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%  Second lecture for TASI 90
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\section{Particle Detectors}

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 be requiring that they satisfy 
certain conditions (such as kinematic cuts).  In principle, 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 the quarks (or hadrons they result in).  On an even 
more abstract level, one would also like the detector to identify any 
gluons, photons and \W\ and \Zzero\ bosons that are also produced.

In practice, these requirements are met by observing the interaction 
of the particles (leptons and hadrons) that are produced in a 
collision  and identifying the constituents in the interactions by the 
different ways in which they interact.  For example, one typically 
can identify electrons with a combination of the following 
techniques:
\begin{itemize}
\item measurement of  the trajectory and momentum of the electron 
candidate with a charged particle tracking  detector;
\item measurement of the Lorentz contraction factor 
$\gamma$\footnote{Here, $\gamma \equiv (\sqrt{1-(v/c)^2})^{-
1}$\ where $v$\ is the velocity of the particle.}\
 using a transition radiation detector (TRD), the amount of 
ionization deposited by the track or the angle of its Cerenkov 
radiation; or
\item measurement of the transverse and longitudinal profiles of the 
shower resulting from the particle interacting in an absorber 
material such as lead or uranium.
\end{itemize}
%
In most detectors, several combinations of
these and other related techniques have been successfully used to 
identify electrons.

The classical technique for identifying $\mu$\ candidates has taken 
advantage of that fact that a  $mu$\ interacts with matter primarily 
through energy loss via ionization and other electromagnetic 
processes. and therefore has a long range in a material.
One therefore builds a detector that effectively measures the range 
of the charged particle;  typical implementations employ several 
meters of iron instrumented with a charged particle detectors 
interleaved with the absorber material.  Candidate $\mu$'s are 
defined to be those charged particles that manage to pass through 
the absorber without interacting.  The amount of ionization left in a 
calorimeter, for example, provides another way of discriminating 
between muons and charged hadrons and electrons.

Tau leptons are more difficult to identify as they decay into several 
particle final states, one of which is a $\nu_\tau$, which can only be 
indirectly detected.  In many detectors, the charged daughters from 
the $\tau$\ decay can be reconstructed, but often the resulting 
candidate sample is significant background contributions from other 
types of events (light quark jets in a collider experiment, for 
example).  In those cases, additional requirements have to be 
imposed;  recently, secondary vertex detectors have been 
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.}\ in the event associated with all other particles 
(charged leptons and charged and neutral hadrons) associated with 
the interaction.  Such energy flow measurements are normally 
performed with a hermetic, finely segmented  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.  In hadron-hadron colliders, this technique is 
limited by the presence holes in the detector through which the 
beams are passed.

We have not observed free quarks but there is now a large body of 
evidence that supports the quark model  with no fundamental 
disagreements between the model's predictions and observation.  
Quarks produced with low energies (less than order 5 GeV)  
manifest themselves as individual hadrons.  More energetic quarks 
under QCD fragmentation and generate ``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 only rely on the incomplete information available from 
a charged particle tracking system.  The fragmentation process 
generates a complex final state, which 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 with a charged 
particle detector with sufficient spatial resolution , the decay vertex 
of the heavy quark can be reconstructed.

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).   Several 
methods are routinely used, examples of which are: 1) a time-of-
flight (TOF)  measurement that determines the particle's velocity 
coupled with an independent momentum measurement provides a 
direct measure of the particles mass,  2) the rate of energy loss 
through ionization (\dEdx) can be used to determine the particles 
velocity, and  3) and the radiation emitted by the particle (in the 
form of Cerenkov or transition radiation)  provides a measure of the 
particles velocity.  

From this summary, we can identify the tools necessary to identify 
and measure the final states resulting from a high-energy 
interaction:
\begin{itemize}
\item  charged particle detectors, providing both 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 in order to reconstruct the 
energy and direction of jets;
\item hermetic calorimeters in order to indirectly detect neutrinos 
using the missing energy technique; and
\item devices to identify individual particles, such as shower 
counters to detect electrons,  muon detectors, and other particle 
identification techniques.
\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), high rate 
capability, and that provide information in a form that is easy to 
digitize and readout.  The concept utilized by all of these devices is 
that one detects the ``primary ionization'' deposited by the charged 
particle in a medium.  Almost all devices in use today have their 
roots in the work done by Charpak \etal\ at CERN in late 1960's on 
proportional wire counters \cite{ref:Charpak}.     

To understand how the general system works, first consider the 
case of
a cylindrical tube with a thin wire running down the axis, and filled
with a gas that ionizes relatively easily, as shown in 
Fig. \ref{fig: geiger tube}.
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 towards the anode with increasing velocity as they near the 
anode, because of the increasing electric field gradient.  Within a 
few $\mu$'s of the anode, the kinetic energy of the electrons is 
high enough that collisions with gas molecules create more 
electron-ion pairs.  Thus the original signal is ``multiplied'' by a 
gain, that typically could be $10^4$\ or $10^5$.
\begin{figure}
\vspace{3in}
\caption{A simple proportional wire detector.  The wire primary 
ionization liberated by a particle traversing the gas volume drifts to 
the wire anode, and ``avalanches'' generating a detectable voltage 
signal. }
\label{fig: geiger tube}
\end{figure}

The voltage ``signal'' generated by the electrons $v^-$\ is given by
\begin{eqnarray}
v^- = -{{Q}\over{2\pi\epsilon_0 l}} \ln({{a+\lambda}\over{a}}),
\end{eqnarray}
but the signal generated by the charged ion cloud drifting away
from the anode, $v^+$, which is given by
\begin{eqnarray}
v^+ = -{{Q}\over{2\pi\epsilon_0 l}} \ln({{b}\over{a+\lambda}}),
\end{eqnarray}
is much larger since the distance 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({{b}\over{a}})\equiv
     {{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.

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, as illustrated in Fig. \ref{fig: avalanche}.
\begin{figure}
\vspace{3in}
\caption{The development of an avalanche on the anode when the 
device is operated in proportional mode. }
\label{fig: avalanche}
\end{figure}
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.  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 large 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.

A large amount of R\&D has been performed to optimize the 
design of these devices.  The choice of gas mixture for these 
chambers has received a great deal of attention as one usually 
wants 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 photo-electrons, and trace amounts of some form of 
alcohol to prevent the
accumulation of polymers on the cathode and increasing the 
lifetime of the chamber. Various groups have also employed 
cathode planes segmented into strips
or pads; the induced charges on the cathode can be measured and 
used to determine the position of the avalanche along
the anode.

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 
are limited to dimensions of order 0.5-1.0 m without having  
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 somewhat 
susceptible to aging effects over long exposures to charged 
particles and other radiation.

\section{Drift Chambers}

Early in the development of MWPC's, it was realized that one 
could combine a proportional counter witha drift region for the 
electrons to measure the charged particle positions. One designs a 
chamber where the electrons liberated by the ionization
process drift in a uniform electric field so that  the time of arrival of
the signal at the wire anode is used to determine the particle 
position.  This is shown conceptually in Fig. \ref{fig: DC}.
\begin{figure}
\vspace{3in}
\caption{A schematic drawing of a conventional drift chamber cell. 
}
\label{fig: DC}
\end{figure}

In such a device, one can have a drift region that is of order 5 cm
long, which presents a considerable cost savings compared to a 
MWPC that provides comparable resolution.  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 $\mu$.  The price one pays for this 
accuracy is that one requires a well understood time-to-distance 
relationship in the drift region (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 on which side of the wire the particle passed.  
There are several ways of doing this:  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.  These have been used in many fixed target
experiments and are now the charged particle detector of choice in
most applications where large areas need to be instrumented with
high spatial resolution detectors.
 
With the advent of storage rings, drift chambers constructed in a 
solenoidal geometry have become ubiquitous.
This geometry raises several complications to the design.  The $B$\ 
field is now $\perp$\ to the $E$\ field so that the electrons 
experience an $E\times B$\ Lorentz force that must be corrected 
for.  An axial position measurement (\ie\ along the axis of the 
solenoid) requires one to use an additional technology; for 
example, charge-division readout is often employed, where the hit 
signal is read out on both ends of the wire and the relative amount 
of charge detected at each end is proportional to the relative 
position of the hit from each end.  Another popular scheme 
employs 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 axial azimuthal position resolution.

The size of drift chamber systems have steadily increased, with 
typical systems in use today consisting of order $5\times10^4$\ 
wires in total 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 $8^10^7$\ 
computer instructions to execute the CDF tracking algorithm on a 
typical interaction at the Tevatron collider.

\section{Time Projection Chambers}

The ultimate in drift chamber technology arises in what is known as
the time projection chamber (TPC), which was developed in the 
late 1970's for large-scale use in 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.  Ions created by a charged track now drift over a large 
distance (or order 1 m) to one end of the chamber.
\begin{figure}
\vspace{3in}
\caption{A schematic drawing of a time projection chamber.  Ions 
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 device.}
\label{fig: TPC}
\end{figure}

The ions are detected with 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.  Another feature of 
many TPC's is that the amount of induced charge on the cathode 
pads are also recorded, thereby providing a measure of the 
particle's ionization.  This can be used to measure the velocity of 
the particle,and with a momentum measurement, its mass.  Position 
resolutions of order 200-300 $\mu$\ have been achieved.

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 used a TPC consisting of $10^4$\ wires and a 
20 cm drift region in their central detector that was located inside a 
dipole magnetic field.  CDF uses 8 vertex-TPC modules (VTPC's), 
each with a drift of 20 cm for charged particle tracking close to the 
interaction region.

\section{Vertex Detectors}

With the discovery of the \c\ quark, $\tau$\ lepton and \b\ quark, all
of which decay weakly and have relatively long lifetimes, there has 
been a great deal of interest placed 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.   The fact that many of the current general purpose 
detectors have incorporated some form of secondary vertex 
detector reflects the importance given to the physics that such a 
device makes accessible.
 

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:
used:
\begin{itemize}
\item high resolution drift chambers and MWPC's,
\item Si strip detectors (and Si diode detectors), and 
\item pixel detectors (CCD's and Si pixel systems).
\end{itemize}

\subsection{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. 

\subsection{High-Resolution MWPC's}

The anode spacing in a proportional wire system is the fundamental 
limitation on the position resolution of such a device  (as the 
position uncertainty is $\sim d/\sqrt{12}$ where $d$\ is the anode 
spacing).  However, the induced charge seen on the cathode also 
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 uncertainty of 10\%\  on 
the charge measurement 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: Cathode Pad}, where the 
peaks reflect the  position uncertainty for a MWPC with
an 8 mm anode-cathode gap and 3 mm wide cathode strips; the 
resolution is $\sim 35$\ $\mu$.
 
However these systems are limited by the the large number of 
channels required for even a modest system consisting of only a fw 
planes of readout, the relatively poor two-track separation of 
thedevice.

\subsection{Si Strip Detectors}

A Si strip detector take advantage of the intrinsic properties of an n-
p junction formed by taking a crystal of Si and enlargening its 
depletion region\footnote{The depletion region is that part of the 
crystal that is depleted in charge carriers.}\ by placing a voltage 
across the junction, as shown in Fig. \ref{fig: Si Detector}.  A 
minimum-ionizing particle will deposit $\sim80$\ ions/$\mu$\ in 
the Si crystal.  These charges drift to the collecting electrodes 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 $\sim 25000$\ 
electrons.   The inherent noise in the detector comes from 
fluctuations in the number of charge carriers available,  which can 
be kept to of order 1000 electrons in size. At that level, this is 
comparable to the input noise on the amplifier and does not 
dominate the total noise.

Such micro-strip detectors have achieved position resolutions on 
the order of 5 $\mu$\ by reading out the charge on each strip  and 
performing ``capacitive charge division'', \ie\ using the relative size 
of the signal observed on adjacent strips to interpolate the position 
of the depostion of ionization in the crystal.  One  potential 
drawback of these detectors is the amount of material they 
introduce into the tracking environment.   A 300 $\mu$\ thick 
wafer contributes 0.3\%\ $\Xzero$\ in material to the tracking 
system which in itself is normally tolerable.  Many layer systems 
however will present many times this amount, which may introduce 
large multiple scattering uncertainties in the charge track positions 
and also act as a photon converter, thereby increasing the number 
of charged particles and high-energy electrons in the detector.  
Radiation damage 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.

\subsection{Charge Coupled Devices}

Pixel tracking detectors offer the benefit of providing high-
precision, three-dimensional coordinate position for charge tracks, 
with the obvious disadvantage that most technologies require each 
pixel to have an independent readout channel thereby increasing 
the cost of an entire system enormously.  However, various 
schemes exist for making feasible pixel devices.  In Fig. \ref{fig: 
CCD}, I show an example of a charged-coupled device (CCD), 
which  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{3in}
\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 
$22\mu\times22\mu$. }
\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, which 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 
readout 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 lcoated at one of the CCD.  The 
contents of the output registers are then clocked out serially at rates 
that typically are several MHz.

CCD systems have several attractive features:  They provide 
excellent position resolution and two-track separation ($sim40\ 
\mu$\ is typical) and high efficiency ($>98$\%).
However, they have to be operated at Li $N_2$\ temperatures to 
keep the pixels from filling with thermal electrons and the readout 
speed of order 70 ms is poorly matched to high-rate applications.

There are many other high-precision charged particle detectors 
under development.   Examples of these are
\begin{itemize}
\item Si pixel detectors, which are similar to CCD's but provide  
digital hit information (as opposed to the analogue information 
provided by a CCD) and have higher readout speeds;
\item Si P-I-N diodes, which are another form of Si pixel detector; 
and
\item Si drift chambers, where one now drifts the ionization 
deposited in a Si wafer over distances of order ?? and uses the drift 
times to determine the particle position.
\end{itemize}
One can expect to see one or more of these technologies mature in
the next few years as the need for higher precision and higher rate
systems increases.

\section{Calorimetry}
\subsection{The Role of a Calorimeters}
As the name suggests, 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.  Because of these 
considerations and the desire to design and build higher 
performance calorimeters, a great deal of effort has been directed 
toward the study of how a high-energy particle deposits its energy 
in a dense medium.  

Calorimeters are generally divided into those that are optimized for 
the measurement of electromagnetic energy (EM calorimeters), 
optimized for the measurement of hadronic energy (hadronic 
calorimeters) and those that have the combined function of 
measuring both EM and hadronic energy.  In order to understand 
the differences between these types of devices, it is useful to first 
review 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 bremsstrahlung radiation given off by highly relativistic 
particles (primarily $e^\pm$'s);
\item pair production $\gamma\rightarrow e^+e^-$\ (\ie\ 
conversions); and 
\item nuclear interactions.
\end{itemize}
Interacting particles usually exhibit many or all of these 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.   From the point of view of calorimetry, what 
we are most interested in is understanding the relationship between 
the energy of the incident particle and the measured quantities.

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 things such as 
stable, super-symmetric particles  that do not interact in material).  
This is done using the missing energy techniques described earlier, 
and require both good energy calorimeter 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. Since the behaviour of an EM 
shower is relatively straightforward to understand, I will start with a 
detailed discussion of the issues raised by EM calorimetry.  This 
will provide us with most of the concepts required for an
understanding of hadronic showers and the special problems they 
present.

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

The interaction of a photon or lepton 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 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}
This is illustrated in Fig. \ref{fig: dEdx loss for EM}\ where we 
plot the average energy loss for both electrons and photons as a 
function of their energy, showing the relative size of each of the 
dominant energy-loss mechanisms.
\begin{figure}
\vspace{2in}
\caption{The average energy loss of an electron (a) and a photon 
(b) as a function of their energy.  The various contributions to the 
energy loss are illustrated. }
\label{fig: dEdx loss for EM}
\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}},
\end{eqnarray}
where $\Xzero$ is the ``radiation length'' and is a characteristic
of each material.  For heavy materials, the formula $\Xzero \sim 
180 A / Z^2$\ g/cm$^2$\ provides a reasonable estimate, where 
$A$\ is the atomic weight of the material (N.B.   Radiation lengths 
are often expressed in terms of the radiation length as defined 
above times the density of the material, as this product often 
appears in various 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 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 into the material) scales 
with the radiation length $\Xzero$\ while the lateral profile is given 
by the ``Moliere radius'' $\rho_M$, which  for heavy materials is 
given by
\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 
Bremsstrahlung and multiple scattering of the electrons in
the medium.

\subsection{EM Energy Resolution}
The ``intrinsic'' resolution of an EM calorimeter is given by the 
fluctuations in the fraction of detected 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 of $e^\pm$'s in the shower, $T$.  We can 
estimate the total track length 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 that 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 intrinisc to an EM 
shower and is plotted in Fig. \ref{fig: energy fraction}.
\begin{figure}
\vspace{3in}
\caption{The fraction of energy in an EM shower carried by 
electrons with energies above a threshold vs the energy threshold. 
}
\label{fig: energy fraction}
\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 approximated by 
$N\sim E/\eta$.  The statistical fluctuations in this are given by
\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 measurement, 
fluctuations in the fraction of energy that leaks out of the 
calorimeter (typically through the back, though depending on 
geometry transverse leakage may also be significant) also increases 
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
(the criteria for one of the SSC EM calorimeters is 25$\Xzero$).

\subsection{Samplig Effects}

Up to this point, we have discussed homogeneous calorimeters and 
have avoided discussing how one measures the ionization energy 
loss in the calorimeter.  There are many schemes for performing 
this measurement:  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 material and the active detector are the same 
component.  In most other calorimeters, one ``samples'' the 
ionization by interleaving plates of absorbers and active detectors. 
There are many implementations of this scheme;  popular methods 
include
\begin{itemize}
\item absorber interleaved with scintillator plates;
\item absorber matrix with scintillating fibres; and 
\item absorber immersed in a liquid ionization detector, which 
could be a cryogenic liquid such as liquid Argon, or a ``warm'' 
liquid such as TMP or TMS.
\end{itemize}
The most important resolution effect in a sampling EM calorimeter 
is usually due to what we call ``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 mechanical construction of 
an EM calorimeter that is segmented into a large number of 
separate cells or towers.  These can be viewed as uncertainties in 
the calibration of the device and will be discussed separately 
below.

\subsection{Hadronic Showers}
\subsubsection{Introduction}
A high-energy hadron interacting in a material can lose energy in a 
large 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.  We can categorize the 
primary energy dissipation processes:
\begin{itemize}
\item the binding energy of nuclear systems that are generated by 
the low-energy nuclear reactions; 
\item EM showers that result from $\gamma$'s generated in  the 
electromagnetic decay of excited hadrons;
\item and charged hadron \dEdx\ loss
\end{itemize}
The response of a calorimeter to a hadron shower depends on how 
the device responds to energy deposited by each of these 
processes.

Empirically, materials are characterized by their nuclear 
``absorption length'' $\lambda$, 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.

A typical hadron calorimeter responds differently when an incident 
hadron  shower has a different structure.  The particles that are 
produce in a hadron shower are a melange
of different species, ranging from particles that interact with the 
calorimeter primarily through electromagnetic interactions (such as 
$e^\pm$'s and $\gamma$'s)  to strongly interacting hadrons to 
particles that interact only weakly (such as $\nu$\ from $K$\ and 
$\pi$\ decays).  The number of particles of each type fluctuates a 
great deal from one shower to the next.  Because the calorimeter 
responds differently to each species, this causes large fluctuations 
in the calorimeter response to hadron showers with identical 
energies.  This effect adds to the uncertainties in the calorimeter 
hadron shower measurement  that arise from sampling.  

\subsubsection{The Issue of Compensation}
One of the obvious differences in calorimeter response arise from 
differences in the way electromagnetic and hadronic energy is 
deposited and detected by the device.  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 the showers 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 not be visible.  This 
results in less energy 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.

One attempt to fix this problem was developed by the CDHS
collaboration, which has an iron and concrete calorimeter that is 
intrinsically non-compensating.  They realized that the observed 
longitudinal development of the shower gave 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).  Since there calorimeter measured the longitudinal energy 
profile, 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}\ where we show 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.  
A detailed understanding of this effect has only recently been 
realized.
\begin{figure}
\vspace{3in}
\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.  }
\label{fig: CDHS}
\end{figure}

\subsubsection{Development of Compensating Calorimeters}
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 U$_{238}$\ 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.  However a 
detailed understanding of why this device performed so well was 
developed  many years later, when detailed Monte Carlo 
calculations began to reliably predict the response of a hadron 
calorimeter as a function of its composition.  We now understand 
the $e/h$\ response to be dictated by
\begin{itemize}
\item presence of hydrogen-rich materials that increase the flux
of low-energy baryons in the shower.
\item nuclear effects occuring at the 1 MeV energy level that
``release'' energy on the time scale of order 100 ns, which
can increase the effective response.
\end{itemize}
One can now develop a design for a compensating calorimeter with 
almost any absorber one desires, although Uranium is still a natural 
choice because of its density and because it compensates well in 
the presence of plastic scintillator, which is an ideal choice for the 
detector material.  

The ZEUS detector being built at DESY for the study of $ep$\ 
collisions at HERA utilizes such a calorimeter, which exhibits very 
good hadronic energy resolution, as shown in Fig \ref{fig: ZEUS 
performance}\ where we plot the hadronic energy resolution of the 
detector as a function of the incident hadron energy.  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{3in}
\caption{The energy response of the ZEUS  calorimeter as a 
function of the incident hadron's energy. }
\label{fig: ZEUS performance}
\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, which 
was known only to $\sim 3$\%.   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 calorimeter energy 
scales has been by performing this calibration in a test beam where 
it is possible to directly establish an absolute incident energy-
response relationship.  Since the response may vary significantly 
from one module to the next, this calibration is typically performed 
for each module or a or a significant
fraction of the modules.

However, it is usually necessary to monitor this energy scale {\it in 
situ}\ in order to verify the energy scale 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 calorimeter with a Uranium absorber) to the calibration of the 
detector using known physics processes.

At an $e^+e^-$\ collider, Bhabha scattering 
($e^+e^- \rightarrow e^+e^-$)  is usually 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 used 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 
$J/\Psi\rightarrow\mu^+\mu^-$.  The UA2  collaboration calibrated 
each  module of their calorimeter in a test beam.  However it is 
diffuclt to use these techniques to obtain absolute energy scales that 
contribute ``constant terms'' in the resolution function much better 
than $\sim1$\%.

\subsection{Momentum Analysis}
The inherent accuacy of a momentum measurement depends on 
the accuracy of the measured charged particle trajectory 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 straight-
through's.  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 Mass}, 
whicj shows the invariant di-muon mass distribution recorded by 
the CDF detector.  One can infer from the clear $J/\Psi$\  and 
$\Upsilon$\ mass peaks resonant masses of 
$m_{J/\Psi} = 3.???\pm??$\ and $m_\Upsilon = 10.??\pm??$.  
Both of these masses are consistent with the world average values 
of ???? and ??? \cite{ref: PDG}, and therefore verify the 
momentum scale of the CDF detector to ??\%.
\begin{figure}
\vspace{3in}
\caption{The dim-muon invariant mass distribution observed by the 
CDF detector for candidate $J/\Psi$\ and $\Upsilon$\ events.  }
\label{fig: JPsi Mass}
\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 the event interactions that will be recorded and how these 
criteria are implemented.   The detector trigger has 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 interesting collision.  This contrasts with thesituation 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 
providing 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: trigger rates}.  
\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 trigger rates at the CDF and Aleph detectors at each 
level of trigger decisions.  The difference in rate reflects the 
relative ratio of interesting signal event rate to overall interaction 
rate at each collider. } 
\label{tab: trigger rates}
\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: ARGUS Bs}, which shows an event in which two 
B meson decays have been unambiguously reconstructed by 
identifying most of the charged particles in the interaction.  The 
decays were
\begin{eqnarray}
B B \rightarrow
\end{eqnarray}
The particle identification was an essential element of the analysis 
in that 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.  An example of 
the former technique is electron identification using the different 
properties of showers generated by an electron and other charged 
hadrons. The velocity measurement is typically made by one of 
several techniques:
\begin{itemize}
\item ionization (\dEdx)
\item time-of-flight (TOF)
\item Cerenkov radiation
\end{itemize}
These methods have very different capabilities and limitations, and 
in particular have discrete ranges of momenta in which they 
function.

\subsection{Particle ID Using Calorimetry}
The difference between an EM and a hadronic shower is often 
used to discriminate between electrons (and $\gamma$'s) and 
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 detectors 
imbedded in (or interleaved with)  the absorber.  Often, one 
employs a calorimeter in this role; an EM calorimeter is 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.  
In such systems, the face of the calorimeters are divided relatively 
finely into towers, so that the transverse shape of the showers can 
be measured.  A schematic of such a system is shown in Fig. 
\ref{fig: EM schematic}.
\begin{figure}
\vspace{3in}
\caption{A schematic view of a calorimeter system designed to 
seperate electrons and photons from charged and neutral hadrons.  
This system has been implemented in the CDF detector operating 
at the Tevatron collider. }
\label{fig: EM schematic}

The performance of such devices is characterized by the electron 
identification efficiency and the hadronic rejection, where the latter 
is often characterized the fraction of hadronic showers 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 $>80$\%.  One 
limitation of this sort ot scheme is that it requires the
lepton 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.

A calorimeter can also 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 usuall 
shower.  This information alone can provide rejections of order 
$10^{-1}$\ and $10^{-2}$\ 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, sicne these will be filtered out in 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 over $10^3$\ for particles 
with momenta in excess of several hundred \GeVc.  The sources of 
fake muon candidates in such a detector are 1) ``interacting punch-
through,'' where a particle showers in the absorber but some 
number of secondaries manage to leak out the back, 2) ``non-
interacting punch-through,'' where a charged hadron passes 
through the absorber without interacting, and 3) decays in flight, 
which result from a charged hadron decay 
$h\rightarrow\mu\nu_\mu X$\ generating a $\mu$\ that then 
registers as a $\mu$\ in the detector.  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.''  In most setups, these 
backgrounds tend to limit the system to charged hadron rejections 
of order $10^3$.  

\subsection{Transition Radiation Detectors}

When the speed of a particle in a medium exceeds that of light in 
the same 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 a ``transition radiation'' detector.  
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 up to ??.

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.
\begin{figure}
\vspace{3in}
\caption{The number of clusters oberved in the x-ray detector of a 
prototype TRD for pions  a) and for electrons b). }
\label{fig: TRD}
\end{figure}

\subsection{Ionization Measurements}

The ionization energy loss of a particle varies by a factor of $\sim 
1.5$\ 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 the particle's 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 however,  by throwing away those measurements that 
have the highest observed \dEdx\  (people often discard 30-40\%\ 
of the measurements).  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 provided by 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 the 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.

\section{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 slights can provide particle ID up to 
particle 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 for a particle is given by the
refractive index in the medium, $n$
\begin{eqnarray}
\gamma > 1/ sqrt{1 - 1/n^2}
\end{eqnarray}
For a particle with a given 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.  For example, 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 separate a number of particle species. 
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).  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} ({{1}\over{/\beta n}}),
\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 also 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 that is of order 1 mm.  The devices that have been 
implemented in large scale detectors use a gaseous photocathode
(typically 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}
\vspace{3in}
\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 
seperation 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}
