good energy resolution and a hermetic device (i.e. one that subtends as much of the solid angle of the interaction as possible).

In the following sections, I will review our current understanding of the physics relevant to calorimeter detectors and discuss how such devices are realized in practice. This topic has been reviewed more exhaustively by Fabjan and Wigmans [20].

5.2 EM Showers

5.2.1 General Characteristics

The interaction of a photon or electron with a high Z material^{‡} depends strongly on the energy of the particle. The energy of the incident particle is absorbed primarily

‡In this section, Z refers to the atomic number of the nucleus of the material.

Figure 9: The average energy lost by an electron (a) and by a photon (b) as a function of their energy for the different processes.

by ionization energy loss when the e^{±} energy falls below a “critical energy,” ϵ_{c}. Electrons with energies near or above ϵ_{c} lose energy primarily by bremsstrahlung (e^{±} → e^{±}γ) and generate a secondary γ. Photons lose most of their energy by “converting” (γ → e^{+}e^{−}), thereby generating an electron-positron pair. For heavy materials (Z > ∼ 15), the critical energy ϵ_{c} ∼ 550/Z MeV and is defined as

dE = −ϵ_{c}(dx/X_{∘}).  (6)

The average energy loss for both electrons and photons as a function of their energy is shown in Fig. 9 for each of the dominant energy-loss mechanisms.

For energies well above ϵ_{c}, the energy lost traversing a distance Δx is given by

ΔE = −E \frac{Δx}{X_{∘}},  (7)

where X_{∘} is the “radiation length” and is a characteristic of each material. For heavy materials, X_{∘} ∼ 180A/Z^{2} g/cm^{2}, where A is the atomic weight of the material (radiation lengths are often expressed in terms of X_{∘} as defined in Eqn. 7 times the density of the material as this product frequently appears in calculations).

An electron or photon entering a high-Z material quickly develops into a large number of low-energy e^{±}’s and γ’s through a combination of the processes discussed above. The initial energy thus becomes spread over a large number of relatively lowenergy secondaries (< ∼ 1 − 10 MeV) and these deposit their energies through dE/dx in the material. The longitudinal profile of the shower (i.e. the distribution of this deposited energy as a function of the depth in the material) scales with the radiation length X_{∘}, with the maximum energy deposition occuring at a depth of ∼6 X_{∘} in the material. The lateral profile is given by the “Moliere radius” ρ_{M}, which for heavy materials is

ρ_{M} ∼ 7A/Z g/cm^{2}.  (8)

The size scale represented by ρ_{M} results from a combination of the characteristic γ production angle in bremsstrahlung and multiple scattering of the electrons in the medium. In most media, about 90% of the shower energy is contained within a cylinder of radius ρ_{M} of the shower axis. Lead, which is frequently chosen as an absorber material in an EM calorimeter because of its short radiation length, has ρ_{M} ∼ 1 cm and X_{∘} ∼ 0.6 cm.

5.2.2 EM Energy Resolution

Most calorimeters are comprised of an absorber material in which the shower develops and where most of the energy is deposited, and a sensitive material that measures the amount of deposited energy (in some technologies, such as Pb glass detectors, a single material acts as the absorber and sensitive material). Fluctuations in the way the energy is deposited and in the detection of that energy lead to uncertainies in relating the response of the calorimeter to the energy of the shower.

The “intrinsic” resolution of an EM calorimeter is given by the fluctuations in the fraction of energy deposited in the calorimeter. Since almost all of the energy is deposited by dE/dx, the incident energy is proportional to the total path length T of e^{±}’s in the shower. We can estimate this by

T = E/ϵ_{c},  (9)

using the the definition dE/dx= −ϵ_{c}/X_{∘}. In the calorimeter, one can typically only detect energy that is deposited by particles above a certain energy threshold η, which is a characteristic of the sensitive material in the calorimeter. The total “detectable” track length can then be written as

T_{d} = F (η/ϵ_{c})E/ϵ_{c},  (10)

where F (η/ϵ_{c}) is the fraction of ionizing particles above the threshold η. The function F is intrinsic to an EM shower in the absorber—a typical distribution is plotted in Fig. 10.

Figure 10: The fraction of energy in an EM shower carried by electrons with energies above a threshold versus the energy threshold.

The intrinsic calorimeter resolution results from fluctuations in the development of the shower or, equivalently, in the number of detected ionizing particles, which can be estimated as N ∼ E/η. The statistical fluctuations in this are

\frac{σ_{int}}{E} = \frac{σ(N)}{N} ∼ \frac{1}{\sqrt{N}} ∼ \begin{matrix}√ & \overline{η} \\ √ & \overline{E} \end{matrix} .  (11)

For example, a typical Pb glass detector has a cutoff energy of η = 0.7 MeV, resulting in an intrinsic resolution of

\frac{σ_{int}}{E} ∼ \frac{2%}{\sqrt{E}} .  (12)

In addition to this statistical uncertainty in the energy deposition, fluctuations in the fraction of energy that leaks out of the calorimeter (typically through the back, though transverse leakage may also be significant for certain geometries) may increase the uncertainty in the calorimeter energy measurement. Empirically, one finds that an EM calorimeter should be at least 20X_{∘} in depth to ensure at least 98% containment [21].

5.2.3 Sampling Effects

The detection of the deposited energy in a calorimeter can be done in one of two ways. In Pb glass and NaI calorimeters, the energy is detected not in the form of dE/dx loss but by the Cerenkov light created by the electrons as they travel through the refractive material. These types of calorimeters are examples of detectors where the absorber and the active material are the same. In other calorimeters, a fraction of the shower energy is deposited in a sensitive medium that effectively “samples” the total energy of the shower. In such sampling calorimeters, a popular sensitive material is scintillator. Typical applications imbed the scintillator in the absorbing material, by either interleaving plates of absorber with scintillator plates, imbedding scintillating fibres in an absorber matrix, or by interleaving absorber plates with liquid ionization detectors filled with a cryogenic liquid such as liquid Argon or a “warm” liquid such as TMP or TMS.

In sampling EM calorimeters, an important resolution effect arises from “sampling” fluctuations. Consider a calorimeter constructed with an absorber with plate thickness d. The number of particles passing through the active detectors is

N_{x} = \frac{T_{d}}{d} = \frac{F (η/ϵ_{c})E}{ϵ_{c}d} = \frac{F (η/ϵ_{c})E}{ΔE} ,  (13)

where we have defined ΔE ≡ ϵ_{c}d as the energy lost in passing through each plate. The fluctuations in N_{x} will then introduce an additional uncertainty in the detected energy of the form

\frac{σ_{sample}}{E} = \frac{σ(N_{x})}{N_{x}} ∼ \frac{1}{\sqrt{N_{x}}} ∼ \begin{matrix}√ & \overline{ΔE/F (η/ϵ_{c})} \\ √ & \overline{E} \end{matrix}.  (14)

For F = 0.5 and ΔE = 5 MeV, the contribution to the resolution would be

\frac{σ_{sample}}{E} = \frac{10%}{\sqrt{E}}.  (15)

In many EM calorimeters, the sampling fluctuations dominate the energy resolution.

Our simple analysis ignores several other resolution effects that in most systems are relatively small (for example, the total track length in the absorber T is underestimated due to multiple scattering effects, and we have ignored Landau fluctuations in the dE/dx energy loss). An issue that is usually of considerable experimental concern is the variation in the response of individual cells of an EM calorimeter. These can be viewed as adding an additional term to the calorimeter energy resolution. This is related to how such devices are calibrated and will be discussed briefly in Sec. 6.1.

5.3 Hadronic Showers

5.3.1 Features of Hadronic Showers

A high-energy hadron interacting in a material can lose energy in a number of ways, making the entire energy-loss mechanism more difficult to understand. For example, about half the time the first (or primary) interaction will be elastic or quasi-elastic, releasing a small number of fast hadrons and/or leptons, while the rest of the time the primary interaction is fully inelastic, leading to the production of many slower particles. The particles produced in a hadron shower are therefore a melange of different species, ranging from those that deposit energy through electromagnetic interactions (such as e^{±}’s and γ’s) to strongly interacting hadrons to particles that interact only weakly (such as ν’s from K and π decays). The number of particles of each species fluctuates from one shower to the next and this may cause large variations in the calorimeter response to hadron showers with identical energies because the calorimeter may respond differently to each species. This effect adds to the uncertainties in the calorimeter shower measurement that arise from the intrinsic response and sampling fluctuations discussed earlier.

The required thickness of a hadronic calorimeter is determined by the nuclear “absorption length” λ of the absorber, which is derived from the probability of a particle interacting in the material as a function of the particle’s path length. Although the primary interaction can take place via several processes, the interaction length depends only weakly on the type of hadron and its energy. Iron, which is a popular absorber material, has λ ∼ 17 cm.

5.3.2 Compensation in Hadronic Showers

One of the largest variations in calorimeter response arises from differences in the way electromagnetic and hadronic energy is deposited and detected. For example, when the incoming high energy hadron interacts and forms an energetic π^{∘}, the particle decays to 2 photons that form an electromagnetic shower. Since most of this energy is deposited via dE/dx, a sampling calorimeter will have access to all of the incoming energy. If the primary interaction generates a large number of hadrons, some fraction of the hadronic energy will be soaked up by nuclear interactions and will reduce the visible energy in the calorimeter. It is possible to design a calorimeter by a judicious combination of absorber and active material so that the relative response to the EM and hadronically deposited energy is equalized. Such “compensating” calorimeters have been shown to have substantially improved energy resolution [22].

A method to partially overcome this problem was developed by the CDHS collaboration, which has an iron and concrete calorimeter that is intrinsically noncompensating [23]. They realized that the observed longitudinal development of the shower gives some information as to the EM fraction of the deposited energy (since that energy is typically deposited at a shallow depth compared to the hadronic energy). They weighted the energy seen at each depth with an algorithm that deemphasized large positive fluctuations in the observed response. The effect of this is seen in Fig. 11, which shows the energy resolution of the CDHS calorimeter as a function of shower energy with and without the use of this algorithm. The improvement in resolution is clear.

The real cure to the non-compensation problem is to make the calorimeter intrinsically “compensating”, i.e., design it so that e/h = 1.0, where e and h refer to the average response of the calorimeter to electromagnetic and hadronic energy. The first large scale calorimeter to illustrate compensation was a sampling device

Figure 11: The energy response of the CDHS calorimeter as a function of the energy of the incident hadron, as measured using incident particles in a test beam. The open circles show how the resolution degrades with increasing energy when the weighting scheme is not employed. The energy resolution for electrons is shown for comparison.

that employed ^{238}U as an absorber material sandwiched between scintillator plates. This device had an intrinsic resolution of

\frac{σ_{int}}{E} = \frac{22%}{\sqrt{E}},  (16)

where E is the energy of the incident hadron [24]. In this case, the compensation mechanism is due to an enhancement of the effective hadron response due to the presence of hydrogen-rich materials that increase the flux of low-energy baryons in the shower, and nuclear effects occuring at the 1 MeV energy level that “release” energy. Our understanding of the details of these mechanisms are precise enough that we can now develop a design for a compensating calorimeter with almost any absorber desired, although Uranium is still a natural choice because of its density and because it compensates well in the presence of plastic scintillator, which is a popular choice for the sensitive material.

The ZEUS detector, being built at DESY for the study of ep collisions at HERA, utilizes such a calorimeter. It exhibits very good hadronic energy resolution, as shown in Fig. 12 where the electromagnetic and hadronic energy resolution of the detector as a function of the incident hadron energy is plotted [25]. In this experiment, the calorimeter response is crucial to many of the physics studies. For example, the measurement of structure functions over the largest possible range of

Figure 12: The energy resolution of the ZEUS calorimeter as a function of the incident hadron and electron energy.

kinematic variables is possible only if the calorimeter’s jet energy response is well understood over several orders of magnitude in jet energy.

6 Energy and Momentum Calibration

Most measurements require the experimenter to understand not only the resolution of the detector but the absolute energy calibration. This is illustrated by the measurements of the W and Z^{∘} boson masses originally performed by the UA1 and UA2 collaborations. The precision of these measurements was limited by the systematic uncertainty in their calorimeter energy scale, estimated at ∼ 3%. Various techniques are used to determine these absolute energy scales, and we will briefly discuss these below.

6.1 Calorimeters

The standard procedure used to determine a calorimeter’s energy scale is to calibrate the device in a test beam where it is possible to directly establish the relationship between average response and the shower energy. Since the response may vary significantly from one module to the next, this calibration is typically performed for each module or for a significant fraction of the modules.

It is usually necessary to monitor this energy scale in situ in order to verify its stability as a function of time. This monitoring can be done using a variety of techniques, ranging from the use of implanted radioactive sources (or the natural radioactivity in a ^{238}U calorimeter) to the calibration of the detector using known physics processes. At an e^{+}e^{−} collider, Bhabha scattering (e^{+}e^{−} → e^{+}e^{−}) is often used to check both the EM calorimeter energy scale and the momentum scale of the tracking chambers since the incoming beam energies are generally well-known. At a hadron machine, more elaborate techniques must be employed. For example, the CDF collaboration uses its tracking chamber and ∼ 20 000 electron candidates to determine the EM calorimeter energy scale for their Z mass measurement using the absolute calibration of their tracking system from the physics process J/Ψ → μ^{+}μ^{−} (see below). The UA2 collaboration has calibrated each module of their calorimeter in a test beam. However it is difficult to use these techniques to obtain calibrations that are better than ∼ 1% of the detected energy.

6.2 Momentum Analysis

The precision of a momentum measurement depends on the accuracy of the measured trajectory of the charged particle and the B field. In large tracking systems, one often can use “straight-through” tracks (typically μ^{±}’s from cosmic ray background) to align the system precisely. This is done by starting with the measured chamber positions derived from a survey of the device and then improving this alignment using the observed tracks. The B field is usually determined by direct measurement and mapping.

The momentum scale can be verified by reconstructing the masses of known particles. This is illustrated in Fig. 13, which shows the invariant di-muon mass distribution recorded by the CDF detector. One can infer from the peaks masses of 3.097 ± 0.001 GeV/c^{2} and 9.469 ± 0.010 GeV/c^{2} for the J/Ψ and Υ resonances, respectively. Both of these masses are consistent with the world average values of 3.097 GeV/c^{2} and 9.460 GeV/c^{2} [26], and therefore verify the momentum scale of the CDF detector to 0.2%.

7 Triggering and Data Reduction

A crucial aspect of any experiment is the manner in which the detector is triggered, i.e. the criteria used to determine the subset of events that will be recorded and how these criteria are implemented. Triggers have traditionally been implemented using a set of fast signals from the detector and then some relatively simple gating logic to derive a logic signal that specifies whether the interaction should be recorded. However, many modern detectors have much more sophisticated trigger systems because of the stringent performance requirements that must be met.

These requirements are governed primarily by how selective the trigger decision must be. For example, the detectors at the SLC e^{+}e^{−} collider, where there is a beam interaction every 1/120 second, will typically record an event if there is even a modest indication of an interesting collision. This contrasts with the situation at the Tevatron collider, where particle interactions occur at a rate of ∼ 50 kHz (resulting from a detectable cross section of ∼ 50 mb at a luminosity of 10^{30} cm^{−2}s^{−1}) but only ∼ 0.1 Hz of this rate corresponds to “interesting physics.” Although this class of events depends on the detailed goals of the experiment, it is usually defined

Figure 13: The di-muon invariant mass distribution observed by the CDF detector for candidate J/Ψ and Υ events.

Trigger Level  CDF  Aleph
Level 1 decisions  5,000  ∼ 200
Level 2 decisions  10  10
Level 3 decisions  1  1

Table 3: The rates of events passing each level of trigger decision at the CDF and Aleph detectors. The difference in rates reflects the relative ratio of interesting events to overall interactions at each collider.

by requiring that the candidate events have some combination of charged lepton candidates, high-P_{T} jets, and neutrino candidates.

In order to provide this level of event rejection, most trigger systems employ several “levels” of decision-making. At each level, a relatively large fraction of the events are rejected, thus giving the next level more time to examine each event. Typical trigger rates for the CDF detector at the Tevatron collider and the Aleph detector at LEP are listed in Tab. 3.

Figure 14: An event display of a B\overline{B} mixing event observed by the ARGUS collaboration.

8 Particle Identification Techniques

Many experiments require that it be possible to unambiguously identify specific particle species. An illustration of this is provided in Fig. 14, which shows an event recorded by the ARGUS detector in which two B meson decays have been unambiguously reconstructed by identifying most of the charged particles in the interaction [27]. The decays were

B^{∘}\overline{B}^{∘} → B^{∘}B^{∘} → (μ^{+}ν_{μ}K^{+}π^{−}π^{−}) (μ^{+}ν_{μ}K^{+}π^{−}π^{−}) .  (17)

The particle identification was an essential element of the analysis as it allowed the experimenters to conclude that they had observed the decay of two B mesons (and not a B\overline{B} pair); since one assumed that a B\overline{B} meson were initially produced, this is dramatic evidence for the existence of B meson mixing.

Particle identification can be performed by either measuring the particle’s interaction in a material or by determing its mass by measuring the particle’s momentum and velocity. These methods have very different capabilities and limitations, and in particular have discrete ranges of momenta in which they function.

8.1 Electron ID Using Calorimetry

The difference between an EM and a hadronic shower is often used to discriminate electrons and γ’s from hadrons. A typical system employs an absorber with a short radiation length such as lead in which the e^{±}’s and γ’s will shower readily. The transverse and longitudinal profiles of the shower are measured, either by using finely-segmented position detectors imbedded in (or interleaved with) the absorber, or by using a calorimeter that is segmented into a large number of cells or towers. An EM calorimeter is often used to “catch” the electromagnetic showers while a hadronic calorimeter consisting of a material with a short interaction length is used to initiate and contain the hadronic showers. The independent measurement of the energy detected in the EM and hadronic calorimeter provides a measure of the longitudinal shower shape, although finer longitudinal sampling is often employed. The transverse shape of the shower is measured using the amount of energy deposited in each calorimeter tower.

The performance of such devices is characterized by the electron identification efficiency and the hadronic rejection, where the latter is often quoted as the fraction of hadrons that would be misidentified as electrons. The inherent limitation to this technique usually comes from π^{±}’s that undergo charge exchange in the front section of the EM calorimeter:

π^{±}p → π^{∘}N  (18)

Such events, which are referred to as “interacting pion” background, are impossible to distinguish from electrons and tend to limit the hadron rejection of this form of identification technique to ∼ 10^{−3} with electron efficiencies > 80%. This scheme requires the electron to be “isolated,” i.e. not accompanied by additional particles that strike the calorimeter in the vicinity of the electron shower. For certain types of physics such as the study of the semi-leptonic decays of charm and bottom hadrons, this may present a severe limitation.

8.2 Muon Identification

A calorimeter can discriminate between μ^{±}’s and other charged hadrons by making use of the fact that a μ will only deposit energy via dE/dx while other particles will usually shower. This information alone can provide rejections of order 10^{−2} against charged hadrons, but it is also only applicable to cases where the μ is isolated from other showering particles. A more effective μ identification technique takes advantage of the fact that an energetic μ will pass through a large amount of material, whereas other charged particles will eventually interact in the material. A charged particle detector located behind the material is used to detect the μ^{±} candidates that pass through the absorber. This type of system works well even when the μ is produced in proximity to other particles, since the latter will be filtered out by the absorber.

The thickness of the absorber is the crucial parameter in such a device. An absorber consisting of at least 8-10 interaction lengths is sufficient to obtain rejection factors of order 10^{−3} for particles with momenta in excess of several hundred GeV/c. The sources of fake muon candidates in such a detector are (i) “interacting punchthrough,” where a particle showers in the absorber but some number of secondaries manage to leak out the back, (ii) “non-interacting punch-through,” where a charged hadron passes through the absorber without interacting, and (iii) decays in flight, which result from a charged hadron decay h → μν_{μ}X generating a real μ. The first two backgrounds are largely controlled by ensuring that there is enough absorber in the detector. The decay-in-flight background is controlled primarily by tracking the particles before they enter the absorber and rejecting candidates that have a visible “kink.”

8.3 Transition Radiation Detectors

When the speed of a particle exceeds that of light in a medium, the particle gives off radiation over a broad spectrum. The visible or near visible part of this spectrum is what we call Cerenkov radiation, but the spectrum extends into the x-ray region for very fast-moving particles. For particle γ’s > ∼ 1000, the emission probability of this radiation can be amplified by having the particle pass through many thin layers of material, resulting in what is called “transition radiation.” Since this emission only occurs for particles with γ above a specific threshold, the presence of this radiation can be used to discriminate electrons from more massive charged particles for electron energies of several hundred GeV.

A typical system consists of order 500-1000 layers of a material that is transparent to x-rays (e.g., a low Z material such as Li) followed by an x-ray detector, which is typically a MWPC filled with a high Z gas such as Xe that causes the high-energy photons to shower in the gas. The best discrimination usually comes from not just counting the amount of x-ray energy, but also counting the number of “clusters” detected in the MWPC above a threshold of ∼ 1 − 5 keV. In Fig. 15, the distribution of the number of observed clusters associated with a hadron is compared with the same distribution for electrons; the separation between these two distributions illustrates the rejection power of a TRD, which can be better than 5 × 10^{−4} for complete systems.

8.4 Ionization Measurements

The ionization energy loss of a particle varies with the Lorentz factor γ by ∼ 1.5 over the range γ ∈ (10, 100). An accurate measurement of this energy loss can thus be used to discriminate between e^{±}’s, K^{±}’s, π^{±}’s and protons in the momentum region below ∼ 10 GeV/c.

The dE/dx measurement is most conveniently performed by sampling a particle’s energy loss along its trajectory in a gaseous medium. Because the sample sizes are relatively small, each measurement is affected by the Landau fluctuations in the

Figure 15: The number of clusters and the total amount of γ ray energy oberved in the x-ray detector of a prototype TRD. The greater separation between the pion and electron signals when cluster counting is used reflects the higher hadron rejection afforded by this technique.

particle’s energy loss. The effect of these fluctuations can be reduced by throwing away those measurements that have the highest observed dE/dx (30-40% of the measurements are often discarded). This technique is well matched to TPC detectors, which make many measurements of the particles charge deposition to obtain the track trajectory.

An illustration of the particle ID capability of this technique is provided in Fig. 16, where we show the observed dE/dx as a function of particle momentum for a sample of particles in a TPC detector. Clear bands corresponding to the different particle species are apparent in the plot. Except in momentum intervals where the bands overlap, this system offers very good charged particle identification up to momenta between 5-10 GeV/c.

8.5 Time-of-Flight

TOF is a one of the classic methods of measuring a particle’s velocity, which can be converted into a mass measurement provided an independent momentum measurement is also made. This technique is limited by the length of the flight path of the particle between measuring stations and the accuracy of the time interval measurement. Because of the required time accuracy, scintillator-based particle detectors are usually used to measure the transit time of a particle. In such a system, the particle passes through a slab of scintillating plastic and generates a large number of photons that propogate to either end of the slab and are detected by a photomultiplier tube, which generates a signal in proportion to the number of incoming photons.

The achieved time resolutions for large systems are of order 200 − 300 ps (the Mark III detector at SPEAR has one of the best systems with a time resolution of < ∼ 200 ps). These time resolutions are limited by the broadening of the timeof-arrival of the photons at either end of the scintillator due to the fact that most

Figure 16: The measured ionization in the Aleph TPC detector versus particle momentum.

of the photons will internally reflect off the sides of the scintillator slab as they propogate to the photomultiplier tube. With typical flight paths of 1-2 m, TOF systems can provide particle ID up to momenta of ∼ 2 − 3 GeV/c. This limits the applicability of these systems to relatively low center-of-mass processes, such as one finds at the CESR and DORIS storage rings.

8.6 Cerenkov Radiation Detectors

The Cerenkov radiation threshold γ_{c} for a particle is related to the refractive index in the medium, n, by

γ_{c} = 1/\sqrt{1 − 1/n^{2}}.  (19)

For a particle with a known momentum, one can use the presence or absence of Cerenkov radiation to tell whether the particle is above or below this γ threshold. Such Cerenkov discriminator counters have seen wide use in fixed target facilities and in beam lines, where one can employ a device with the necessary radiator material followed by a photon detector. Secondary beam lines often have several such counters with different refractive media in order to obtain several different γ thresholds that can be used to uniquely identify several different particle types. This method is limited by the fact that each counter has only one threshold and these devices do not perform well in high particle-multiplicity environments.

Over the last 15 years, several groups have been developing a more flexible type of device known either as a Ring Imaging Cerenkov counter (RICH) or a Cerenkov

Figure 17: A schematic of the SLD CRID system. The device employs two separate radiators in order to provide particle ID over the largest possible momentum regime. The CF_{4} radiator is used in a proximity focusing mode, whereas the the Cerenkov photons from the continuous gas radiator are focused by the spherical mirror onto the photodetector.

Ring Imaging Detector (CRID) (see Ref. [28] for a recent review). These devices not only detect the Cerenkov radiation but image the “ring” of Cerenkov radiation given off by the particle. A particle emits Cerenkov radiation at a specific angle θ_{C} given by

θ_{C} = cos^{−1} (\frac{1}{βn}) ,  (20)

where β is the velocity of the particle (in units of c) and n is the refractive index of the media. In a continuous media, the radiation emitted at this angle can be focused by a spherical mirror onto a plane perpendicular to the particle’s path. The focused image forms a ring whose radius is directly related to the particle’s Cerenkov angle, and hence its velocity. This is illustrated in Fig. 17, which shows a schematic of the CRID system developed for the SLD detector. This figure also illustrates an imaging scheme kown as “proximity focusing,” where the particle passes through a short section of radiator material and the resulting Cerenkov photons form a ring on a plane downstream of the radiator.

The technical challenge with such a device is the design of the photon detector that forms the focal plane. This device has to be able to detect single photons with high efficiency and a position accuracy of order 1 mm. The devices that have been implemented in large scale detectors use a gaseous photocathode (typically a gas such as TEA or TMAE). The γ is absorbed by a gas molecule that subsequently releases a photo-electron. The e^{−} drifts up to ∼ 1 m in an electric field to one

Figure 18: The performance of the SLD CRID system, as measured by the number of standard deviations that would separate each particle species from the other charged leptons and hadrons. This separation comes entirely from the measurement of the Cerenkov angle using the size of the ring imaged in the TMAE photodetector.

end of the device. It is then detected in a MWPC operating at high gain (∼ 10^{5})^{§}. The advantage of these devices is that they provide particle ID up to ∼ 20 GeV/c in momentum, and are expected to work well even in dense particle environments. Fig. 18 shows an example of the expected particle seperation power of the SLD CRID as a function of momentum, illustrating the power of this device.

9 An Example of a Complete Detector

Having discussed in the preceding sections the various technologies that are currently in use, I will illustrate how these technologies are combined together to make a complete general-purpose detector. I have chosen as my example the Aleph detector at LEP—it is a good model to use as it employs various, well-proven technologies that function well together.

Aleph is a general-purpose detector operating at LEP, designed to study the

§The higher gain compared with normal MWPC’s compensates for the fact that this detector must be efficient for single e^{−}; normal MWPC’s detect a cloud of e^{−}’s and so only need to operate at gains of order 10^{4}.

Figure 19: A schematic of the Aleph detector at LEP.

decay modes of the Z^{∘} and to reconstruct e^{+}e^{−} collisions up to \sqrt{s} of 200 GeV [16]. The detector, illustrated in Fig. 19, consists of a tracking system, an electromagnetic and hadronic calorimeter, and a muon identification system.

The tracking system is composed of

• a Si micro-strip vertex detector (two layers of Si wafers at a radius of ∼8 cm),

• an inner tracking chamber comprised of a high precision drift chamber with position resolution of σ ∼ 100 μ, and

• a TPC with outer radius 1.4 m, giving ∼ 20 space points along each track (∼ 60, 000 channels),

all inside a solenoid magnet generating a 1.5 T field. Together, these devices give a momentum resolution of

\frac{Δp}{p} ∼ 0.001p ⊕ 0.003.  (21)

(the ⊕ symbol implies that the two terms should be folded together in quadrature).

The Aleph EM calorimeter consists of 22 X_{∘} of lead plates sandwiched between proportional wire chambers. The wire chamber cathodes are segmented into 3 cm×3 cm pads that record the ionization deposited in the calorimeter. This calorimeter is located inside the solenoid magnet in order to avoid the degradation in energy resolution that results if e^{±}’s and γ’s were to pass through the magnet coil. The calorimeter is organized into ∼ 74, 000 towers, and provides an energy resolution of

\frac{ΔE}{E} ∼ \frac{18%}{\sqrt{E}} ⊕ 1.6%.  (22)

The hadron calorimeter consists of ∼ 20 layers of Fe plates sandwiched between Iarocci tubes (proportional wire chambers with cathode readout). The calorimeter is 7 interaction lengths thick and has a resolution of

\frac{ΔE}{E} ∼ \frac{85%}{\sqrt{E}}.  (23)

A muon identification system is located outside the hadron calorimeter, and consists of two layers of Iarocci tubes separated radially by ∼ 0.5 m.

The Aleph design emphasizes excellent charged particle tracking, good EM calorimetry with fine segmentation for electron and photon identification, and particle identification provided by the calorimeter system, the TPC dE/dx measurement and the muon system. The detector has performed well during the first full run of the LEP collider, with essentially all of the systems being commissioned during that period. As an example of the detailed physics studies that can be performed by this detector, I have considered the measurement of the Z^{∘} branching fraction to b\overline{b}, which is a difficult measurement to perform as it requires some means of separating b quarks from the lighter quark jets [29].

The Aleph collaboration chose to do this by tagging b quarks using their semileptonic decay modes B → eν_{e}X and B → μν_{μ}X. This requires the detector to be able to identify electrons and muons that are buried in the middle of the lighter quark jet that acompanies the lepton daughters. Fig. 20 shows the distribution of a variable that characterizes the longitudinal profile of a shower observed in the EM calorimeter. This variable discriminates between showers that are initiated by electrons from those that result from hadrons, and illustrates a clear electron signal. An analysis of the data from the μ chambers results in a similar rate of such events in the μ decay mode. The resulting branching fraction is

\frac{BR(Z^{∘} → b\overline{b})}{BR(Z^{∘} → all)} = 0.220 ± 0.016 ± 0.024,  (24)

in good agreement with the Standard Model prediction.

10 Future High Energy Physics Experiments

In the upcoming years, experimental high energy physics will see the commissioning of the HERA ep collider and along with that the ability to accurately measure

Figure 20: The variable R_{1} for the Aleph event sample showing a clear signature for the electrons from b quarks in Z^{∘} decays at Aleph.

the structure of the proton using both the charged and neutral weak current. The ongoing program at Fermilab’s Tevatron collider will see several large collaborations continue to study the standard model using large samples of W and Z^{∘} bosons, and to search for the top quark and other new phenomena. The experimental program at LEP will see the four collaborations continue their detailed studies of the weak neutral current, and eventually W^{+}W^{−} production.

Finally, studies of the multi-TeV energy scale will become possible by the end of the decade with the completion of the SSC and perhaps the LHC. In addition to these frontiers, several active fixed-target programs (which I haven’t had time to discuss) will continue to push on specific frontiers that are inaccessible to the collider experiments.

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