%
%  Second lecture for TASI 90
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\section{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 ($e^\pm$'s, $\mu^\pm$'s and $\tau$'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 \Zzero\ 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
\begin{itemize}
\item a measurement of  the momentum of the electron 
candidate with a charged particle tracking  detector,
\item a measurement of the Lorentz contraction factor 
$\gamma$\
using a transition radiation detector (TRD), the amount of 
ionization deposited by the electron or the angle of its Cerenkov 
radiation, or
\item a measurement of the transverse and longitudinal profiles of the 
shower resulting from the electron interacting in an absorber 
such as lead or uranium.
\end{itemize}
%

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
(\ie\ 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 $\mu$'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 $\nu_\tau$\ that can only be 
indirectly detected.  In many detectors, the charged daughters from 
the $\tau$\ decay can be reconstructed, but the resulting 
candidate sample often has significant background contributions from other 
types of events (\eg, light quark jets in a collider experiment).
Secondary vertex detectors are commonly
employed to measure the vertex position of the candidate $\tau$\ 
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''\footnote{By energy flow, we mean 
the direction and energy of the particles produced in the 
interaction.}\ 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 (\ie\ 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 
\cite{ref: Lifetimes}.

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 
(\dEdx) 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
\begin{itemize}
\item  charged particle detectors, providing the direction (and 
in most cases the momentum) of each charged hadron and lepton,
\item vertex detectors that can measure with high precision the 
position of the particles near the interaction point,
\item finely segmented calorimeters that measure the 
energy and direction of jets,
\item hermetic calorimeters that indirectly detect neutrinos 
using the missing energy technique, and
\item devices that identify particles, such as electromagnetic shower 
counters,  muon detectors, and TOF systems.
\end{itemize}
We will discuss in more detail the principles involved in these 
detection techniques and outline how they are implemented in 
modern day particle detectors.

\section{Charged Particle Detectors}


Most modern-day charged particle detectors are electronic devices 
that have fast response times ($\lessim 1\ \mu$s), 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 \etal\ on 
proportional wire counters \cite{ref: Charpak}.     

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. \ref{fig: geiger}.
\begin{figure}
\vspace{1.2in}
\caption{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.}
\label{fig: geiger}
\end{figure}

The voltage signal $v^-$\ generated by the electrons is given by
\begin{eqnarray}
v^- = -{{Q}\over{2\pi\epsilon_0 l}} \ln\left({{a+\lambda}\over{a}}\right)
\end{eqnarray}
and the signal generated by the positive ion cloud drifting away
from the anode, $v^+$, is given by
\begin{eqnarray}
v^+ = -{{Q}\over{2\pi\epsilon_0 l}} \ln\left({{b}\over{a+\lambda}}\right),
\end{eqnarray}
where $\lambda$\ 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
\begin{eqnarray}
v^+ + v^- = {{Q}\over{2\pi\epsilon_0 l}}\ln\left({{b}\over{a}}\right) =
     {{Q}\over{l C}},
\end{eqnarray}
where $C$\ is the capacitance/unit length of the tube and  $Q$\ is 
the total charge.  The dielectric constant $\epsilon_0$\ is 
$\sim8.85$\ 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 \etal\ 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. \ref{fig: aval}.
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 $\sim50$\ 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.
\begin{figure}
\vspace{1.5in}
\caption{A schematic of a multi-wire proportional counter showing the 
anode sense wire plane and the two cathode planes. }
\label{fig: aval}
\end{figure}

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 planes help at high voltage.  Practical chambers 
cannot be larger than $\sim$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 $\sim1$\ C/cm of total charge over their lifetime.

\subsection{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. \ref{fig: DC}.
\begin{figure}
\vspace{1in}
\caption{A schematic drawing of a conventional drift chamber cell. 
}
\label{fig: DC}
\end{figure}

Typical electron drift speeds 
of $\sim 40$\ $\mu$/ns imply that an accuracy of a few 
nanoseconds in measuring the time of arrival yields position 
resolutions of order 100 $\mu$. 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 {\it 
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 $E\times B$\ 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-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 
($\sim4^\circ$\ 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 $\sim5\times10^4$\ 
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.

\subsection{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. \ref{fig: TPC}, 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.
\begin{figure}
\vspace{2.5in}
\caption{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.}
\label{fig: TPC}
\end{figure}

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 $\mu$\ have been 
achieved \cite{ref: Aleph description}.

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.

\subsection{Vertex Detectors}

With the discovery of the \c\ quark, $\tau$\ 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 $c\tau$\ of these particles is of order 100 to 500 $\mu$, so that 
charged particle detectors with resolutions better than 100 $\mu$\ 
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 ($<100$\ $\mu$).  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).

\subsubsection{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 $\delta$-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 $\sim50$\ microns
with this device \cite{ref: ARGUS microvdc}.

\subsubsection{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 $\sim d/\sqrt{12}$). 
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 
$\sim2$\%\ of the strip width.  An example of the performance of 
such a system is shown in Fig. \ref{fig: Cath}, 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 $\sim 35$\ $\mu$\ \cite{ref: High precision MWPC}.
\begin{figure}
\vspace{2.5in}
\caption{The resolution of a cathode strip system.
Each peak corresponds to the location of an anode. }
\label{fig: Cath}
\end{figure}
 
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).

\subsubsection{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\footnote{The depletion region is that part of the 
crystal that is depleted in charge carriers.}\ in the crystal
by placing a voltage across the top and bottom surfaces,
as shown in Fig. \ref{fig: Si}.  A 
minimum-ionizing particle will deposit $\sim80$\ ions/$\mu$\ 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 Si wafer with 300 
$\mu$\ thickness, 300 Volts across the junction is sufficient to 
completely deplete the Si, resulting in a signal of $\sim$25~000 
electrons.   The inherent noise in the detector comes from 
fluctuations in the number of available charge carriers,  which can 
be kept to $\sim$1000 electrons in size. 
Micro-strip detectors with 50 micron strip pitch 
have demonstrated  position resolutions on 
the order of 5 $\mu$.
This has been achieved by
employing ``capacitive charge division'', \ie\ using the relative size 
of the signal observed on each strip to interpolate the position 
of the ionizing particle.  
\begin{figure}
\vspace{2 in}
\caption{A schematic of a silicon micro-strip detector.
The device shown has a strip pitch of 20 microns. }
\label{fig: Si}
\end{figure}

A  potential 
drawback of these detectors is the amount of material they 
introduce into the tracking environment.   A 300 $\mu$\ 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 high-energy 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.

\subsubsection{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 $\sim$10\ microns
with two-track separations of $\sim$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. \ref{fig: CCD}, 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 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.
\begin{figure}
\vspace{3.4in}
\caption{ 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 
$22\mu\times22\mu$. }
\label{fig: CCD}
\end{figure}

A typical CCD has a depletion region $\sim 1$\ $\mu$\ 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 $\sim10^5$\ 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 $\sim$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 \cite{ref: Damerell}.

\section{Calorimetry}
\subsection{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
\begin{itemize}
\item energy loss (\dEdx) from low-energy collisions with nuclei,
\item {\it bremsstrahlung}\ radiation given off by relativistic 
particles (primarily $e^\pm$'s),
\item pair production $\gamma\rightarrow e^+e^-$, and
\item nuclear interactions.
\end{itemize}
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 (\ie\ 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 \cite{ref: Fabjan}.

\subsection{EM Showers}
\subsubsection{General Characteristics}

The interaction of a photon or electron with a high Z 
material\footnote{In this section, Z refers to the atomic number of 
the nucleus of the material.}\ depends strongly on the energy of the 
particle.  The energy of the incident particle is absorbed primarily 
by ionization energy loss when the $e^\pm$\ energy falls below
a ``critical energy,'' $\epsc$.   Electrons with energies  near or 
above $\epsc$\ lose energy primarily by {\it bremsstrahlung}\
($e^\pm \rightarrow e^\pm \gamma$)  and generate a secondary $\gamma$.  
Photons lose most of their energy by  ``converting'' 
($\gamma \rightarrow e^+e^-$), thereby generating an electron-positron pair.  
For heavy materials ($Z\gessim15$), the critical energy $\epsc \sim 
550/Z$\ MeV and is defined as
\begin{eqnarray}
dE = -\epsc (dx/\Xzero).
\end{eqnarray}
The average energy loss for both electrons and photons as a 
function of their energy is shown 
in Fig. \ref{fig: dEdx}\ for each of the 
dominant energy-loss mechanisms.
\begin{figure}[t]
\vspace{4.75in}
\caption{The average energy lost by an electron (a) and by a photon 
(b) as a function of their energy for the
different processes. } 
\label{fig: dEdx}
\end{figure}

For energies well above $\epsc$, the energy lost traversing a
distance $\Delta x$\ is given by
\begin{eqnarray}
\Delta E = - E {{\Delta x}\over{\Xzero}},
\label{eqn: Xzero}
\end{eqnarray}
where $\Xzero$\ is the ``radiation length'' and is a characteristic
of each material.  For heavy materials, 
$\Xzero \sim 180 A / Z^2$\ g/cm$^2$, where 
$A$\ is the atomic weight of the material  (radiation lengths 
are often expressed in terms of $\Xzero$\ as defined 
in Eqn. \ref{eqn: Xzero}\
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 $e^\pm$'s and $\gamma$'s\ 
through a combination of the processes discussed above.  The 
initial energy thus becomes spread over a large number of 
relatively low-energy secondaries ($\lessim 1-10$\ MeV) and 
these  deposit their energies through \dEdx\ in the material.  The 
longitudinal profile of the shower (\ie\ the distribution of this 
deposited energy as a function of the depth in the material) scales 
with the radiation length $\Xzero$, with the maximum energy deposition
occuring at a depth of $\sim$6 $\Xzero$\ in the material. 
The lateral profile is given 
by the ``Moliere radius'' $\rho_M$, which  for heavy materials is 
\begin{eqnarray}
\rho_M \sim 7 A/Z\  {\rm g/cm}^2.
\end{eqnarray}
The size scale represented by $\rho_M$\ results from a 
combination of the characteristic $\gamma$\ production angle in 
{\it 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 $\rho_M$\ of the shower axis.
Lead, which is frequently chosen as an absorber material in an EM calorimeter
because of its short radiation length, has $\rho_M\sim1$\ cm and 
$\Xzero\sim 0.6$\ cm.

\subsubsection{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 \dEdx,
the incident energy is proportional to
the total path length $T$\ of $e^\pm$'s in the shower.  We can 
estimate this by
\begin{eqnarray}
T={E / \epsc},
\end{eqnarray}
using the the definition \dEdx$= - \epsc/\Xzero$.
In the calorimeter, one can typically only detect energy that is  
deposited by particles above a certain energy threshold $\eta$, 
which is a characteristic of the sensitive material in the calorimeter.  
The total ``detectable'' track length can then be written as
\begin{eqnarray}
T_d = F(\eta/\epsc) E / \epsc,
\end{eqnarray}
where $F(\eta/\epsc)$\ is the fraction of ionizing particles above 
the threshold $\eta$.  The function $F$\ is intrinsic to an EM 
shower in the absorber---a typical distribution
is plotted in Fig. \ref{fig: F-eta}.
\begin{figure}
\vspace{2.8in}
\caption{The fraction of energy in an EM shower carried by 
electrons with energies above a threshold versus the energy threshold. 
}
\label{fig: F-eta}
\end{figure}

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
$N\sim E/\eta$.  The statistical fluctuations in this are 
\begin{eqnarray}
{{\sigma_{int}}\over{E}} = {{\sigma(N)}\over{N}} \sim
{{1}\over{\sqrt{N}}} \sim {{\sqrt{\eta}}\over{\sqrt{E}}}.
\end{eqnarray}
For example, a typical Pb glass detector has a cutoff energy of 
$\eta=0.7$\ MeV, resulting in an intrinsic resolution of
\begin{eqnarray}
{{\sigma_{int}}\over{E}} \sim {{2\%}\over{\sqrt{E}}}.
\end{eqnarray}
 
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 $20\Xzero$\ in depth to ensure at 
least 98\%\ containment \cite{ref: Bitinger}.

\subsubsection{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 \dEdx\ 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
\begin{eqnarray}
N_x = {{{T_d}\over{d}} = {{F(\eta/\epsc) E}\over{\epsc d}}
             = {{F(\eta/\epsc) E}\over{\Delta E}}},
\end{eqnarray}
where we have defined $\Delta E \equiv \epsc d$  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
\begin{eqnarray}
{{\sigma_{sample}}\over{E}} = {{\sigma(N_x)}\over{N_x}} \sim
{{1}\over{\sqrt{N_x}}} \sim
{{\sqrt{\Delta E / F(\eta/\epsc)}}\over{\sqrt{E}}}.
\end{eqnarray}
For $F=0.5$\ and $\Delta E = 5$\ MeV, the contribution to the 
resolution would be
\begin{eqnarray}
{{\sigma_{sample}}\over{E}} =
 {{10\%}\over{\sqrt{E}}}.
\end{eqnarray}
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 
\dEdx\ 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.

\subsection{Hadronic Showers}
\subsubsection{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 
$e^\pm$'s and $\gamma$'s)  to strongly interacting hadrons to 
particles that interact only weakly (such as $\nu$'s from $K$\ and 
$\pi$\ 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'' $\lambda$\ 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 $\lambda\sim17$\ cm.


\subsubsection{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 
$\pi^\circ$, the particle decays to 2 photons that form an 
electromagnetic shower.  Since most of this energy is 
deposited via \dEdx, 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 \cite{ref: Wigmans}.

A method to partially overcome this problem was developed by the CDHS
collaboration, which has an iron and concrete calorimeter that is 
intrinsically non-compensating \cite{ref: CDHS}.  
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 de-emphasized large positive fluctuations in the 
observed response.  The effect of this is seen in Fig. 
\ref{fig: CDHS}, 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.  
\begin{figure}[t]
\vspace{3.5in}
\caption{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.  }
\label{fig: CDHS}
\end{figure}

The real cure to the non-compensation problem is to make the 
calorimeter intrinsically ``compensating'', \ie, 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 that employed $^{238}$U\ as an absorber material 
sandwiched between scintillator plates.  This device had an intrinsic 
resolution of
\begin{eqnarray}
{{ \sigma_{int}}\over{E}} = {{22\%}\over{\sqrt{E}}},
\end{eqnarray}
where $E$\ is the energy of the incident 
hadron \cite{ref: first compensation}.  
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. \ref{fig: ZEUS cal}\
where the electromagnetic and hadronic energy resolution of the 
detector as a function of the incident hadron energy is plotted
\cite{ref: ZEUS calib}.  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 kinematic variables is 
possible only if the calorimeter's jet energy response is well 
understood  over several orders of magnitude in jet energy. 
\begin{figure}
\vspace{2.5in}
\caption{The energy resolution of the ZEUS  calorimeter as a 
function of the incident hadron and electron energy. }
\label{fig: ZEUS cal}
\end{figure}

\section{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 \Zzero\ 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 $\sim 3$\%.   Various techniques are used to 
determine these absolute energy scales, and we will briefly discuss 
these below.

\subsection{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 {\it 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 
($e^+e^- \rightarrow e^+e^-$)  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 $\sim20~000$\ 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 
$J/\Psi\rightarrow\mu^+\mu^-$\ (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 $\sim 1$\%\ of the detected energy.

\subsection{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 $\mu^\pm$'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. \ref{fig: JPsi}, 
which shows the invariant di-muon mass distribution recorded by 
the CDF detector.  One can infer from the 
peaks masses of 
$3.097\pm0.001$\ \GeVcc\ and $9.469\pm0.010$\ \GeVcc\ for the 
$J/\Psi$\ and $\Upsilon$\ resonances, respectively.
Both of these masses are consistent with the world average values 
of 3.097 \GeVcc\ and 9.460 \GeVcc\ \cite{ref: PDG}, and therefore verify the 
momentum scale of the CDF detector to 0.2\%.
\begin{figure}
\vspace{3.3in}
\caption{The di-muon invariant mass distribution observed by the 
CDF detector for candidate $J/\Psi$\ and $\Upsilon$\ events.  }
\label{fig: JPsi}
\end{figure}

\section{Triggering and Data Reduction}
A crucial aspect of any experiment is the manner in which the 
detector is triggered, \ie\ 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 
$\sim50$\ kHz (resulting from a detectable cross section of 
$\sim50$\ mb at a luminosity of $10^{30}\ \cms$)  but only 
$\sim0.1$\ 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 by requiring that the candidate 
events have some combination of charged lepton candidates, 
high-\Pt\ 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. \ref{tab: trig}.  
\begin{table}
\vskip .2 in
\tabskip=1em plus2em minus.5em
\def\thickfill{\leaders\hrule height1.5pt\hfill}
\vbox{\offinterlineskip
\halign to \hsize
{\vrule 
width1.5pt#&\strut\quad#\hfil&\vrule#&\strut\hfil#\hfil&\vrule#
&\strut\hfil#\hfil&\vrule width1.5pt#\cr
 \omit\span\omit\span\omit\span\omit\span\omit%
 \span\omit\span\omit \thickfill\cr
height 4 pt &\omit&&\omit&
            &\omit& \cr
& Trigger Level &&      CDF     &&      Aleph       &\cr
height 4 pt &\omit&&\omit&
            &\omit& \cr
 \omit\span\omit\span\omit\span\omit\span\omit%
 \span\omit\span\omit \hrulefill\cr
height 4 pt &\omit&&\omit&
            &\omit& \cr
& Level 1  decisions        &&    5,000     &&       $\sim200$&\cr
height 4 pt &\omit&&\omit&
            &\omit& \cr
& Level 2   decisions      &&       10     &&             10 &\cr
height 4 pt &\omit&&\omit&
            &\omit& \cr
& Level 3   decisions      &&        1     &&              1 &\cr
height 4 pt &\omit&&\omit&
            &\omit& \cr
 \omit\span\omit\span\omit\span\omit\span\omit%
 \span\omit\span\omit \thickfill\cr
}}
\caption{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. } 
\label{tab: trig}
\end{table}

\section{Particle Identification Techniques}
Many experiments require that it be possible to unambiguously 
identify specific particle species.  An illustration of this is provided 
in Fig.  \ref{fig: Bs}, 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 \cite{ref: ARGUS Bs}.  The 
decays were
\begin{eqnarray}
B^\circ \overline{B}^\circ \rightarrow
B^\circ B^\circ \rightarrow
\left(\mu^+ \nu_\mu K^+ \pi^- \pi^- \right)\>
\left(\mu^+ \nu_\mu K^+ \pi^- \pi^- \right).
\end{eqnarray}
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.
\begin{figure}[t]
\vspace{3.75 in}
\caption{An event display of a $B\overline{B}$\ mixing event observed
by the ARGUS collaboration. }
\label{fig: Bs}
\end{figure}

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.

\subsection{Electron ID Using Calorimetry}
The difference between an EM and a hadronic shower is often 
used to discriminate electrons and $\gamma$'s from
hadrons.   A typical system employs an  absorber with a short 
radiation length such as lead in which the $e^\pm$'s and 
$\gamma$'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 $\pi^\pm$'s that undergo charge 
exchange in the front section of the EM calorimeter:
\begin{eqnarray}
\pi^\pm p \rightarrow \pi^\circ N
\end{eqnarray}
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 $\sim10^{-3}$\ with electron efficiencies $>80$\%.   
This scheme requires the
electron to be ``isolated,'' \ie\ 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.

\subsection{Muon Identification}
A calorimeter can discriminate between $\mu^\pm$'s and 
other charged hadrons by making use of the fact that a $\mu$\ will 
only deposit energy via \dEdx\ 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 $\mu$\ is isolated from other 
showering particles.  A more effective $\mu$\ identification 
technique takes advantage of the fact that an energetic $\mu$\ 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 
$\mu^\pm$\ candidates that pass through the absorber.  This type of 
system works well even when the $\mu$\ 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 \GeVc.  The sources of 
fake muon candidates in such a detector are (i) 
``interacting punch-through,'' 
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 
$h\rightarrow\mu\nu_\mu X$\ generating a real $\mu$. 
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.''  

\subsection{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 $\gamma$'s 
$\gessim 1000$, 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 $\gamma$\ 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 (\eg, 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 
$\sim 1-5$\ keV.  In Fig. \ref{fig: TRD}, 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 $5\times10^{-4}$\ for complete systems.
\begin{figure}
\vspace{2in}
\caption{The number of clusters and the total 
amount of $\gamma$\ 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. }
\label{fig: TRD}
\end{figure}

\subsection{Ionization Measurements}

The ionization energy loss of a particle varies 
with the Lorentz factor $\gamma$\ by $\sim 
1.5$\ over the range $\gamma\in (10,100)$.  An accurate 
measurement of this energy loss can thus be used to discriminate
between $e^\pm$'s, $K^\pm$'s, $\pi^\pm$'s and protons in the 
momentum region below $\sim 10$\ \GeVc.

The \dEdx\ 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 
particle's energy loss.  The effect of these fluctuations can be 
reduced by throwing away those measurements that 
have the highest observed \dEdx\  (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. \ref{fig: dEdx performance}, where 
we show the observed \dEdx\ 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 \GeVc.
\begin{figure}
\vspace{3.5in}
\caption{The measured ionization in the Aleph TPC detector versus particle
momentum. }
\label{fig: dEdx performance}
\end{figure}

\subsection{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 $\lessim 200$\ ps).  These time 
resolutions are limited by the broadening of the time-of-arrival of 
the photons at either end of the scintillator due to the fact that most 
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  $\sim2-3$\ \GeVc.  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.

\subsection{Cerenkov Radiation Detectors}
The Cerenkov radiation threshold $\gamma_c$\ for a particle is related to the
refractive index in the medium, $n$, by
\begin{eqnarray}
\gamma_c =  1/ \sqrt{1 - 1/n^2}.
\end{eqnarray}
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 $\gamma$\ 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 $\gamma$\ 
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 Ring Imaging Detector 
(CRID) (see Ref. \cite{ref: RICH review}\ 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 $\theta_C$\ 
given by
\begin{eqnarray}
\theta_C = \cos^{-1} \left({{1}\over{\beta n}}\right),
\end{eqnarray}
where $\beta$\ 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. \ref{fig: CRID}, 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.  
\begin{figure}
\vspace{3in}
\caption{ 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.}
\label{fig: CRID}
\end{figure}

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  $\gamma$\ is absorbed by a gas 
molecule that subsequently releases a photo-electron.  The $e^-$\ 
drifts up to $\sim 1$\ m in an electric field to one end of the device.  
It is then detected in a MWPC operating at high gain ($\sim 
10^5$)\footnote{
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 $10^4$.}.  
The advantage of these devices is that 
they provide particle ID up to $\sim 20$\ \GeVc\ in momentum, 
and are expected to work well even in dense particle 
environments.  Fig. \ref{fig: CRID performance}\ shows an 
example of the expected particle seperation power of the SLD 
CRID as a function of momentum, illustrating the power of this 
device.
\begin{figure}[t]
\vspace{3.8in}
\caption{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. 
}
\label{fig: CRID performance}
\end{figure}
