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A Appendix: The Greek Alphabet

lower upper case case English name Qronunciation a A alpha ß B beta BAY-ta 'Y r gamma 5 ~ delta E E epsilon ( Z zeta ZAY-ta 'fl H eta AY-ta e e theta THAY-ta L r iota K, K kappa ,\ A lambda f-L M mu MEW v N nu ~ - xi 0 0 omicron 7r II pi P P rho ROE (J ~ sigma T T TAOW 'U Y upsilon cjJ phi X X chi 1jJ W psi SrGH w n omega o-MEG-a B Appendix: Glossary

accelerator: A machine used to accelerate to high speeds (and thus high , as compared to their rest -energy). angular moment um: Angular moment um is a conserved quantity, which is used to describe rotational much like moment um for linear motion. Rotational motion can be orbital motion of two bodies around one another or the rotation of a rigid body. The intrinsic angular moment um of a is called "." In mechanics, angular moment um and spin are quantized quantities: They can only have certain discrete values, measured in multiples of Ti, which is Planck's constant h divided by 21f. : A process in which a particle meets its corresponding and both disappear. The energy appears in some other form, perhaps as a different particle and its antiparticle (and their ), perhaps as many , and perhaps as a single, neutral , such as a ZO boson. The produced particles may be any combination allowed by , , electric, and other charge types and by other rules. antifermion: The antiparticle of a . See also antiparticle. antirnatter: Material made from antifermions. We define the 212 Glossary

that are common in our as and their as antirnatter . In the particle theory, no apriori distinction exists between matter and antirnatter . The asymmetry of the universe between these two classes of particles is a deep puzzle for which we are not yet completely sure of an explanation. antiparticle: For every fermion type, another fermion type exists that has exact1y the same mass but the opposite value of all other charges (quantum numbers). This is called the antiparticle. For example, the antiparticle of an is a particle of positive called the . also have antiparticles, except for those that have zero value for all charges, for example, a or a composite boson made from a and its corre• sponding antiquark. In this case, the particle and the antiparticle have no differences; they are the same object. antiquark: The antiparticle of a quark. An antiquark is denoted by putting a bar over the corresponding quark symbol (d, u, s, etc .. ). astrophysics: The of astronomical objects such as stars and galaxies. B Factory: An accelerator designed to maximize the production of B mesons. The properties of the B mesons are then studied with specialized detectors. [BARE-ee-on]: A made from three The (uud) and the (udd) are both . They may also contain additional quark-antiquark pairs. baryon-antibaryon asymmetry: The that the uni• verse contains many baryons but few antibaryons; a fact that needs explanation. beam: The particle stream produced by an accelerator usually clustered in bunches. theory: The theory of an expanding universe that begins as an infinitely dense and hot medium. The initial instant is called the Big Bang. boson [BOZE-on]: A particle that has integer intrinsic angular momentum (spin) measured in units of 1i (spin = 0,1,2, ... ). All particles are either fermions or bosons. The particles associated B. Glossary 213 with all fundamental interactions () are bosons. Composite particles with even numbers of fermion constituents (quarks) are also bosons. (b): The fifth fiavor of quark (in order of increasing mass) , with electric charge -1/3. calorimeter: A device that can measure the energy deposited in it (originally, devices to measure thermal energy deposited, using change of temperaturej particle physicists use the word for any energy-measuring device). CERN: The major European international accelerator laboratory located near Geneva, Switzerland. charge: A quantum number carried by a particle. This quantum number determines whether the particle can participate in an interaction process. A particle with electric charge has electrical interactions, one with strong charge has strong interactions, etc. : The observation that electric charge is conserved in any process of transformation of one group of particle into another. (c): The fourth fiavor of quark (in order of increasing mass) , with electric charge +2/3. collider: An accelerator in which two beams traveling in opposite directions are steered together to provide high-energy collisions between the particles in one beam and those in the other. colliding-beam experiments: Experiments done at colliders. : The quantum number that determines participation in strong interactions; quarks and carry nonzero color charges. color neutral: An object with no net color charge. For composites made of color-charged particles, the rules of neutralization are complex. Three quarks (baryon) or a quark plus an antiquark () can both form color-neutral combinations. confinement: The property of the strong interactions by which quarks or gluons are never found separately but only inside color• neutral composite objects. 214 Glossary

conservation: When a quantity (e.g., electric charge, energy, or moment um) is conserved, it is the same after areaction between particles as it was before. cosmology: The study of the history of the universe. : Matter that is in space but is not visible to us because it emits no by which we can observe it. The motion of stars around the centers of their galaxies implies that about 90% of the matter in a typical galaxy is dark. Physicists speculate that dark matter also exists between the galaxies, but this is harder to verify. decay: A process in which a particle disappears and in its place two or more different particles appear. The sum of the of the produced particles is always less than the mass of the original particle. (The mass-energy is conserved, however.) detector: Any device used to sense the passage of a particle. Also, the word detector is used for a collection of such devices designed so that each serves a particular purpose in allowing physicists to reconstruct particle events. (d): The second flavor of quark (in order of increasing mass), with electric charge -1/3. electric charge: The quantum number that determines participa• tion in electromagnetic interactions. electromagnetic interaction: The interaction due to electric charge; this includes magnetic effects, which have to do with moving electric charges. electron [e-LEC-tron] (e): The least-massive electrically charged particle, hence, absolutely stable. It is the most common , with electric charge -1. : In the , electromagnetic and weak interactions are related (unified); physicists use the term electroweak to encompass both of them. : What occurs when two particles collide or a single particle decays. Particle theories predict the probabilities of various possible events occurring when many similar collisions or decays are studied. They cannot predict the outcome for any single event. B. Glossary 215

exclusion principle: See fermion. : Fermi National Accelerator Laboratory in Batavia, Illinois (near Chicago). N amed for pioneer . fermion [FARE-mee-on]: Any particle that has odd, half-integer (1/2, 3/2, ... ) intrinsic angular momentum (spin), measured in units of n. As a consequence of this peculiar angular momentum, fermions obey a rule called the Pauli Exclusion Principle, which states that no two fermions can exist in the same state at the same place and . Many of the properties of ordinary matter arise because of this rule. , , and are all fermions, as are all fundamental matter particles, quarks and . fixed-target experiment: An experiment in which the beam of particles from an accelerator is directed at a stationary (or nearly stationary) target. The target may be asolid, a tank containing liquid or gas, or a gas jet. flavor: The name used for the different quark types (up, down, strange, charm, bottom, top) and for the different lepton types (elec• tron, , tau). For each charged lepton flavor, a corresponding flavor exists. In other words, flavor is the quantum number that distinguishes the different quark/lepton types. Each flavor of quark and charged lepton has a different mass. For , we do not yet know if they have a mass or what the masses are. freeze out: As the universe expands and cools, the probability of any collision-driven process decreases, because the rate of the necessary collisions decreases. A process can be ignored when the average time between collisions is long compared to the age of the universe at that time. Such a process is then said to have frozen out. : In the Standard Model, the funda• mental interactions are the strong, electromagnetic, weak, and gravitational interactions. At least one more fundamental inter• action (Riggs) is in the theory; it is responsible for fundamental particle masses. Five interaction types are all that are needed to explain all observed physical phenomena. fundamental particle: A particle with no internal substructure. 216 Glossary

In the Standard Model, the quarks, leptons, , gluons, W± bosons, and ZO bosons are fundamental. All other objects are made from these. galaxy: A collection of stars held together by gravitational forces. : The theory of gravitation formulated by Einstein. generation: A set of one of each charge type of quark and lepton, grouped by mass. The first generation contains the up and down quarks, the electron, and the . [GLUE-on] (g): The carrier particle of strong interactions. : Any of a class of theories that contain the Standard Model, but go beyond it to predict furt her types of interactions mediated by particles with masses of order 10 15 GeV /e 2 . At large energies compared to this mass ( e2 ), the strong, electromagnetic, and weak interactions are seen as only different aspects of one unified interaction. gravitational interaction: The interaction of particles due to their mass-energy. : The carrier particle of the gravitational interactions (not yet directly observed). hadron [RAD-ron]: A particle made of strongly interacting constituents (quarks and/or gluons). These include the mesons and baryons. Such particles participate in residual strong interactions. half-life: The rate of decay of a radioactive material measured by how long it would take for half of the in a given bunch to have randomly decayed. Riggs boson: The carrier particle (or quantum excitation) of the additional needed to introduce particle masses into the Standard Model (not yet observed). interaction: A process in which a particle decays or annihilates or it responds to a force due to the presence of another particle (as in a collision). Also used to me an the underlying property of the theory that causes such effects. jet: Depending on their energy, the quarks and gluons emerging from a collision will materialize into 5-30 particles (mostly mesons B. Glossary 217

and baryons). At high momentum, these particles will appear in clusters called "jets," that is, in groups of particles moving in roughly the same direction, centered about the path of the original quark or gluon. (K): A meson containing a and an anti-up (or an anti-down) quark, or an anti-strange quark and an up (or down) quark. lepton [LEP-tahn]: A fundamental fermion that does not partici• pate in strong interactions. The electrically charged leptons are the electron (e), muon (/L), tau (T), and their antiparticles. Electrically neutral leptons are called neutrinos (v). LHC: The at the CERN laboratory in Geneva, Switzerland. LHC will collide protons into protons at a center-of-mass energy of ab out 14 TeV. When completed in the year 2005, it will be the most powerful in the world. It is hoped that it will unlock many of the remaining secrets of particle physics. light year: An astronomical unit of length. A light year (ly) is the distance light travels during a year; 1 ly = 0.9461 . 1016 m. lifetime: The time between the creation and the decay of a type of particle. The lifetime of an individual particle cannot be predicted. We can just measure an average (or mean) lifetime by observing the random decay in a sampie of a given type of unstable particles. linac: An abbreviation for linear accelerator, that is, an accelerator that is straight. mass: The mass (m) of a particle is the mass defined by the energy of the isolated (free) particle at rest, divided by c2 . When particle physicists use the word "rnass," they always me an the "rest mass" (m) of the object in question. The total energy of a free particle is given by

where p is the momentum of the particle. Note that for p = 0 this simplifies to Einstein's famous E = mc2 • For a general particle with mass and momentum, it can also be written as E = 'Ymc2, where 'Y = 1/ }1 - v 2 / c2 . Some text books on identify 'Ym as the "rnass" of a moving particle; this definition is not used 218 Glossary

in particle physics. The quantity Eincludes both the mass-energy and the kinetic energy. meson [MEZ-on]: A hadron made from an even number of quark constituents. The basic structure of most mesons is one quark and one antiquark; some of multiples of this. microwave: An electromagnetic wave with wavelength in the micrometer range. muon [MEW-on] (J.L): The second fiavor of charged lepton (in order of increasing mass), with electric charge -l. muon chamber: The outer layers of a particle detector capable of registering tracks of charged particles. Except for the chargeless neutrinos, only reach this layer from the collision point. neutral: Having a net charge equal to zero. Unless specified otherwise, it usually refers to electric charge. neutrino [new-TREE-no] (v): A lepton with no electric charge. Neutrinos participate only in weak and gravitational interactions and therefore are very difficult to detect. Three known types of neutrino exist, all of which are very light and could possibly even have zero mass. neutron [new-TRON] (n): A baryon with electric charge zero; it is a fermion with a basic structure of two down quarks and one (held together by gluons). The neutral component of an is made from neutrons. Different of the same element are distinguished by having different numbers of neutrons in their nucleus. : A proton or a neutron; that is, one of the particles that makes up a nucleus. nucleosynthesis: The process by which protons and neutrons combined to form nuclei in the early universe. nucleus: A collection of neutrons and protons that forms the core of an (plural: nuclei). parsec (pc): An astronomical unit of length. It is equal to the distance at which the sun-Earth separation subtends an angle of one second; 1 pc = 3.2616 light years. particle: A subatomic object with adefinite mass and charge. B. Glossary 219 photon [FOE-tahn] (-y): The carrier particle of electromagnetic interactions. [PIE-on] (7T): The least-massive type of meson, can have electric charges ±1 or O. plasma: Agas of charged particles. positron [PAUSE-i-tron] (e+): The antiparticle of the electron. proton [PRO-tahn] (p): The most common hadron, a baryon with electric charge (+ 1) equal and opposite to that of the electron ( -1). Protons have a basic structure of two up quarks and one down quark (bound together by gluons). The nucleus of a atom is a proton. A nucleus with electric charge Z contains Z protons; therefore, the number of protons is what distinguishes the different chemical elements. quantum: The smallest discrete amount of any quantity (plural: quanta). : The laws of physics that apply on very small scales. The essential feature is that energy, momentum, and angular moment um as well as charges come in discrete amounts called quanta. quark [KWORK] (q): A fundamental fermion that has strong interactions. Quarks have electric charge of either 2/3 (up, charm, top) or -1/3 (down, strange, bottom) in units where the proton charge is l. residual interaction: Interaction between objects that do not carry acharge but do contain constituents that have charge. Except for those chemical substances involving electrically charged ions, much of is due to residual electromagnetic interactions between electrically neutral atoms. The residual between protons and neutrons, due to the strong charges of their quark constituents, is responsible for the binding of the nucleus. rest mass: See mass. scintillation: A charged particle traversing matter leaves behind it a wake of excited . Certain types of molecules will release a small fraction of this energy as light. This light can be detected by a phototube in a detector. 220 Glossary

SLAC: The Stanford Linear Accelerator Center in Stanford, Cali• fornia. spin: Intrinsic angular moment um of a particle, given in units of n, the quantum unit of angular momentum, where n = h/27f = 6.58 X 10-34 J s. Spin is a characteristic property for each type of particle. stahle: Does not decay. A particle is stable if no processes exist in which the particle disappears and in its place two or more different particles appear. Standard Model: Physicists' name for the theory of fundamental particles and their interactions, as described in this book. It is widely tested and accepted as correct by particle physicists. strange quark (s): The third flavor of quark (in order of increasing mass), with electric charge -1/3. strong interaction: The interaction responsible for binding quarks, antiquarks, and gluons to make . Residual strong interactions provide the nuclear binding force. suhatomic particle: Any particle that is small compared to the size of the atom. : An old star that has burnt most of its hydrogen collapses due to gravitational attraction, but then explodes from the onset of nuclear burning of more massive elements. synchrotron: A type of circular accelerator in which the particles travel in synchronized bunches at fixed radius. tau [TAOW] lepton: The third flavor of charged lepton (in order of increasing mass) , wi th electric charge -l. Collider: An accelerator at Fermilab that collides protons and with center-of-mass energy of 2 TeV (2000 GeV). : The sixth fiavor of quark (in order of increasing mass) , with electric charge 2/3. Its mass is much greater than any other quark or lepton. track: The record of the path of a particle traversing a detector. tracking: The reconstruction of a "track" left in a detector by the passage of a particle through the detector. B. Glossary 221

Uncertainty Principle: The quantum principle, first formulated by Heisenberg, that states that it is not possible to know exactly both the x and the moment um p of an object at the same time, b..xb..p ~ ~li. It can be written as b..Eb..t ~ ~li, where b..E means the uncertainty in energy and b..t means the uncertainty in lifetime of astate (see ). up quark: The least-massive flavor of quark, with electric charge 2/3. vertex detector: A detector placed very close to the collision point in a colliding-beam experiment so that tracks coming from the decay of a short-lived particle produced in the collision can be accurately reconstructed and seen to emerge from a "vertex" point that is different from the collision point. virtual particle: A particle that exists only for an extremely brief instant as an intermediary in a process. The intermediate or virtual particle stages of a process cannot be directly observed. If they were observed, we might think that conservation of energy was violated. However, the Heisenberg (which can be written as b..E . b..t > li/2), allows an apparent violation of the conservation of energy. If one sees only the initial decaying particle (such as a meson with the c quark) and the final decay products (such as s + l/e + e+), one observes that energy is conserved. The "virtual" particle (such as the W±) exists for such a short time that it can never be observed. "w± boson: A carrier particle of the weak interactions. It is involved in all electric-charge-changing weak processes. : The interaction responsible for all processes in which flavor changes, hence, for the instability of heavy quarks and leptons, and particles that contain them. Weak interactions that do not change fla,vor (or charge) have also been observed. 2fJ boson: A carrier particle of weak interactions. It is involved in all weak processes that do not change flavor. c

Appendix: How Detectors Work

C .1. Tracking Particles and Measuring a Particles Mornen• turn We can measure the direction and moment um of charged particles using a combination of a tracking chamber and a strong magnet. Since high-energy charged particles leave an trail in agas volume without losing a significant fraction of their total energy, we can re cord the tracks over distances large enough to measure both their initial direction and the bending of the track due to the magnetic . This information allows us to determine each particle's moment um and the sign of its charge. For example, a computer-reconstructed particle track from a tracking device is shown in Fig. C.I and a numerical example of calculating the moment um of a particle can be found in Ap• pendix D.5.2. Some tracking devices are described in more detail in the following sections. 224 How Detectors Work

Fig. C.l: Computer-reconstructed tracks from an electron-positron annihilation event recorded by a cylindrical multiwire proportional chamber in the TASSO collider detector. The white dots mark the wires perpendicular to the plane. Note the curvature of the tracks caused by a magnetic field, which is also perpendicular to the plane. The TASSO detector was located at the PETRA collider at DESY.

C.1.1. Vertex Detectors Those hadrons that contain heavy quarks and decay only via the weak interaction (such as the D+ = cd) travel about 0.2 mm or less before decaying. Because the tracks of the decay product emerge from the decay point, we call this point a "vertex." Reconstructing this decay point requires a high-resolution tracking device called a "vertex detector" as dose as possible to the production point (where the initial collision occurs) (see Fig. C.2). This device must be able to distinguish the production point from the decay point (vertex ). If the vertex is inside the beam pipe, it cannot be detected but can be pinpointed by extrapolating the observed tracks back to their intersection. When a vertex is found that does not correspond to the collision point that produced the first outgoing partides, this indicates the decay of a very short-lived undetected partide. The vertex detector may use any charged partide tracking method; popular versions involve small proportional counters or drift chambers or silicon strip devices. C.1. Tracking Particles and Measuring a Particles Momentum 225

Tracking View

3 meters

Two Vertex View Tevatron

~;t&:::::::b=svx tags

.....f---- 5 centimeters

Magnlflcatlon

Prlmary Secondary\ Vertex ,... - Vertex ~ Ellipses ...... f---- 5 mm ..

Fig. C.2: Example of the reconstruction of the decay point from particle tracks in a vertex detector. The three views: Tracking View, Two Vertex View, and Magnijication show the same event in increasingly bigger scales. 226 How Detectors Work

C.1.2. Proportional Counters The simplest device to track charged particles is a cylindrical metal tube, filled with an appropriate gas. A thin, central wire (the "anode") at positive potential is placed in the tube (which itself serves as the "cathode"), producing a radial electric field. Any electron liberated in the gas by the ionization process will drift towards the anode wire, gaining energy from the electric field. If it gains sufficient energy to exceed the ionization energy of the gas, fresh ions are liberated. A chain of such processes results in an "avalanche" of electrons at the anode wire. This avalanche can be sensed as a current in the wire by a suitable electronic circuit. The device is called a proportional tube or chamber, because the signal is proportional to the energy deposited in the gas by the original partiele. C.1.3. Drift Chambers A modern refinement of the idea of proportional counters led to the device called a drift chamber. This chamber contains many anode wires (wires at positive potential), each surrounded by a grid of cathode wires (negative potential relative to the anode wires). Each anode wire collects ions from the region between itself and the nearest set of cathode wires (see Fig. C.3). Because the speed of the high-energy partiele is much greater than that of the ions, the "drift time," that is, the time taken for the ionization to travel from its point of origination to the wire, is proportional to the minimum distance between the track and the anode wire. Since the outward-going partiele travels at elose to the speed of light, its time of passage through the chamber is known and the time of arrival of the ionization at the wire can be measured. Therefore, the drift time can be used to determine accurately the nearest approach of the line of ionization and thus to reconstruct the path of the initiating charged partiele. In a drift chamber, the interwire spacing can be several cen• timeters while still permitting spatial resolution of tracks to about 100 micrometers (1 micrometer = 10-6 m). A typical design of the set of wires forming the basic unit or "celI" of a drift chamber is shown in Figures C.3 and C.4. 0.1. Tracking Particles and Measuring a Particles Momentum 227

Grid Cathode Wires

Fig. C.3: The layout of the wires of a cylindrical multiwire chamber of a collider detector (Mark II from SLAC). 228 How Detectors Work

Fig. CA: The design üf a cylindrical drift chamber für a cüllider detector: MARK II SLAC. C.1. 'Iracking Particles and Measuring a Particles Momentum 229

C.1.4. Silicon Strip Devices A modern option for tracking uses a thin layer of silicon that can be built into an electronic circuit that gives a signal when a charged particle passes through the silicon. The silicon can be very finely segmented into strips or pixels. They may be used for the inner tracking region or vertex detector, where high resolution is most important (see Fig. C.5).

5 III

50 j.lm Pitch 1

Fig. C.5: Silicon microstrip detector. 230 How Detectors Work

BASIC PHYSICS Silicon Microstrip Detectors (SMDs) Modern microelectronic techniques make possible the sil• icon microstrip detectors. How do SMDs work? When a charged particle traverses a thin crystal of pure silicon, it deposits energy that frees electric charges to migrate. If an appropriate voltage is applied across the crystal, the migrating charges will produce signals on metal electrodes. The signals, suitably amplified by sensitive electronics off the silicon plate, are digitized and recorded for later analysis. On SMDs, the electrodes are closely spaced strips, typically 25 to 50 micros from center to center, with amplifiers attached to each strip. The large number of strips allows experimenters to record the passage of many charged particles through each detector, reduces the capacitative load on the fronts of the amplifiers, and improves the achievable spatial resolution. The SMD signal collection takes just a few billionths of a second, making SMDs useful in the intense high-rate environments that characterize more and more particle physics experiments. (Reproduced from BLAG Beam Line, vol. 28, no. 1, 1998).

C.2. Electromagnetic Calorimeters All charged particles lose energy as they pass through matter, because they ionize the atoms they encounter. In materials con• taining certain compounds known as scintillators, charged particles also lose energy by exciting the scintillator molecules. When these molecules make a transition back to their ground state, light is emitted; the material is said to scintillate. In clear plastic material containing scintillator compounds, both the passage of a charged particle and the amount of energy it deposits can be measured by capturing the scintillation light in a phototube (a device that converts light to an electrical signal via the photoelectric effect). For electrons with energy of order tens of megaelectronvolts (Me V), another phenomenon dominates the energy loss in solid materials. Because electrons are of very low mass, their paths are 0.2. Electromagnetic Oalorimeters 231

strongly deflected by the electric fields inside the atoms that they pass through. This causes them to radiate photons and thus lose energy. Each photon then typically creates an electron and positron pair. This electron and positron in turn lose energy by radiating further photons, and the cycle repeats itself until the energy is fully absorbed. Therefore, as an electron traverses a dense medium, it loses energy rapidly, producing a "shower" of electron-positron pairs along its path. The same shower phenomenon will be initiated if a high-energy photon arrives at this dense material, since such a photon creates electron-positron pairs in the field of an atom. To distinguish electrons from photons, one looks at whether a charged particle seen in the tracking region entered the calorimeter at the shower location.

EXPLANATION Identifying Electrons The strategy for identifying an electron among the hun• dreds of particles in an event is as follows: 1) it should leave a track in the tracking chamber, since it is charged; 2) it should leave most of its energy in the electromag• netic calorimeter and little energy in the hadronic calorimeter directly outside it; 3) since the electron mass is very small, the energy measured in the calorimeter should be equal to the momentum measured in the tracking chamber; 4) the track in the chamber should point in the same direction as the energy deposit in the electromag• netic calorimeter.

A device to measure electromagnetic showers is called a shower counter or an electromagnetic calorimeter. The energy deposited by all particles in the shower is equal to the initial particle energy, so the energy can be found if we measure a signal proportional to the ionization of all shower particles. Two kinds of electromagnetic calorimeters are most common: One consists of material, usually an inorganic crystal, such as cesium iodide, that emits light when 232 How Detectors Work

excited by the ionizing particles. The other consists of thin plates of a dense absorber, such as lead, separated by layers of gas or liquid sensitive to ionization, so that the ionizing particle path length is sampled. In either case, the signal is proportional to the energy of the incident electron or . Although a muon possesses exactly the same interactions as an electron, it is about 200 times more massive. This means that it passes through the electric field inside the atoms without significant deflection and therefore does not create a shower. It leaves just a very little signal in an electromagnetic calorimeter.

C.3. Hadron Calorimeters Until now, we have discussed no detector component that could detect hadrons that are electrically neutral and relatively stable, such as neutrons. The hadron calorimeter is designed to detect not only neutrons, but also charged hadrons (7[+, 7[-, K+, K-, and protons). Hadrons lose energy in passing through matter as they collide with the nuclei of the atoms. Considerably more material is required to absorb hadrons than photons or electrons-therefore, hadron calorimeters are made from dense material, usually steel or uranium. The hadron calorimeter is typically placed immediately outside the electromagnetic calorimeter. For charged hadrons, the calori• meter adds a complimentary energy measurement to the momentum measurement obtained from the tracking chamber. In many sit• uations, particularly at higher energies, the calorimetric energy measurement is more precise than the momentum measurement obtained from tracking. The charged particle directions, however, are measured considerably better by the tracking chamber. C.4. Hadron Identification In many detectors, we are satisfied to identify a particle as a charged hadron but cannot distinguish a proton from a pion (7[) from a kaon (K). Some detectors, however, have the capability of determining the mass of the produced hadrons and thereby distinguishing the identity of the particle. The mass is not measured directly, but can be determined if we are able to measure both the moment um and the velocity of the hadron (since particles of different mass have different speeds at the same momentum). 0.4. Hadron Identification 233

The speed can be determined by measuring the energy lost per unit length (!::1E I !::1x) by a particle traversing a gaseous medium. Over some range of speeds, this quantity depends on the speed and charge of the ionizing particle and on properties of the medium such as its , the amount of energy required to ionize its atoms, and its density.

The Cerenkov Detector Another method to measure the speed of a particle makes use of Cerenkov radiation. This radiation occurs when the speed v of a charged particle exceeds the velo city of light in a given medium, i.e., when vlc > Iln, where n is the refractive index ofthe medium. The Cerenkov radiation is (see Fig. C.6) emitted in a cone of half-angle () , the axis of the cone being the incident-particle direction. The angle () is given by the expression c cos() =• (C.I) nv

A Cerenkov detector is made from a transparent material and uses optical devices to measure the angle ().

ij/._ ..- --~ / ~erencov photons

aircraft or particle

vt ------... Fig. C.6: The Cerenkov effect and its analogy in aerodynamics. 234 How Detectors Work

Specialized devices are required to identify hadrons. In general, it is hard to use a single device to separate all of the charged particle types over the full range of momenta produced.

BASIC PHYSICS The Mach Cone A mechanical analogy to Cerenkov radiation is the mach cone, the wavefront originating from an aircraft moving at supersonic speed (see Fig. C.6).

C.5. Muon Detection Because the muon is so much more massive than the electron, it is deflected very little by the electric fields in the atoms that it passes through. Therefore, muons do not shower in the electromagnetic calorimeters. In addition, muons rarely undergo nuclear collisions in a dense absorber like steel, because they are not affected by the strong force. Hence, high-energy muons will travel large distances through steel before their energy is depleted due to ionization processes. Typically, they leave the detector before much of their energy is gone. Therefore, muon detection is achieved by placing an additional charged particle tracking device outside the hadron calorimeter and outside the magnet coil that produces the field for the inner (main) tracking chamber. The only charged particles produced at the collision point that can penetrate so much material (and remain energetic) are high-energy muons. The track trajectories in the outer region can be linked to the track trajectories that the muon made in the first tracking region. In addition, no significant energy should be deposited in the calorimeter. This is the way muons are identified. D

Appendix: Basic Physics Concepts Applied to Particles

Outline

D.l. Why Classical Physics Fails D.2. Force, Energy, and Momentum in Classical Physics D.3. Going Beyond Classical Physics: Energy, Momentum, Mass, and Time in Particle Physics D.4. Relating Momentum and Wavelength (Particles and Waves) D.5. Forces, Fields, and Charges D.6. The Mass of Composite Objects D.7. Lifetime and the Decay Law D.8. Angular Momentum and Spin D.9. The Heisenberg Uncertainty Principle D.l0. Note on Units

This appendix reviews some physics concepts that are essential to the understanding of particle physics. Concepts such as energy, momentum, force, mass, and velo city have much more specific meanings in physics than in everyday life. 236 Basic Physics Concepts Applied to Particles

This appendix does not replace an introductory physics text• book to define these concepts; it assurnes the reader has access to one. Our purpose here is to link the language and ideas, as typically presented in introductory physics courses, to the way that partiele physicists use and think ab out the same basic concepts. The physics that is based on everyday experience is called "elassical physics." In partiele physics, one must go beyond the definitions taught in introductory physics elasses (beyond elassical physics) to account for relativity and quantum mechanics. There• fore, we stress the points where partiele physics must go beyond Newtonian physics and use instead the more accurate equations of special relativity and quantum mechanics. While an elementary knowledge of calculus would benefit the reader of this appendix, most of the content can be understood without knowing calculus.

D.1. Why Classical Physics Fails Why is elassical physics not sufficient to describe the Standard Model? The physics we deal with in the world of partiele physics experiments differs from the physics experiments that we observe in the everyday world in two significant ways. First, partiele physicists often deal with partieles that are traveling at speeds very elose to the speed of light. We must use Einstein's Special Theory of Relativity to describe their rather than Newton's laws. Newton's laws are the approximate form only when all speeds are small compared to the speed of light (roughly 300,000 kilometers per second). Second, the partieles we deal with are very small, and for such objects, we must use the laws of quantum physics rather than elassical physics. Both these theories, special relativity and quantum mechanics, are built into the Standard Model of particles and interactions and have been tested over and again, with no disproofs found so far. Despite the theories' successes, objects of such sizes and speeds behave in ways that are unfamiliar and even see m to be counter to our common sense. How could physicists adopt such crazy ideas? The reason is simple enough. Common sense is based on our own experience, which takes place at small speeds compared to the D.2. Force, Energy, and Momentum in Classical Physics 237 speed of light; furthermore, we only observe objects made from many millions of atoms-never the individual atoms themselves. Everyday common sense simply should not be assumed to apply in the realm of individual particles. Instead, physicists have had to painstakingly learn the rules of this regime, testing the models again and again to be sure they could not be proved wrong. The statements made below are all extremely well-tested and well-understood properties of basic physics as seen in the world of particles.

D.2. Force, Energy, and Momentum in Classical Physics D.2.1. Forces and Momentum Before focusing on particle physics, let us discuss the ideas of force Fand momentum p in general~ Later, we will investigate the relationship between forces, force fields, and energy, but for now we focus on the effects rather than the causes of forces. Central to our considerations of a body in motion are its position r, its velocity v = ~, and its a = 1[. The usual form in which Newton's laws are taught are as follows. 1) A body remains in astate of rest or of unchanging motion in a straight line unless acted upon by a force (v is constant).

2) For any one body of mass m at any instant, the rate of change in velo city due to a force F on it is given by

F=ma, (D.l)

where a is acceleration, which is the rate of change of velocity = 1[. (In calculus, this is written ~).

3) If body A exerts a force F on body B, then at the same instant body B exerts a force of equal magnitude but in the opposite direction (-F) on body A. (This is sometimes referred to as the law of action and reaction.) There are three things we need to observe here, as follows.

* In this book our convention is to use boldface letters to represent vec• tor quantities, meaning those that have direction as weH as magnitude, and the same letter without boldface to represent the scalar quantity, meaning one with no implicit direction, that is, the magnitude of the vector. 238 Basic Physics Concepts Applied to Particles

Firstly, Law 1 is in some sense not reallyaseparate law at all. It could be thought of as arestatement of a consequence of Law 2: if F = 0 then a = 0 and the speed does not change. Secondly, Law 2 is a simplified version of a more general statement, which applies even if the mass is also changing, or even if it is zero. The more generally correct form is

(D.2)

(using calculus, we write F = ~~) or force equals rate of change of momentum. Momentum, p given by

p=mv, (D.3)

is a quantity that, like velo city, has both a magnitude and a direction. Written in the form Equation (D.2), Newton's law remains true for relativistic particles. Forces play the same role in relativistic dynamics as they do in the everyday dynamics of slow objects, they cause changes in momentum. Elementary physics courses typically deal only with constant forces, and thus constant . This is done just to keep the mathematics simple, the equality between the force and the rate of change of moment um is true at any instant, no matter how the force changes. The third observation is that Newton's Third Law now has a clear relationship to conservation of momentum. If two particles collide, each exerts a force on the other. The forces at any instant are equal and opposite; therefore, by the second law, the changes in moment um at any instant are equal and opposite, so the total moment um does not change. The fact that the total energy is also conserved is aseparate phenomenon, not to be understood just from Newton's laws. We will return to this point later. D.2. Force, Energy, and Momentum in Classical Physics 239

D.2.2. Energy Energy in our everyday warld comes in a huge variety of forms: motion (called kinetic), thermal (as heat) , sound, light (calIed radiant), electrical, chemical, etc. Each form seems to be something entirely different from the others. We learn, however, that energy can be transformed from one form to another, but never just disappear. It can, however, move around and spread, so it can be extremely difficult to keep track of it. It all seems quite ad hoc and mysterious. Many people are not able to define what energy actually iso Worse yet, they offer as adefinition that energy is the capacity to do work, in which work is defined as the change in energy due to the action of a force~a circular and hence meaningless definition!

Energy at Everyday Scales Each of the everyday forms of energy can be understood in terms of particle kinetic energy plus , as follows. 1) Thermal energy is the energy of the random motions of atoms, both the vibrations of atoms and of molecules and the translational motion of the molecules themselves (or of atoms for monatomic substances) in agas or a liquid. Temperature is a measure of the average energy per atom for each type of motion it can undergo. 2) Sound energy is also carried in the motion of atoms, but it is an organized motion, apressure wave traveling through gases, liquids, and solids. 3) Light energy is carried by a traveling electromagnetic wave. In the quantum world, we find that each photon carries a discrete amount of energy. 4) Electric currents also involve motion, electrons in motion due to an electromagnetic potential difference between two ends of a wire. It is the collisions due to this motion that makes the wires in a toaster get red hot and the filament of an incandescent electric light bulb glow white hot. 5) Perhaps the most mysterious type of energy when viewed from the human scale is stored chemical energy. Chemical processes can give off energy, for example, in a fire or in a 240 Basic Physics Concepts Applied to Particles

car engine where combustion pro duces thermal energy (which produces the pressure to drive a piston). But other chemical processes require energy to make them happen; for ex am pIe , in cooking, when heat added to an egg causes it to change its structure, what is going on? 6) A second type of stored energy that also seems mysterious at the human scale is gravitational potential energy. Somehow, when an object is raised above the surface of the Earth or taken up a hill, it stores up some energy. Both of the last 2 forms of energy can be related to energy stored in force fields, chemical energy in the electromagnetic force fields within molecules, and gravitational potential energy in the gravitational force field between the Earth and the object. Both can be called potential energy and will be discussed again in Section A.6 about force fields.

Kinetic Energy and Momentum In introductory physics courses, you meet two quantities related to the motion of a particle with mass m and velo city v:

momentum, p = mv, [see Eq. (D.3)] and kinetic energy, E kin , given by

(D.4)

a quantity that has a magnitude, but not an associated direction. In everyday usage, the concepts of moment um and energy are often not clearly distinguished, but in physics they play distinct, though related roles. Both of them are conserved quantities, which just means that the energy and moment um of the whole system do not change in any process. Conserved quantities are useful properties to keep track of in any particle collision or decay process because they limit the possible outcomes. D.3. Going Beyond Classical Physics 241

D.3. Going Beyond Classical Physics: Energy, Momentum, Mass, and Time in Particle Physics D.3.1. Frames of Reference The magnitude of velocity depends on the motion of the person observing it. Imagine two spaceships passing each other in empty space. A passenger on one would be confused as to whether 1) her ship was standing still and being passed by the other ship, 2) her ship was moving and the other ship was not moving, or 3) both ships were moving. Meanwhile, a passenger on the other ship would be equally confused. In other words velo city depends on the . This is certainly true for particles. Therefore, the values of kinetic energy and moment um of particles also depend on the frame of reference in which we measure the velocity. The marvel of the physics, built into the associated mathematics, is that both conservation of energy and conservation of moment um work no matter which (unaccelerated) frame of reference we use to define them and to study the collision. One exception to the frame dependence of velocities is the speed of light (or any other ) in empty space, which has the same magnitude for any observer. Although this is very odd by the standard of everyday experience, it is a firmly established property of light. It is a key feature of Einstein's special theory of relativity that light has the same speed relative to me whether I am sitting in my house or sitting in a plane passing above my house at 800 km an hour. All other properties of that theory can be derived from the independence of the speed of light on the reference frame plus the assumption that the laws of physics are the same for all (unaccelerated) observers. The "speed of light" is represented by the letter c and numerically is approximately 300,000 km per second. 242 Basic Physics Concepts Applied to Particles

D.3.2. Energy, Momentum, and Mass: Relativistic De• scription In particle physics, we must use more exact and slightly more complicated definitions for momentum and energy than those given above, because we deal with objects traveling at close to the speed of light. Physicists call this relativistic kinematics. Kinematics means the equations keeping track of conservation of energy and momentum. Relativistic kinematics means doing so using expressions that are correct for any value of v / c, where c is the speed of light. The relativistic equations for momentum p and total Energy E are

mv (D.5) p = -Jr:;=1=-=;(=v /=;=c~) 2

and

E = Vp2C2 + m 2c4 • (D.6) One may define a quantity "( I "(= , (D.7) VI - (V/C)2 such that p = "(mv. (D.8) Substituting in Equation (D.6), we find

E = "(mc2 • (D.9)

The definition of energy given in Equation (D.9) can be sepa• rated into two terms

(D.IO)

The first term mc2 is independent of the speed and is the mass-energy or the rest energy of the particle; the second is the D.3. Going Beyond Classical Physics 243

quantity called "kinetic energy" (for a low-speed object, it is ~mv2). The rest energy of any partide is its mass, or rather, since we use different units for energy and mass, the rest energy is related to the mass by the famous Einstein formula, E = mc2 . One can show (using calculus) that the relativistic energy and momentum definitions are equivalent to the nonrelativistic express ions when v/c is a small number. When (v/c) is very small, the Equation (D. 7) can be very accurately approximated by a sum of terms with increasing powers of (v / c):

where the ... means we have not written the infinite number of terms with higher powers of (v / c). Since (v / c) is small, each successive term is much smaller than the term before it. This gives, from Equations (D.8) and (D.9),

1 p = mv(1 + 2(V/C)2 + ... ) (D.12)

and (D.13)

The nonrelativistic expressions are then obtained simply by dropping the (V/C)2 (and higher terms) which are very small for low-speed objects. The usual, nonrelativistic expressions for kinetic energy Eq. (D.4) and moment um Equation (D.3) are approximate forms of the more exact forms. They are very good approximations when• ever (v/c) « 1, but no good at all as (v/c) gets dose to 1 (that is, v dose to c). In the everyday world, we deal with speeds where (v/c) is tiny. Even for a supersonic plane, (v/c) « 1/100. 244 Basic Physics Concepts Applied to Partic1es

.Exercise 1: Relativistic usage of energy, momentum, and mass 1) Calculate the percentage difference between the relativistic definition and the usuallow-speed definition of the moment um for a car (pick an appropriate mass) moving at 50 km per hour. (Hint: Use the power series expansion for I from above.) 2) Calculate the percentage difference between the relativistic (always correct) definition and the usual low-speed definition for the momentum for a electron moving at v = 0.99ge. What is the energy of this electron? (Hint: calculate ")

D.3.3. A Note About the Usage of the Word "Mass" Some introductory textbook sections on special relativity intro• duce the idea that the quantity M == ,m can be thought of as the mass of the moving particle. They use the notation mo for the "rest mass" of the particle (the quantity we write everywhere as m). This subterfuge has the advantage that it makes p = Mv and E = M e2 true equations for any speed V. Particle physicists do not use this trick, because the notion that there are frame-dependent and frame-independent properties reflects real physics. The mass m is a characteristic property of a particle type that is independent of the frame from which the particle is observed, while energy and moment um are frame dependent. From this point of view, it makes sense to talk about the "mass-energy or rest energy" of a particle of mass m, which is just the energy when p is zero, E = me2 , but it does not make sense to introduce a frame-dependent particle mass. We can rewrite the energy-momentum-mass relationship [Eq. (D.6)] as

(D.14)

If we can measure E and p separately (or E and v), then we can use this relationship to determine the mass of the particle in quest ion. Of course, as the particle gets closer and closer to the speed of light, this gets more difficult, because both E and pe get very big compared to me2 , and so we have to measure them extremely accurately to be able to evaluate the difference correctly. D.3. Going Beyond Classical Physics 245

.Exercise 2: About mass Determine how accurately you will need to measure the speed of a partiele that has energy 2 Ge V to determine whether it is a pion 7r (mass = 0.14 GeV /c 2 ) or a K meson (mass = 0.49 GeV /c 2 ). D.3.4. Conservation of Energy One of the beauties of looking at the world at the scale of fundamental particles is that energy and its conservation law can be understood. All forms of energy can be reduced to two. One form is the rest energy of particles and the energy associated with partieles' motion. The other is potential energy, which is seen to be energy stored in force fields. Potential energy can come from a gravitational force field between two massive objects, electromagnetic force fields between charged or magnetic objects, or a strong force field, between quarks and gluons.

Time and Distance in Special Relativity One frequently mentioned aspect of relativity is the so-called "dilation of time" for an observer (at rest) relative to an object moving with high velo city. People often find this hard to understand or believe, but in partiele physics, this effect is directly seen. When particles are accelerated to speeds elose to that of light, their lifetimes are greatly altered, and this is easily measured. Imagine, for example, a physicist observing a partiele that moves with speed v relative to hirn. He will realize that the partiele's "internal elock" runs slower by a factor

(D.15) than his laboratory watch, which is at rest relative to hirn. This effect is called "time dilation." The observer can confirm this if he measures the lifetime of the moving partiele, which will be extended by factor ,. In order to measure the lifetime, he can observe the distance the partiele travels relative to hirn until it decays. 246 Basic Physics Concepts Applied to Particles

.Exercise 3: Fast-moving pions

A pion at rest has an average lifetime of 2.6 x 10-8 S. • What is the lifetime an observer will measure, when the pion moves with a speed of v = 0.95 c relative to hirn? • How far (measured in the rest-frame of the observer) can the pion travel? • How far would the pion travel if there were no time dilation. Compare. • Calculate the kinetic energy of the pion. D.4. Relating Momentum and Wavelength (Particles and Waves) A Quick Look into Quantum Mechanics The of the observation being made determines whether it is more convenient to think of a particular effect as a traveling wave or as a traveling particle. Both light and electrons exhibit properties that, at the human scale, we think of as particle properties, e.g. discreteness, definite energy, count ability. Both light and electrons also, under different observational circumstances, exhibit properties we associate with waves; for example, they show interference effects (see the example below). Much of quantum mechanics is concerned with the particle-wave relationship. As a result, there is one more important equation for particles. Since all particles also behave as waves, they have adefinite wavelength >. related to their momentum by

p = hl>' , (D.16)

where his Planck's constant (h = 6.626 X 10-34 Js). This relationship is true for any part icle , whether or not it has a mass. It is the unique prescription for the moment um of a photon or any other particle that has zero mass. A particle with zero mass travels at the speed of light in any frame of reference. The relationship between momentum, energy, and mass given in Equation (D.6) remains true for zero-mass particles, but when m = 0, it can be written more simplyas E = pe (or E = hel>'). DA. Relating Momentum and Wavelength (Particles and Waves) 247 eExercise 4: Matter waves 1) Find the moment um (in units of eV je and mkgjs) for a photon of red light (wavelength 650 nm). 2) Find the wavelength (in units of nm) for an electron traveling at a speed v = 0.99 e. 3) Use the momentum-wavelength relationship to find the wave• length (in units of nm) of the wave associated with a fast tennis ball. Compare this to the size of the tennis ball. Explain why this tells you that you should not expect to be able to observe wave-like properties for tennis balls. (Use your best estimate for the speed and size of the tennis ball. We are interested here in orders of magnitude, not in precise numbers) eExample: Electron diffraction and the radius of nuclei In a fixed-target experiment, electrons with energy of 500 Me V are scattered from a target of lead nuclei. The resulting angular distribution of the elastically scattered electrons shows a pronounced interference pattern (see Fig. D.1). The pattern looks similar to the intensity distribution that occurs when a lightwave is diffracted by tiny spheres of radius r. We know from the theory of optical diffraction that the first interference minimum occurs at an angle Odrad] ~ 0.61(Vr) . (D.17)

In the picture of matter waves, the incoming electron beam can be viewed as a plane wave and the corresponding wavelength of the electrons can be calculated [using Equations (D .16) ) and (D. 6) 1 for A = 2.5 X 10-15 m. From the figure, we get 01 ~ 12°. Calculating from the formula above (Equation (D .17)), we get the radius of a lead nucleus as r = 7.3 x 10-15 m. 248 Basic Physics Concepts Applied to Particles

x

10 5 x

x fF) Q) x XX X ~ 10 4 X X «I X a. x u Q) Qj 103 x t:: «I 0 fF) x '0 x 2 Q)~ 10 .D x E x :::J c:: x x

10' x x

scattering angle (degrees)

Fig. D.l: Angular distribution of 500-MeV electrons scattered from lead nudei. Redrawn experimental data.

eExample: Calculate the top quark mass The following example shows how the relativistic energy formula and the law of moment um conservation are used in analyzing events in a collider experiment. The example, using areal (but very special) collider event, is presented as a simplified version of a more careful analysis, performed at Fermilab in 1995, in order to calculate the mass of the top quark.

The event A highly energetic proton (800 GeV) collides with a highly energetic (also 800 GeV) to create two top quarks-a top (t) and an antitop (l)-each about 180 times the mass of the protons. In the collision process, the total energy of the colliding protons is converted into kinetic energy and into the mass of two top quarks mt and other particles~ The top and the antitop decay

* These other partieles, ftying mostly elose to the direction of the beam, D.4. Relating Momentum and Wavelength (Partic1es and Waves) 249 extremely rapidly. All that can be seen in a detector are the tracks of the particles from the decays (see Fig. D.2). Physicists predicted and have now observed that the top quark decays by t -+ b + W+. W+ and b can decay in different ways. In experiments, detectors look for typical decay signatures that tell them that a tt pair has been produced. For this particular event, the decay pattern shown he re is most certainly the correct pattern.

b

Fig. D.2: A possible decay pattern of a top---antitop pair, showing four jets, two muons, and two corresponding neutrinos. This pattern is used in our example.

In Figure D.3, the corresponding computer-generated event diagram shows four "jets" (clusters of particles) and two outgoing particles, identified by the detector as muons. These are all decay products of the top quark and the top antiquark. Furthermore, the computer has already determined and written all the momenta on the plot and noticed that the momentum does not balance. From this, physicists know that there is at least one outgoing neutrino. Its energy and direction are drawn on the diagram (the energy of the second neutrino is negligible).

can easily be separated from the particles originating from the top quark decay. They are not shown in computer-generated event displays. 250 Basic Physics COllcepts Applied to Particles

D-Zero Detector at Fermi National Accelerator Laboratory

- M

7.3 GeV/c

Fig. D.3: Computer-generated endview of the top- antitop decay, taken from the D0 detector at Fermilab in 1995. The directions of the four jets are marked by the bar pattern, showing the energy of the jet particles, deposited in the detector. The line and the dotted line mark outgoing muons, and the bar (down right) without a line marks the direction of the outgoing neutrino and its energy. The calculated momenta of all outgoing jets and particles are printed on the plot.

Neutrinos are not observable in this detector, so their presence is found by looking at the total moment um of the system in a collision. The total momenturn is zero before and after the collision. It is easy to verify from Figure D.4 that the surn of momentum vectors of the outgoing charged particles is far from zero (by adding the vectors together graphically). The computer calculates the missing rnomentum as 56.9 GeV je. D.4. Relating Momentum and Wavelength (particles and Waves) 251

54.8 GeV/c

Fig. D.4: Sketch of the momentum vectors from the four jets and the two muons found by the detector in the top decay event. The vectors are redrawn from the event picture.

Calculating the mass of the top quark In order to calculate the mass of the top quarks from the event, we have to know the kinetic energies of all outgoing particles and then use the relativistic energy formula

(D .18)

In our particular case, we can write:

• E = Edebris , which is the sum of the total (kinetic + rest mass) energies of all outgoing particles; • p, is the total moment um (a vector sum) of all outgoing particles; • m = 2mt, is the total (rest) mass mt of the two top quarks. In this example, we use a very special event, where the debris has no motion in the direction of the beams. The event takes place in a plane perpendicular to the axis of the proton and the antiproton. This allows us to approximate the event as a two• dimensional problem. When one observes that the net moment um in a plane perpendicular to the beam direction before the collision is the same as the moment um after the collision and that value is 252 Basic Physics Concepts Applied to Particles

zero, we can rewrite the energy equation, after taking the square root, as (D.19)

(since both a top and an antitop quark are produced). Edebris, is the sum of the energies of all jets and outgoing particles. Because almost all of the energy after the collision emerges from the decay of the top and antitop, we can add the energies of the four jets and the other outgoing particles. The energy of a jet or an outgoing particle can be ca1culated from its moment um given in the event picture as follows .

• We use E 2 = p2 C2 + (mc2 )2 again, but this time we use it for a single particle or jet. For every particle, we can write E = Eparticle and neglect its mass, because these particles are highly relativistic; since their mass is much smaller than their momentum, we get Eparticle = PparticleC. Thus, the known values of the momenta can be written as energy values. This is approximately true for the jets also.

• According to the equation Edebris = 2mtc2, the mass of the top quark can be ca1culated when the value for the missing momentum of the neutrino and all values of the momenta of the outgoing particles and jets (now written in energy units) are added as scalars: 61.2 GeV + 7.3 GeV + 95.5 GeV + 58.6 GeV + 54.8 GeV + 17.0 GeV + 53.9 GeV = 348.2 GeV. The mass of the top is then approximately mt = ~ . 348.2 GeV /c 2 = 174.2 GeV /c 2 . D.5. Forces, Fields, and Charges D.5.1. The Electromagnetic Force Forces have been defined as causing a change in a particle's motion. Forces exist at a fundamental level, because particles have an attribute we may call "charge" that affects other particles possessing that same attribute. This "charge" may be the mass, in which case the force involved is specified by Newton's Law of Universal Gravitation. It may be electric charge, in which case the force is specified by Coulomb's and Ampere's Law. It may be the strong color charge, in which case the force is specified by QCD. The fundamental interactions of the Standard Model are all caused by the existence of a particular "charge." D.5. Forces, Fjelds, and Charges 253

We need force fields to describe many everyday phenomena-the of the Earth acts on satellites, the electromagnetic fields of power lines were reputed to affect the human body. A field in physics is a quantity that can be defined at each point in space. Scalar fields are fields that just have a magnitude at every point. For example, we could define a field whose value at every point is average temperature in adefinite small volume around that point. Vector fields are quantities that have both a magnitude and a direction at every point. For example, we could define a field whose value at every point is the average wind velocity in adefinite small volume around that point. These concrete analogies are just to give you amental picture of a field; they are not force fields. Electrically charged objects create electric and (if they are moving) magnetic fields around themselves. These fields have real physical presence, in that they both cause forces on other particles and contain energy and momentum. Unless the fields are quite strong, we cannot feel them ourselves. To gain an understanding of their presence, we can observe a variety of effects they cause. A small compass can be used to find magnetic fields by how they affect its orientation. A small ball of styrofoam suspended from a thread and rubbed with a piece of plastic wrap will acquire an electric charge and then can be used to detect electric fields around other charged objects. eExercise 5: Visualize field lines Spread iron filing thinly in the lid of a shoe box and place it over a magnet. Tap the box lid gently, and watch the iron filings arrange themselves in a pattern that shows a map (of a slice) of the magnetic force field of the magnet. Accelerators that increase particle energies depend on utilization of the effects of electric and magnetic field on charged particles. Neutral (i.e. uncharged) particles feel essentially no effect of these fields. The force on an electric charge q moving with velo city v in an electric field E and a magnetic field B is

F = qE + q(v x B). (D.20)

Here we need one more definition to understand the magnetic part of the force law. We again use boldface letters to represent 254 Basic Physics Concepts Applied to Particles

quantities that have direction as well as magnitude. The quantity (v x B), (called the "cross product" of the vectors) has a magnitude vB sin e, w here e is the angle between the direction of v and the direction of B. The direction of this force is perpendicular to the plane that contains v and B at the particle's current position. To fully define this, we need one more thing, since there are two directions perpendicular to a plane (e.g. up or down for a horizontal plane). The convention is a "right-hand rule." The fingers of your right hand curl one way but not the other. Place your right hand so your fingers point along the direction of v with your palm facing so you can curl your fingers towards the shortest way to direction of B. Then stick your thumb out, perpendicular to your fingers, and it will be pointing in the direction of the cross product force on a positively charged particle. For a negatively charged particle, the force revers es sign, which simply me ans that it points in the opposite direction.

eExercise 6: Direction of magnetic forces Find the direction of the magnetic forces on two side-by side parallel wires, each carrying a direct current flowing in the same direction.

D.5.2. Accelerating Charged Particles The force exerted by a magnetic field is always perpendicular to the direction of motion of a charged particle and therefore cannot be used to change its speed. A force perpendicular to a motion changes only the direction of the motion, not its speed, and does not change its energy or the magnitude of its momentum. In contrast, the forces due to electric fields are independent of the direction of motion of a particle and can be used to change the energy of the particle (change the speed of the particle). So, magnetic fields are used to steer particles and to focus beams, but only electric fields can be used for change of speed. These are the basic principles of accelerator design. D.5. Forces, Fjelds, and Charges 255

Increasing the Energy: What Is an electronvolt? According to Equation (D.20), a charged particle experiences a force parallel to an electric field of strength E (D.21) In an accelerator, the charged particles are moving in an evacuated region (so experience no collisions) and thus each particle gains (kinetic) energy

E kin = FE' d = qE . d. (D.22) In this equation, d is the distance the particle travels in the field, and the electric field strength E is assumed to be constant. We can use the equation V=E·d, (D.23) which relates the voltage difference V, through which the particle moves to the electric field strength. Then we can write for the (kinetic) energy of the accelerated particle:

E kin = qV . (D.24)

In particle physics, energy is generally measured in units of electronvolts (e V). This unit of energy is equal to the kinetic energy acquired by an electron accelerated by a potential difference of one volt, approximately 1.602 x 10-19 joule. The notations 1 GeV (gigaelectronvolt) = 1 X 109 e V and 1 Me V (megaelectronvolt) = 1 X 106 e V are often used .

• A N umerical Example: Electrons in a TV tube What is the speed of an electron that has been accelerated by a voltage of 20 kV in a TV tube? (See Fig. 2.13 in the main part of the book) We use the relativistic energy formula from Equation (D.9), written as (D.25) where the kinetic energy is E kin = qV = 0.02 MeV and the mass• energy of the electron is mc2 = 0.51 MeV. Therefore Etotal = 0.53 MeV. 256 Basic Physics Concepts Applied to Particles

Again from Equation (D.9)

mc2 (D.26) Etotal = )1 _ (V/C)2 '

we get

(D.27)

After taking the square root, we get (v/c) ~ 0.27, or 27% of the speed of light.

eExercise 7: Electrons in the SLAC accelerator In the 3-km electron accelerator at SLAC, the electrons acquire an energy of approximately 50 GeV. 1) What is their moment um ? 2) What is their speed as a fraction of the speed of light? [Note: find 1 - (V/C)2.] You will need to know that the mass of an electron is 5.1 x 10-4 GeV / c2 or 9 x 10-31 kg. 3) What is the average electric field that they were in as they traveled down the 2-mile accelerator? (The simplest way to answer is to use force x distance = change in energy). 4) What was their speed after the first 3 m? 5) What was their moment um and their energy after the first 3 meters?

eExercise 8: Calculate the fraction of the energy that is mass-energy for an electron that has energy 50 Ge V, which is a typical electron energy reached at, e.g., SLAC. What is I for such a partide? As Exercise 8 above shows, for a partide that is traveling dose to the speed of light, the term "acceleration" is somewhat of a misnomer. The partide changes energy and momentum, but the change in its speed is very small. This is why the rate of change of moment um version of Newton's Second Law is dearly the appropriate one. We should call these devices "energizers" rather than accelerators! D.5. Forces, Fields, and Charges 257

Bending Charged-Particle Bearns in a Magnetic Field Remember: A charged particle moving in a plane perpendicular to the direction of a homogeneous magnetic field feels a force perpendicular to its motion and the magnetic field B. The presence of the magnetic field does not change the energy of the particle. The force is FB=qvxB. (D.28)

The "cross" (x) product can also be written as FB = qvBsin((}). (} is the angle between the velo city of the particle and the direction of the magnetic field.

In our case, B is perpendicular to v. The force F B then is always in the radial direction. If the particle has constant energy, it follows a circular trajectory. F B is the centripetal force F B = mv2 Ir, and we can write mv2 Ir = qvB. If momentum p = mv is introduced, we get

p = Bqr = 300 Br, (D.29) for p in MeV le, B in tesla, r in meter, q in units of e (assuming that the particle has the charge of a proton), and 300 is the correction factor for the units. Equation (D.29) is also correct in the relativistic case, when

(D.30)

eExample: Identifying a particle by rneasuring its rnornen• turn We can measure the direction and momentum of charged particles using a tracking chamber in a strong magnet. Since high-energy charged particles leave an ionization trail in a gas volume without losing a significant fraction of their total energy, we can record the tracks over distances large enough to measure both their initial direction and the bending of the track due to the magnetic field. This information allows us to determine each particle's moment um and the sign of its charge. Tracking devices are described in more detail in Appendix C. 258 Basic Physics Concepts Applied to Partic1es

For example, imagine that a partiele track from a tracking device is found to have a radius of curvature of 20 cm in a magnetic field of 2.0 tesla (see Fig. C.l). The momentum of the partiele can be found from Equation (D.29):

p= (300·2.0·0.2) MeV/c= 120 MeV/c. (D.31)

If, in addition, the partiele's speed is measured as v = 0.65 c, the partiele itself can be identified by calculating its mass from the relativistic momentum formula:

_ 120 MeV /c 2 _ 2 m - 0.65c V(1 - 0.65 ) - 140 MeV /c . (D.32)

This result is very elose to the value of the mass of a pion (m ~ 139 MeV /c 2 ) •

• Exercise 9: Bending of a particle track in a magnetic field An early eloud chamber photograph shows an moving on a circular track in a homogeneous magnetic field of 1 tesla. Its radius of curvature is measured to be 33.8 cm. Calculate its kinetic energy in megaelectronvolts (Me V) using the nonrelativistic formula. 1s the nonrelativistic result justified or do you need to recalculate using relativistic equations? Explain. D.5.3. Three Languages to Describe Forces Between Parti• cles We have seen not only that electric fields and magnetic fields act on particles with charge, but also that electric and magnetic fields are caused by particles with charge. This is a typical pattern for all force fields: Any partiele that is affected by the force field is also a source of that same type of force field, which is feIt by other particles. So we begin to understand how Newton's law of action and reaction applies for objects at a distance from one another. Partiele A creates a force field feIt by partiele B, and particle B creates a force field feIt by partiele A. Let us first look at electromagnetic forces between two oppo• sitely charged partieles; then, having developed some insight there, we can move on to other interactions. Consider a hydrogen atom. D.5. Forees, Fjelds, and Charges 259

We use three different languages for the force between the proton and the electron. • We can talk about forces between charged particles-Le. Coulomb's law. • We can talk about forces on charged particles due to electric fields. • We can talk about forces due to the spatial variation of potential energy. All three are different but equivalent descriptions of the same physical effect.

The Force Law We can say simply that the proton attracts the electron, because opposite electric charges attract with a force

F "-' qpqe (D.33) r 2 ' where qp = +e is the charge of the proton, qe = -e is the charge of the electron, and r is the distance between them. Written in SI units (in which charge is measured in Coulombs and distance in meters), the force law is

F = k qpqe (D.34) r 2 ' where k is the Coulomb constant 9 x 109 Nm 2 / c2 • Of course by Newton's laws we know that the electron pulls the proton with an equal but oppositely directed force. While this description correctly describes the forces, it makes no reference to any mechanism that explains how the force is transmitted from one particle to the other. 260 Basic Physics Concepts Applied to Particles

eExercise 10: Coulomb's Law

Calculate the force on an electron at a distance 10-10 m from a proton.

Forces Due to Fields We can also describe the attraction of the electron and proton in term of fields. An electron in an electric field E p is subject to a force F = qeEp. Since the force is measured experimentally to be F rv qpqe/r2, we know that Ep rv qp/r2. Since the electric field of the proton decreases as 1/r2 , it is possible to think of the proton's field as a certain number (N) of field lines pointing radially outward in all directions. To understand this, imagine putting a small imaginary sphere around the proton. Exactly N lines point through the surface of the sphere. Make the sphere much bigger. Still, exactly N lines point through the surface. The area of the sphere is proportional to r 2 . Hence, the field strength (the number of lines of field passing through a unit area perpendicular to the field lines) must decrease as 1/r 2 , so that the number N of lines remains constant. Just as for the proton, an electric field exists about the electron E e rv ee/r2. The proton is affected by a force qpEe because it sits in this field. Notice that both particles produce fields proportional to their charges and are affected by forces due to any external field. On the other hand, electromagnetic fields arise due to charges and their motions (i.e. they have a source) and are feIt by moving, charged particles. Why was it useful to complicate the story by conceptualizing the force as due to a field? The reason is that these fields are real (that is detectable) physical phenomena. Once we know what they are and what their sources are, we can produce them, either in static form like the coulomb field described above or in traveling form, as a radio wave or a light wave or any other electromagnetic wave. The understanding of electromagnetic fields and the forces they exert on charged particles was a triumph of the physics of the 19th century. It is summarized by Maxwell's equations, which describe this physics at least at the classical (prequantum) level.

One important feature is that electromagnetic fields contain D.5. Forces, Fjelds, and Charges 261 energy, with an energy density* proportional to E 2 + B 2 (where E and B denote the field strengths of the electric and the magnetic fields, respectively). This is how energy can travel from the Sun to Earth-as a traveling wave of electromagnetic fields, for example, light. So we understand why light is a form of energy (radiant energy), once we understand that electromagnetic fields store energy. Keeping track of the fields allows physicists to deal with a lot more complications. We can follow how the fields change as weIl as keep track of the motions of particles. Their effects on one another as they move can be described in a fashion that is both frame independent and correctly causal. Also, as it turns out, the treatment can be relativistic and quantum mechanical. As an example, suppose we consider two charged particles one meter apart. When one of these particles moves, the simple force law might imply that the force on the other is instantaneously changed; but the full theory using fields says it takes time for any disturbance of the field due to the motion of the first particle to travel, at the speed of light, to influence the other particle. Experiment teIls us the second description is the correct one.

Forces and Potential Energy A third language for talking about the interaction between charges is to introduce the concept of potential energy.

Consider two (small) charges separated first by a distance d1 and later by a distance d2 • Then, the electrostatic potential energy is the difference between the energy stored in the electric fields at separation d1 and the energy at separation d2 .

The first separation (d 1 ) could be a reference configuration, e.g., when the charges are infinitely far apart. In this reference, configuration, the total energy (called U1 ) can be set (by definition) to zero.

The second separation (d2 ) is of interest, and the total energy is called U2 • Note: Potential energy is a relative thing. We may choose any point we wish as the zero of potential energy. In the case

* energy per unit volume. 262 Basic Physics Concepts Applied to Particles

of Newton's Law of Universal Gravitation and Coulomb's Law, it is convenient to choose the potential energy at infinite distance of separation as the zero point. Suppose we have two charges of the same sign. As they are brought doser together, their electric fields add to one another, and since the energy density in the fields is proportional to the square of the electric field strength E 2 , the total energy increases. Clearly, the two fields tend to cancel on the straight line that connects of the two charges, but if you look at the whole field distribution from a greater distance, you will realize that the fields add to one another.

We call the energy difference U2-U1 "potential energy" U, because if we let the charges move freely they will fly apart, converting the stored energy to kinetic energy. It is called potential energy because it has the potential to produce kinetic energy. Let us next consider what happens if the two charges have opposite signs. Again, when they are infinitely far apart, each has its Coulomb field. Now, when they are brought doser together the fields tend to cancel-so the energy stored in the field decreases. Even though this energy difference is negative, we still use the term "potential energy" for the difference between the energy in the two configurations, but now the charges cannot fly apart unless something else provides the energy. A gravitational potential energy difference arises in much the same way; it is the difference in the energy stored in the gravitational field in two configurations. It is more convenient to choose as the reference situation an object at the surface of the Earth rat her that infinitely far from it, so that is what is usually done. In a situation in which the two interacting masses are very different, such as the Earth and a ball, or a nudeus and an electron, we often treat the larger mass as if it is a fixed object, unable to move, and assign all potential energy to the less massive object~ Any object will always move in such a way as to reduce its potential energy if this is possible-the ball falls to earth, the two like charges move apart, and the two opposite charges move together.

* The less massive object or the smaller charge is often called the test mass or test charge. D.5. Forces, Fields, and Charges 263

Mathematically, we can describe the variation of potential energy by a potential energy function U(r), where r is a position vector in a coordinate system. For the case of an electron in the field of a nucleus (of charge Ze), U(r) is given by

U(r) rv Ze2 Ir. (D.35)

The map of this function is shown in Figure D.5.

Fig. D.5: Map of the Coulomb potential energy function.

The map for the electron approaching a nucleus is particularly simple. U(r) depends only on the distance r between the nucleus and the electron. We can also describe all this in terms of forces. Mathematically, the force can be calculated from the potential energy function U (r ). The two objects (the electron and the nucleus), feel equal attractive forces proportional to the slope of the potential energy function U (r ). In our special case (electron and nucleus) we can 264 Basic Physics Concepts Applied to Particles

write F = - t::..U I !J.r . (D.36)

Here, !J.U = U2 - U1 and t::..r is the difference r2 - r1 in radial direction. In the language of calculus,

F = -dUldr. (D.37)

F is a vector that points in the direction opposite the slope of the potential function. This slope has both a size and a direction in any point of space. In our case, the force points to the radial inward direction, and gets more positive, as r becomes smaller ~ For those who know calculus, we can calculate the well• known equation for the Coulomb force Equation (D.33) from Equations (D.35) and (D.37) as

(D.38)

Alternatively, we do experiments that give the Coulomb force [Eq. (D.33)] and then determine Coulomb potential energy U:

CX!

U = JF(r) . dr rv Ze2 Ir. (D.39) r

These relationships also show why the quantity called "work" was introduced in physics. If the slope of the potential energy determines a force, then a force times the distance through which it pushes a particle is the potential energy. We call this "the work done on the particle." We often are interested in the potential energy per charge, which is known for short as the "potential" and given the symbol V. The potential is related to the field that gives rise to the force. For us, U gives the potential energy for an electron charge -e in the field of a nuclear charge e.

* Here we are using a test charge with charge -e, whereas in the usual definition the Coulomb potential is for a unit test charge. D.5. Forces, Fields, and Charges 265

The potential is defined so it gives the potential energy for a unit test charge, so we must divide the potential energy by -e to get the potential for the case of interest (but beware, unit charges are after all a matter of whose units you are using; particle physicists usually use units that the charge of a proton or an electron is 1 unit). Therefore, the Coulomb potential (of a nucleus of charge Z e) is

V(r) rv Ze/r. (D.40) .

If the trick of defining potential energy sounds like mathematical game playing, it iso The concept of potential energy is very useful, however, because it also applies in situations that are much too complicated to keep track of all the fields. Only in the special case in which a force comes from a simple source, such as the field of a single charge, can we truly play this game from the ground up and relate the potential energy to the underlying force fields.

Summary We can predict the motion of the test particle either by considering a force due to a field and using Newton's equations or by considering a potential energy function and using conservation of energy. The concepts of a Coulomb force field and a Coulomb potential are just two names for the same physical effect viewed through two slightly different mathematical lenses.

D.5.4. Recapitulation for All Interactions There are a variety of possible forces on particles: Forces due to gravitational fields, forces due to electric or magnetic fields, and forces due to strong interaction force fields. In each case, the story is very similar. Just as in the electric case, each field is always due to some source, either a single particle or a collection of particles. Particle A feels forces due to the fields for which particle B is the source, and particle B feels the fields of particle A. This is only true, however, if both particle A and particle Bare "charged," that is, if they carry a quantity that both makes them a source of the particular field in question and makes them sensitive to the presence of such fields from any other source. 266 Basic Physics Concepts Applied to Particles

For electromagnetic fields, the quantity in quest ion is electric charge; for gravitational fields, it is mass-energy; for strong force fields, it is color charge; and for weak interaction field, it is called weak charge. If we include all such source particles as part of our system of study, then for such a system we find that the force-field description ensures conservation of moment um and energy, just as Newton's laws ensured conservation of momentum. When the fields do work on a particle, the motion energy of the particles change and the potential energy changes by an equal and opposite amount. Usually, elementary books say gravitational forces are propor• tional to the mass of the object feeling the force, but in fact this is just a nonrelativistic (v «:: c) approximation, since for v «:: c most of the energy is from the mc2 term with only a tiny fraction from the ~mv2 term. For particles with speeds dose to c, we need to remember that gravity pulls on energy, so photons feel gravitational effects, as was demonstrated in the famous eclipse experiments sug• gested by Einstein. (The fictional mass M = "(mo may be a useful subterfuge to avoid saying gravitational forces are proportional to energy, but it leaves open the quest ion of what happens for massless particles. ) In most high-energy particle physics situations, we ignore the effects of gravity altogether. We do not ignore them for the huge equipment, where indeed they matter, but for the individual particle collisions, where they are a truly tiny correction compared to the other fundamental forces. D.5.5. Residual Forces What are "residual" forces, and how are they related to fundamental forces? In this book we have introduced the term "residual forces" for the forces between uncharged objects due to the fact that they have charged substructure. Thus, we call the forces between atoms that cause them to form molecules a "residual electromagnetic effect," to distinguish it from the "fundamental" electromagnetic forces between charged objects. In both cases, the forces are due to the same thing-possible re arrangement of the charged objects, which reduce or increase the total energy stored in fields within the system. The distinction between fundamental and residual effects is thus more a distinction about the nature of the objects feeling the D.6. The Mass oi Composite Objects 267 force than about the nature of the force itself. All forces are due to possible changes in energy stored in force fields. Fundamental and residual strong forces depend on the strong or color force field. Electromagnetic and residual electromagnetic forces depend on energy stored in electromagnetic fields. Gravitational forces depend on energy stored in gravitational fields; since no "gravitationally neutral" objects exist (i.e. objects with zero total energy), there are no residual gravitational effects. To summarize: • All forces are due to changes in energy stored in fundamental force fields. • Composite objects can only be subject to fundamental forces if they carry acharge for that field. • Forces are called residual if they are acting on composite objects that have zero total charge but charged substructure.

D.6. The Mass of Composite Objects For fundamental particles, their mass is a characteristic quan• tity. For composite objects, however, things are more complicated: An atom is stable because its mass is slightly less than the sum of the masses of particles in the nucleus plus the masses of the electrons within the atom, so conservation of energy prevents it from falling apart. But how can this be? Fields can allow us to understand the masses of atoms and ( eventually) the energetics of chemistry. The binding energy, or mass deficit, is the difference between • the energy stored in the electric fields surrounding the nucleus and each individual electron when they are all at rest and very far apart and • the sum of the energy that is stored in the electromagnetic fields associated with those same particles when bound inside the atom and their kinetic energies. Since the nucleus and the electrons have opposite electric charges when they are close together, most of their electromagnetic fields are canceled out (for a neutral atom), with only a tiny region 268 Basic Physics Concepts Applied to Partic1es

of fields left inside and near to the atom. To be more precise, the mass of the atom ineludes both the mass and the kinetic energy of the constituents within it, as weIl as the (negative) potential energy of the electromagnetic fields inside the atom compared to the fields of the separated constituents. N otice how the line between mass and energy is getting very blurred here. We can say mass is a form of energy, but for a compound object such as an atom, the mass of the compound is the sum of all forms of energy within it (of course, with the ever useful E = mc2 relationship to take us back and forth between energy units and mass units.) The smaller the scale at which we look, the smaller the distinction we find between energy and mass. In summary, for composite objects, their mass (multiplied by c2 ) ineludes the motion energy J(p2C2 + m 2c4) of its fundamen• tal constituents and the potential energy due to the interactions between them. N ow we can also understand the energetics of chemistry.

Energetics of Chemistry While atoms are electrically neutral objects, electromagnetic fields exist within them, and actually even a little outside of them (though these fields fall off much more rapidly with distance than the Coulomb field of a charged object). When two atoms are elose enough together, the fields of one atom can affect the electrons in the other atom, and some rearrangement of the electrons can take place because of this. If the electrons can find an arrangement that has lower total field energy than the two separated atoms, then a can form. Chemical bonds are a name for the energy effects of these electron rearrangements. In a chemical process, it is most often carried off as kinetic energy of the reaction products. D.6. The Mass oE Composite Objects 269

Chemical-Binding Energy Chemists tell us that mass is conserved in chemical processes. They mayaiso point out that, while this is a very good and useful approximation, it is not in fact an exact statement. What they actually mean is that the sum of the masses of the atoms does not change in any chemical process because atoms are neither created nor destroyed in such processes. A very precise measurement would reveal that the mass of any stable molecule is a tiny bit less than the sum of the masses of the atoms from which it is buHt. This difference, called the bin ding energy of the molecule, occurs because the energy stored in the electromagnetic fields of the atoms involved is reduced a little when the atoms are together, as compared to what the energy is when the atoms are separate. This is wh at causes atoms to form molecules. We count the potential energy within the atoms as apart of the mass of the atom (by the E = me2 relations hip ). So, if we reduce this energy by putting the atoms together, we get a mass for the mole eule slightly less than the sum of atom masses.

Hadronic-Binding Energy at Smaller Scales It is useful to understand what is going on at the level of molecules to make stable compound objects, because the same principles continue to apply as we move to even smaller scales. At the subatomic level, much is the same, except that the nature of the force field changes. In any stable nudeus, the mass of the nudeus is less than the sum of the masses of the protons and neutrons from which it is made (see the exercise below about the deuteron). As protons and neutrons are put together to form a nudeus, the residual strong interactions between the neutrons and protons yield a negative potential energy, thereby reducing the mass. Recall that atoms (which are electrically neutral) combine to form molecules because of residual effects of their internal charge structure. In the same way, color-charge-neutral protons and neutrons combine to form nudei. This happens when they are dose together because of the effects of the internal color-charge structure of themselves and their neighbors. 270 Basic Physics Concepts Applied to Partic1es

eExample: The binding energy of the deuteron

A deuteron (Hf) is composed of a proton (mass m p = 1.007825 u) and a neutron (mass m n = 1.00867 u). The mass of a deuteron-measured by a mass -is found to be mD = 2.014102 u. (u is the atomic mass unit u = 931.5016 MeV/c2 ). From these values, we can calculate the mass deficit (or the binding energy) as tlm = mD - (mn + m p ) = -0.002393 u or tlm = -2.23 MeV/c2 .

eExercise 11: Energy from nuclear fusion

In astar, the element helium (He~) can be produced (among other reactions) by a nuclear fusion reaction between deuterium (Hf) and tritium (Hf):

2 H3 H 4 1 H1 + 1 = e2 + n o . (D.41) Calculate the amount of energy (Me V) released in this reaction.

(use: mtritium = 3.01605 u and mhelium = 4.00260 u)

Quarks Inside Protons and Neutrons For the quarks in protons and neutrons, the story is quite different, because the fundamental strong force (and the potential energy) has a very different form. As a result the masses of the proton and the neutron are much larger than the quark masses. As discussed in Section 3.3.3 (in the main part of the book), most of the masses of the proton and the neutron comes from the color field potential and the kinetic energy of the quarks.

* See also Section 3.4 in the main part of the book. D.7. Lifetime and the Decay Law 271

D.7. Lifetime and the Decay Law Most of the particles we produce in experiments are unstable; after a tiny fraction of a second, they decay into two or more lighter particles. Much can be learned by studying the lifetime of a particle or, actually, a sufficiently large number of that type of particle. The lifetime of an individual particle cannot be predicted, which means that there is no way for us to know when an individual particle will decay! Decay is a statistical process. We can just define an average (or mean) lifetime T of a given type of particle in the following way: If we observe a given sample of N unstable particles, the (relative) probability P that a small number !:1N of them will decay within a given time interval !:1t is

P _ !:1N _ !:1t = N ------;- (D.42) or, using calculus, P _ dN _ dt = N - -~. (D.43)

(The minus sign has to be introduced, because the number of surviving particles decreases with time.) If we introduce the term "decay rate" ('7:: or dd~)' which is the number of particles per se co nd decaying, we find from the above equation

!:1N N (D.44) !:1t T or dN N (D.45) dt T

This is the famous equation, which means that the decay rate is always proportional to the number of surviving particles N(t). If we solve this equation by integration, we get

(D.46)

This gives the number of particles expected to survive to a time t, given the number No present at time t = O. It is easy to verify from 272 Basic Physics Concepts Applied to Particles

the above equation that the mean lifetime T is the time at which the relative number of particles surviving !:a = e-1 = 0.368. On the other hand, especially in the case of radioactivity, we can ask how long it would take for half of the atoms in a given sampie to have randomly decayed. This time, called "half-life" Tl, is related to the 2 me an lifetime by

Tl = T . In 2 = 0.69 . T. (D.47) 2

.Example: Measuring the mean lifetime of a muon Lifetimes of muons can be measured in a "delayed coincidence" experiment, in which muons are stopped in a scintillator. One measures the time between the start-signal (i.e. when the particle enters the scintillator) and the electrical signal produced by the decay-electron. Out of a sampie of 327 observed muons, you would observe that • 120 muons survive 2 f.LS or more, • 48 muons survive 4 f.LS or more, • and only 5 muons survive 8 f.LS or more. The me an lifetime can then be estimated, using Equation (D.46) and two data points, e.g., t 1 = 2 f.LS and t 2 = 4 f.Ls,

(D.48)

and from this,

(D.49) D.8. Angular Momentum and Spin 273 eExercise 12: Calculating the muon's lifetime from a plot

A more exact value for the lifetime T of the muon can be found when the numbers of surviving muons (N (t)) are plotted on a logarithmic scale versus time (on the horizontal axis). Make a drawing of this plot using the numbers of surviving muons from above, find the "best" straight li ne through these data points, and calculate the mean lifetime from the slope of this line. eExercise 13: Radioactivity The decay rate of an unknown radioactive substance drops by a factor of 12 within 20 min. What is the half-life of the substance? eExercise 14: The decay of a proton Because protons are expected to have a me an lifetime of about T ~ 1031 years or more, it is very unlikely to detect the decay of a proton. Therefore, physicists using phototubes observe a huge amount of pure water in an effort to detect a decaying proton. For 10 years, three experiments (in different parts of the world) have observed an amount of about 3000 tons of water, and have found no decaying protons at all. [See the Kamiokande detector photograph (Fig. 8.2) in Chapter 8.] e Calculate, from the data given above, how many decaying protons these experiments should have detected. e Calculate a lower limit for the lifetime of a proton from the outcome of these experiments. (Rint: Assurne that one decay has been observed during the 10 years.)

D.8. Angular Momentum and Spin D.8.I. Introduction Angular moment um is a conserved quantity related to rota• tional motion, much like momentum for linear motion. Angular momentum is used to describe the orbital motion of two bodies (particles) around another or the rotation of a rigid body (e.g., a top). 274 Basic Physics Concepts Applied to Particles

D.8.2. Definitions Consider the simple case of an object orbiting a much more massive object on a circular trajectory of radius r. Then, the orbital angular moment um J can be defined in analogy to the linear moment um p = mv of the body. The angular momentum is

J=rxp. (D.50)

Again, the "cross" (x) product can also be written as

IJI = Irl·lpl· sine , (D.51)

where e is the angle between the moment um of the object and the direction of r. In our case, rand p are perpendicular, so

J=rp=rmv, (D.52)

Introducing w = vjr, the angular velo city of the rotation, we can also write

J = mr2w . (D.53)

Since J is proportional to w, we can describe the intrinsic angular momentum of a spinning rigid body as

J= Iw, (D.54)

where I is called the "moment of ." I depends on the shape of the body (e.g., for a uniform solid sphere of radius rand mass m: I = ~mr2). D.S. Angular Momentum and Spin 275

D.8.3. Atomic and Subatomic Physics

Particle physicists found that the conservation law of angular moment um remains true at the microscopic level, but only if you take into account the intrinsic angular momentum of the particles, which is given the name of spin. Spin and angular momenta are important concepts in particle physics because

• In atomic physics, angular momenta label the various distinct orbital states of shell electrons.

• Like mass, intrinsic angular moment um (spin) is a character• istic property for each type of particle.

• The conservation of angular moment um is used (together with other conservation rules) to describe the results of particle reactions, such as decays and collision processes. From conservation of angular moment um in a particle reaction, we can calculate the spin of new, unknown particles. In quantum mechanics, angular moment um , is quantized (can only have certain discrete values): It comes in multiples of Planck's constant h, divided by 27f. For convenience, we define 1i = h/27f. Ordinarily, angular moment um of rotating systems comes only in integer multiples of this amount. This idea go es back to the early days of atomic physics when Bohr and his collaborators tried to explain atomic spectra. Bohr proposed that the angular momenta of the electrons within the atoms had to be quantized. A way we can understand this is to imagine the circular motion of an electron described in classical trajectories. Its orbital angular moment um [Eq. (D.50)] is J = r x p. Introducing de Broglie waves with p = h/ A, we realize that-in order for the wave to match itself after one orbit (to avoid destructive interference )-the orbit must contain an integral number n = 1,2,3, ... of de Broglie wavelengths:

27fT = nA . (D.55)

From this, we can write the orbital angular momentum 276 Basic Physics Concepts Applied to Particles

J = rh/>" = nh/27f = nn. (D.56) So the angular moment um must be an integral multiple of n. The modern picture of the atom differs from Bohr's simple model, but possible electron states are still found to have well• defined angular momenta given in integer multiples of n. This classical picture has its limitations, but quantitative calcu• lations at the more fundamental level of quantum mechanics show that the results presented here are correct. Furthermore, these calculations tell us that the description [Eq. (D.56)] given here is also valid for intrinsic angular momenta of particles. There are two peculiarities of spin for fundamental particles . • The first is that some particles (fermions) have spins which are odd half-integer multiples of n (~n, ~n, ~n, .. .) . • The second, and perhaps even more puzzling aspect of spin, is that it is an intrinsic property of the particles, but cannot be interpreted in a classical way as the rotation of some structure internal to the particle. If you take the example of an electron, the problem can be stated by trying to model the rotating particle. Imagine that the electron has all its mass in a thin ring at radius r e from the center of the particle. High-energy electron scattering experiments put an upper limit on the size of this sphere as less than 10-19 m. N ow, let this ring rotate so that any point in it is traveling at the speed of light, and calculate the angular momentum of the system. If you do the calculation, you will find it is much much less than ~n. Any other way of distributing the electron's mass within the size limit given by the scattering experiments gives even less angular momentum. You cannot make a model for a rotating electron that gives n/2 of angular momentum. So we are forced to simply give up trying to picture what is rotating and simply state that an electron is an object with an intrinsic angular moment um (of n/2) with no classical model for the structure of that object. Conservation of angular momentum only works when we include adefinite amount of angular moment um for each type of particle, D.S. Angular Momentum and Spin 277 which we call the spin of the particle. The spin is a fundamental property of a particle that cannot be changed. D.8.4. The Discovery of Spin: An Experiment The intrinsic angular moment um of electrons was discovered by Stern and Gerlach (1921) in a famous atomic-beam experiment. They made use of the fact that spin and orbital angular momenta of electrically charged particles are accompanied with a magnetic field and so particles with spin are like tiny magnetic dipoles. Orbiting electrons form a small loop of electric current and set up a magnetic field. The spin of an electron is another loop of electric current and sets up another magnetic field. Therefore, atoms behave like a small dipole magnets. These atomic dipole-magnets can be influenced by external magnetic fields. In a non-uniform magnetic field, an electrically-neutral atom (a magnetic dipole) not only rotates but also experiences a force that causes a displacement (pointing in the direction of the field gradient ~~ ). Strength and direction of this force depend on the orientation of the atomic magnets in space. Stern and Gerlach-in order to examine this deflection-let a beam of electrically-neutral silver atoms * pass through a region in which there is a non-uniform magnetic field in the vertical z direction (see Fig. D.6). After passing through this region the vertically deflected atom strikes a photopIate where it activates a silver grain and makes a visible dot. In the classical picture we would expect that atomic magnetic dipoles in the beam would behave like tiny tops. All possible orientations in space would be allowed and we would observe a vertically smeared-out pattern on the photopIate. Stern and Gerlach however observed two vertically spaced dots instead, which means that magnetic moments (and therefore spins) can only have certain two discrete orientations in space} They came

* Silver atoms behave like hydrogen atoms with one electron. The atom has no magnetic moment and should not be deflected by the magnetic field. Therefore, all deflections to be observed are due to the intrinsic angular momentum of the electron. This picture is true only if the orbital moment um of the electron is zero (I = 0 ground state). 278 Basic Physics Concepts Applied to Particles

y

x.

z-axis C is bearn direction

Fig. D.6: Layout of the Stern-Gerlach experiment.

to the conclusion that the electron rnust have half-mlrnbered values of spin cornponents in space 8 z = ±~.

Angular momentum: Examples and exercises

eExample: ß decay and the spin of the neutrino We rnention in Chapter 3 that, in order to understand en• ergy conservation in the neutron ß decay, a new particle-the (anti)neutrino-has to be introduced:

n ---7 P + e- + IJ .

Before it was realized that a neutrino was involved in neutron decay, it appeared that the decay was

This decay would violate the conservation of angular rnornenturn because the spins of the decay products-the proton (8 = ~) and the electron (8 = ~ )-never add to the spin of the original particle, the neutron (8 = ~). Their surn is zero, when the spins of the D.9. The Heisenberg Uncertainty Principle 279 proton and the electron are antiparallel, or 11i, when the spins are parallel. eExercise 15: Check the example above: Introducing a third particle of spin (8 = %)-the neutrino--makes conservation of angular moment um possible. eExercise 16: The spin of the proton Write the possible values of the spin of a proton, when the proton is composed from three quarks (uud) of spin (8 = %). Which spin configuration (parallel and/or antiparallel) of the u and the d quarks represents a proton of spin 8 = %? D.9. The Heisenberg Uncertainty Principle D.9.1. Uncertainty Principle The Heisenberg Uncertainty Principle is a result of the quantum behavior of particles (or waves). It states that we cannot measure exactly both the position and the momentum of a particle at the same instant. The more accurately we seek to measure its position, the more we disturb its momentum (increase the uncertainty in its momentum). Likewise, if we try to make an accurate measurement of momentum, we can do so only at the price of introducing an uncertainty into our knowledge of its position. Written in terms of algebra, the Heisenberg Uncertainty Princi• pIe is

ßx· ßp > li/2. (D.57) That is, for any particle, ßx (the uncertainty in its position) times ßp (the uncertainty in its momentum) is greater than or equal to li/2, where li = h/27r = 1.05 X 10-34 Js. We can measure either position or momentum of the particle precisely. The more accurate we determine one, the less we can know about the other (see Example 1). This fundamental property of quantum mechanics is important at the tiny scale of atoms, , and all fundamental particles. For example, since the quarks within the nucleons are confined to a 280 Basic Physics Concepts Applied to Particles

very small area, their position is weIl known. Then, the uncertainty and their momentum and kinetic energy cannot be too small (see Example 2). We can perhaps understand this conundrum a little by thinking about wave properties for quantum particles. Remember that the momentum p of a particle is inversely proportional to its wavelength A. A free particle traveling with constant speed (and constant momentum p) in the direction of the x axis can be represented by a sinusoidal plane wave. This wave has a single, well-defined wavelength A. Therefore, the momentum of the particle is given with great accuracy. Nevertheless, because a plane wave extends in the y, z directions, the probability of finding the particle at a position (x, y, z) is the same all over the space: The position of the particle is essentially unknown. When we measure the position of a particle, we are identifying a small region where it exists. This can be thought of as a "wave packet," for which the waves are zero away from the particle. In this region, there must be a superposition of waves with wavelengths the size of the region divided by an integer. Hence, for a smaller region, the range of wavelengths is smaller and the moment um is

larger (since p rv 1/A). Conversely, if we want to accurately measure the momentum of some wave, we need to look at a significant fr action of a wavelength, so the position of the object whose moment um we are measuring is not weIl determined. No quantum state in any system, whether the electron in an atom or a light wave in free space, can be accurately described as a particle with both a definite position and definite momentum at the same instant in time. We can and do, however, make such descriptions all the time for classical objects. This is possible because, for any object that we can see, the uncertainty principle intro duces such a small effect that it is a very good approximation to ignore it. D.9. The Heisenberg Uncertainty Principle 281

D.9.2. Some Consequences of the Uncertainty Principle eExample 1: Measurement of position and momentum The position x of an electron is known with aprecision of ~x = ±O.Ol mm. What is the minimum uncertainty of its velo city ~vx (from ~p = m~vx)? Ti ~vx > -- = 11.6 mjs, where m e = 9.1 x 10-31 kg is the - me~x mass of the electron. eExercise 17: Uncertainty relation The position of a marble (m = 0.01 kg) at rest is measured with aprecision of 10-7 m. What is the minimum uncertainty of its velocity ~vx? eExample 2: Particle in a box A particle is confined to a one-dimensional box of length L, which me ans its x position is known to aprecision of ~x = L. This causes an uncertainty in the x component of its momentum ~Px > Tij L. Assuming that Pm in is described by ~P, we can get an estimate of the minimum value of its moment um and-using 2 E kin = ;m -an estimate of its minimum kinetic energy:

(D.58) eExercise 18: Particles in a box What is the minimum kinetic energy e of an electron confined in an atom? e of a proton confined in a nucleus? e of a quark confined in a proton? 282 Basic Physics Concepts Applied to Particles

eExample 3: Virtual Particles Note also that the relationship [Eq. (D.6)] among energy, mo• mentum, and mass is what distinguishes areal particle, by which we me an one that can travel a measurable distance, from a "virtual particle." Any real observable particle always obeys this rela• tionship. "Virtual particle" is a name physicists invented for an unobservable state that occurs at an intermediate stage of calcula• tions for particle processes. These unobservable intermediate stages are fiction, or if you prefer, a description of a calculation. These calculations correctly predict rates, so physicists often talk as if the intermediate stages are processes that actually happen; it gives us a convenient way to describe and think about the processes. Be warned, however, there are many peculiarities in intermediate stages of quantum calculations. They are not observable without changing the outcome of the experiment. A description of processes in terms of virtual particles is never quite a true story in the sense of everyday experience, though it is a very useful description of a correct calculation of the expected outcome. When we try to describe an interaction by the exchange of force carrier particles, energy and moment um conservation appear to be violated. This is because these force carriers appear during an intermediate stage of the process, even though not enough energy is present to create such massive particles. To understand how this is possible, we must consider the Heisenberg Uncertainty Principle. When such a boson exists only for an extremely brief instant as an intermediary in a process, there can be-as a consequence of the Heisenberg Uncertainty Principle-an apparent violation of the conservation of energy. Specifically, energy conservation can be violated by the amount tlE (or tlmc2 ) , for a limited time tlt, as long as an analog of the Uncertainty Principle is obeyed:

tlE . tlt ;(; n. (D.59)

You can use that as a rationalization. A particle that is created just by a fluctuation of energy is called a "virtual particle," because it is not observable (by definition!). However, if one sees only the initial decaying particle and the final decay products, one observes that energy is conserved. An example is c quark ----> s + W+ ----> S + l/e + e+. The "virtual" particle (the W+) exists for such a short time that it D.lO. Note on Units 283 can never be observed. Most processes among fundamental particles are mediated by virtual carrier particles.

D.I0. Note on Units Units in physics, as in the world in general, are mostly historical accidents. Once we understand the naturallaws, we can use more natural units. Dimensionful, fundamental constants found in nature can be used to relate units of one type to units of another. The two important ones for particle physics are c, the speed of light, which relates distances to time [astronomers talk about light-years, particle physicists about light-nanoseconds (10-9 seconds)] and h, Planck's constant, which has units of energy times time. So particle physicists prefer to relate units of energy to units of time, or when combined with c, energy or mass units to length units. Electrical units are also a matter of historical conventions. U nits of volts per meter for are standard. For the potential energy difference of an electron moving from one point to another (infinity to radius r) in a potential, the units are electronvolts (e V). This is why particle physicists choose to express all particle energies in units of electronvolts. In high-energy physics, the notation 1 GeV = 1 x 109 eV is often used (GeV is gigaelectronvolts). Then, by using units of electronvolts divided by c2 for masses, we use the Einstein relationship between mass and energy to make the units of mass and energy more or less interchangeable. (In fact, particle physicists go a step furt her and choose units of length so that c has magnitude 1.) In making predictions for the physical world measured in Inter• national System units, the dimensionful factors in any expression are always fixed by putting the right number of factors of n and c to give the quantity the right dimensions. A useful number to remember for unit conversions is nc = 200 MeV fm (or, more precisely, 197.327053 ± 0.000059.)*

* 1 fm = 1 femtometer = 10-15 m. E

Appendix: Suggested Reading

E.1. Articles Particle Physics Articles E. Bloom and G. Feldman, "," Seientijie Ameriean (May 1982) p. 66. J. Boslough, "Worlds Within the Atom," National Geographie (May 1985) p. 634. D. Cline, C. Rubbia, and S. van der Meer, "The Search for Intermediate Vector Bosons," Scientijic Ameriean (March 1982) p. 48. D. Cline, "Low Energy Ways to Observe High Energy Phenomena," Seientijie American (September 1994). F.E. Close and P.R. Page, "," Seientijie Ameriean (Novem• ber 1998) p. 52. J.W. Cronin, S.P. Swordy and T.K. Gaisser, "Cosmic Rays at the Energy Frontier," Seientijie American (January 1997) p. 44. M.J. Duff, "The Theory Formerly Known as Strings," Scientijic American (February 1998) p. 64. 286 Suggested Reading

H. Georgi, "A Unified Theory of Elementary Particles and Forces," Scientijic American (April 1981) p. 48. C. Grab, H. Breuker, H. Drevermann, and A.A. Rademaker, "Tracking and Imaging of Elementary Particles," Scientijic American (August 1991) p. 42. H. Harari, "The Structure of Quarks and Leptons," Scientijic American (April 1983) p. 56. R.C. Howis and H. Kragh, "P.A.M. Dirac and the Beauty of Physics," Scientijic American (May 1993) p. 62. M. Kaku, "Into the Eleventh Dimension," New Scientist (January 18, 1997) p. 32. A.M. Litke and A.S. Schwarz, "The Silicon Microchip Dctector," Scientijic American (February, 1994) p. 56. C. Mann, "Armies of Physicists Struggle to Discover Proof of a Scot's Brainchild," Smithsonian (March 1989) pp. 106-117. C. Quigg, "Elementary Particles and Forces," Scientijic American (April 1985) p. 84. C. Quigg, "Top-ology," Physics Today (May 1997) p. 20. H.R. Quinn and M.S. Witherell, "The Asymmetry Between Matter and ," Scientijic American (October 1998) p. 76. C. Sutton, "Subatomic Forces," New Scientist (February 11, 1989) p. 1. C. Sutton, "Four Fundamental Forces," New Scientist (November 19, 1988) p. 1. C. Sutton, "The Secret Life of the Neutrino," New Scientist (January 14, 1988) p. 53. M. Veltman, "The ," Scientijic American (November 1986) p. 76. ' S. Weinberg, "The Discovery of Subatomic Particles," Scientijic American (1983) p. 206. S, Weinberg, "A Unified Physics by 20507," Scientijic American (December 1999). D.H, Weingarten, "Computing Quarks," Scientijic American (Febru• ary 1996) p. 116. E.l. Articles 287

E. Witten, "Duality, Spacetime and Quantum Mechanics," Physies Today (May 1997) p. 28. E. Witten, "Reflections on the Fate of Spacetime," Physies Today (April 1996) p. 24.

Accelerator Physics Articles R. Winick, "Synchrotron Radiation," Seientijie Ameriean (Novem• ber 1987) p. 88.

Cosmology Articles J.N. Bahcall and F. RaIzen, "Neutrino Astronomy: The Sun and Beyond," Physies World (September 1996) p. 4l. N. Bahcall, J.P. Ostriker, S. Perlmutter, and P.J. Steinhardt, "The Cosmic Triangle: Revealing the State of the Universe," Seienee (May 1999) p. 148l. S.G. Brush, "Row Cosmology Became a Science," Seientijie Ameri• ean (August 1992) p. 34. M.A. Bueher and D.N. Spergel, " in a Low-Density Uni• verse," Seientijie Ameriean (January 1999) p. 62. W. Freedmann, "The Expansion Rate and the Size of the Universe," Seientijie Ameriean (July 1993) p. 70. R. Gore, "The Onee and Future Universe," National Geographie (June 1983) p. 704. C.J. Rogan, RP. Kirshner, and N.B. Suntzeff, "Surveying Spaee• time with Supernovae," Seientijie Ameriean (January 1999) p.46. R Irion, "The Lopsided Universe," New Seientist (February 1999) p.26. L.M. Krauss, "Cosmologieal Antigravity," Seientijie Ameriean (Jan• uary 1999) p. 52. L.M. Krauss and G.D. Starkman, "The Fate of Life in the Universe," Seientijie Ameriean (November 1999) p. 58. D.E. Osterbroek, J.A. Gwinn, and RS. Brashear, "Rubble and the Expansion of the Universe," Seientijie Ameriean (November 1992) p. 30. 288 Suggested Reading

D. Schramm and G. Steigman, "Particle Accelerators Test Cosmo• logical Theory," Scientijic American (June 1988) p. 66. C. Sutton, "Cosmic Changelings," New Scientist (March 16, 1996) p.28. M.S. TUrner, "Cosmology: Going Beyond the Big Bang," Physics World (September 1996) p. 3l. E.2. Books Particle Physics Books RK. Adair, The Great Design: Particles, Fields and Creation (University Press, 1987). 1. Asimov, Atom: Journey across the Subatomic Cosmos (Truman Talley Books, 1991). L. Brown and L. Hoddeson, Eds., The Birth of Particle Physics (Cambridge University Press, 1983). B. Bunch, Reality's Mirror: Exploring the Mathematics of Symmetry (Wiley Science Editions, 1989). RN. Cahn and G. Goldhaber, The Experimental Foundations of Particle Physics (Cambridge University Press, 1989). N. Calder, The Key to the Universe (Penguin Books, 1978). R Carrigan and P. Trower, Ed., Particles and Forces at the Heart of Matter, Readings from Scientijic American (Freeman, 1990). C. Caso, et al. , (Particle Data Group) Particle Physics Booklet (Springer Verlag, 1998). F. Close, M. Marten, and C. Sutton, The Particle Explosion (Oxford University Press, 1987). RP. Crease, C.C. Mann, and T. Ferris The Second Creation: Makers of the Revolution in 20th Century Physics (Rutgers Univ. Press, 1996). P.C.W. Davies, The Forces of Nature (Cambridge University Press, 1986). B. Devine and F. Wilczek, Longing for the Harmonies (Norton, 1988). G. Fraser, The Particle Century (Institute of Physics, 1998). E.2. Books 289

G. Fraser, The Quark Maehines: How Europe Fought the Particle Physies War (Institute of Physics, 1997). G. Fraser, E. Lillestoel, and 1. Sellevag, The Seareh for Injinity: Solving the Mysteries of the Universe (Facts on File, 1995). H. Fritzsch, The Creation of Matter: The Universe from Beginning to End (Basic Books, 1984. Translated from German 1981). S. Glashow, Interaetions: A Journey through the Mind of a Particle Physieist and the Matter of this World (Warner, 1988). J. Gribbin, Q is for Quantum: An Eneyclopedia of Particle Physics (Free Press, 1999). J.R. Gribbin, The Search for Superstrings, Symmetry, and the (Little Brown, 1999). A.H. Guth and A.P. Lightman, The Infiationary Universe: The Quest for a New Theory of Cosmie Origins (Perseus Press, 1998). M. Kaku, Hyperspace: A Seientijie Odyssey through Parallel Uni• verses, Time Warps, and the 10th Dimension (Oxford Univ. Press, 1994). G. Kane, The Particle Garden (Addison-Wesley Publishing Com• pany, 1995). L.M. Krauss, Fear of Physics (Basic Books, 1993). L.M. Lederman, The God Particle: If the Universe is the Answer, Wh at Is the Question? (Houghton Miffiin, 1993). L.M. Lederman and D.N. Schramm, From Quarks to the Cosmos: Tools of Diseovery (Scientific American Library, Freeman, 1989). J.H. Mauldin, Particles in Nature: The Chronologieal Discovery of the New Physies (Tab Books, 1986). Y. Ne'eman and Y. Kirsh, The Particle Hunters (Cambridge University Press, 1986).

L.B. Okun, 0:, ß, , ... Z, A Primer in Particle Physies (Harwood Academic Publishers, 1987). H. Pagels, Perfeet Symmetry (Simon & Schuster, 1985). 290 Suggested Reading

A. Pais, Inward Bound-Of Matter and Forces in the Physical World (Oxford University Press, 1988). M. Riordan, The Hunting of the Quark (Simon & Schuster, 1987). M. Riordan and D.N. Schramm, Shadows of Creation: Dark Matter and the Structure of the Universe (Scientific American Library, Freeman, 1991). C. Schwarz, A Tour of the Subatomic Zoo (American Institute of Physics, 1992). E. Segre, From X-mys to Quarks: Modern Physicists and Their Discoveries (W.H. Freeman, 1980). G. Smoot and K. Davidson, Wrinkles in Time (Avon Books, 1994). N. Solomey, The Elusive Neutrino: A Subatomic Detective Story (Scientific American Library Series, 1997). C. Sutton, Spaceship Neutrino (Cambridge University Press, 1992). S.J. Traweek, Beamtimes and Lifetimes (Harvard University Press, 1986). J.S. Trefil, From Atoms to Quarks (Doubleday, 1994). P. Watkins, Story of the Wand Z (Cambridge University Press, 1986). S. Weinberg, Dreams of a Final Theory (Pantheon, 1992). A. Zee, Fearful Symmetry (Macmillan, 1986).

Cosmology Books J.D. Barrow and J. Silk, The Left Hand of Creation (Oxford Univ. Press, 1994). F. Close, The Cosmic Onion (Springer-Verlag, 1986). T. Ferris, Coming of Age in the Milky Way (Morrow, 1988). D. Goldsmith, Einstein's Greatest Blunder? The Cosmological Constant and Other Fudge Factors in the Physics of the Universe (Harvard University Press, 1995). B. Greene, The Elegant Universe: Superstring, Hidden Dimensions, and the Quest for the Ultimate Theory (W.W. Norton, 1999) E.2. Books 291

S.W. Hawking, ABrief History of Time (Bantam, 1988). L.M. Krauss, The Fijth Essence; The Search for Dark Matter in the Universe (Basic Books, 1989). L.A. Marschall, The Supernova Story (Plenum Press,1988). H. Pagels, The Cosmic Code (Simon & Schuster, 1982). M. Roos, Introduction to Cosmology (Wiley, 1994). J. Silk, The Big Bang (Freeman, 1989). S. Weinberg, The First Three Minutes (Basic Books, 1977). People Index 293

PEOPLEINDEX

Alvarez, Luis 36 Marsden, Ernest 12, 192 Anderson, Carl D. 36, 195, 196 Noether, Emmy 92 Bequerel, Antoine Henri 19, 191 Panofsky, Wolfgang 5, 197 Bohr, Niels 193 Pauli, Wolfgang 48, 83, 193 Bose, Satyendra Nath 84 Penzias, Arno 158 Chamberlain, Owen 34 Perl, Martin 7, 47, 202 Charpak, Georges 102 Pierre, Fran~ois 113, 202 Cowan, Clyde 48 Planck, Max 57, 192 Cronin, James 94 Rabi, Isidor I. 47 Curie, Marie 19, 191 Reines, Frederick 48 de Broglie, Louis 28, 193 Richter, Burton 2, 109, 202 Democritus 11 Roentgen, Wilhelm Conrad 18 Dirac, Paul 32, 194, 205 Rubbia, Carlo 77, 115, 121, 204 Einstein, Albert 67, 84, 92, 148, 149, 192 Rutherford, Ernest 12, 192, 193 Fermi, Enrico 84, 195, 197 Salam, Abdus 77, 79, 170, 200, 201, 203 Feynman, Richard 197, 200 Schwartz, Melvin 52, 91, 199 Fiteh, Val 94 Schwitters, Roy 3 Friedman, Jerome 65, 200 Segre, Emilio 34 Geiger, Hans 12, 192 Steinberger, Jack 52, 91, 197, 199 Gell-Mann, Murray 36, 57, 59, 63, 198, Taylor, Richard 65, 200, 203 199, 201 Thomson, Joseph J. 19, 45, 191, 192 Glaser, Donald 58 't Hooft, Gerard 64, 201 Glashow, Sheldon 77, 79, 170, 199, 201, Ting, Samuel 1, 110, 202 203, 207 van der Meer, Simon 77, 115, 121, 204 Goldhaber , Gerson 4, 113, 202 Veltman, Martinus 64, 201 Heisenberg, Werner 81, 194 Weinberg, Steven 77,79, 170, 173, 200, Hubble, Edwin 149 201, 203 Kendall, Henry 65, 200 Wilson, Robert 158 Lawrence, Ernest 127 Yang, Chen Ning (C.N.) 94, 197, 198 Lederman, Leon 52, 91, 112, 199, 203 Yukawa, Hideki 29, 47, 195, 196 Lee, Tsung-Dao (T.D.) 94, 198 Zweig, George 36, 59, 63, 199 General Index 295

GENERAL INDEX accelerating charged particles 26-27, 125, accelerator types (cont'd) 254-256 electrostatic 123 accelerating universe 151-153 linear 123-127 accelerator(s) 26, 96, 123-141, 211 synchrotron 127 as microscope 26-28 TV tube as accelerator 27 B factories 137 alpha, beta, gamma (a, ß, 1) radiation, basic design history of 19 circular 127-131 alpha (a) decay 19-20, 24 linear 123-127 angular moment um 56, 211 basic principles 26-28, 125, 254-256 conservation in subatomic physics 275 booster 139 definition of 274 energy of accelerated particles 254 spin 273-279 limiting factors in accel. design 132 annihilation 71, 211 used in search for in colliding-beam experiments 96-100, antiparticles 78 116, 224 W± particles 77-79 in early universe 164-165 ZO particle 77-79 of electron and positron 75, 97, 224 accelerators as colliders 96 of proton and antiproton 165 electron-positron collider 136 antibaryon 62 electron-proton (DESY) 140 search for 165 LEP collider (CERN) 105,204 anticolor 60 LHC collider (CERN) 133, 140-141,217 antifermion 211 PEP collider (SLAC) 137 antimatter 31, 211 proton collider 138 antibaryon 62 accelerators at Brookhaven 198 antiproton discovery 34 accelerators at CERN antiproton production 78 ISR 138 antiquark 31, 36, 53, 60, 67, 75-76, 90, LEP 105,204 97, 212 LHC 133, 140 in collider experiments 105-106 SPS 77 Dirac's theory of 32 accelerators at DESY matter-antimatter imbalance 33, 164-165 HERA 140 positron discovery 34 PETRA 224 antiparticles (see also antimatter) 34, 212 accelerators at FNAL 139 symbolic notation 34 accelerators at SLAC antiproton discovery 34 PEP 137 antiproton production 78 SLAC linac 124, 126 antiquark (see also antimatter) 31, 36, 53, accelerator types 60, 67, 75-76, 90, 97, 212 circular 127-131 astrophysics 143, 212 cyclotron 127 atomic nucleus 22 electron linac 256 discovery of 19 296 General Index

atomic structure 11, 37-38 CERN 49, 77, 105, 121, 213 B factories 97, 137, 212 colliders 136, 138, 140 BaBar detector at SLAC 97 charge 59-84, 213 balloon-borne experiments 165 and interactions 73, 265 baryon 35-36, 55, 84, 166, 212 color charge 60, 213 baryon-antibaryon asymmetry 164-165, conservation 85, 214 212 electric charge of quarks 59 baryons, discoveries; timeline of 31 strong charge 39 examples of 56 charm quark (c) 7, 58-59, 64, 213 patterns of 35, 63 and 112-115 quantum number, conservation 88-90 and Jj'IjJ 110-112 beam(s) (of particles) 14, 25-27, 212 flavor of 89 beam and magneto-optical elements 129 chronology 189 bending 131, circular accelerator 127 257-258 cloud chamber 20-21, 29, 32, 55, 258 colliding-beam 77, 96-98 COBE satellite 158-160 in accelerators 121-132, 139 collider 96, 213 proton-antiproton beam 121 proton collider 138 beta (ß) decay 24, 40, 49, 79 electron-positron collider 136 beta (ß) radiation 24 electron-proton collider 140 bibliography 285 hadron collider (LHC) 98 big-bang theory 146-168, 212 colliding-beam experiments 96, 134-135,213 binding energy 267-270 color 39, 42, 59-62, 74 of the deuteron 270 color charge (see also color) 213 180-187 color force 60, 266 booster 139 color neutral 61, 213 boson 83, 212 composite particles 40, 84 bottom quark (b) 58, 59, 64, 112, 213 mass of 267 Brookhaven National Laboratory 1, 110 computer-generated event pictures bubble chambers 34, 50, 58, 78, 115 105-107, 250 calorimeter 101-106, 213 computer simulations 99 electromagnetic ~ 101, 132, 229-231 confinement 65, 68, 70, 74, 80, 213 hadron ~ 101, 231 conservation laws 85-94, 214 carriers of forces 53, 71-84, 173 and charge 213 electromagnetic ~ 73 and quantum numbers 85-89 exchange mechanism 73 and symmetry 92-94 gluon as ~ 74-76 and virtual particles 80-81, 221 graviton as ~ 83 angular moment um 275 photon as ~ 73 energy 239-240, 245 pions as ~ 75 in classical physics 239 weak interaction ~ 77-79 relativistic description 241 W, Z bosons as ~ 73-79 momentum 238, 240 cathode rays 46 and event pictures 248-252 Cerenkov detector 232 measurement of particle's ~ 257 Cerenkov radiation 232-233 and the Standard Model 89-91 General Index 297

cosmic microwave background 157-160 detector( s) (cant' d) 95-119, 214 cosmic rays 29, 30 measurement of cosmological constant 152, 155 muon lifetime 272-273 cosmological parameters 155 particle lifetimes 246 cosmology 146, 214 particle mass 245 Coulomb potential 263 particle momentum 257 Coulomb's law of 23, 259 proton lifetime 166 and Gravity 23 top quark mass 64, 117-119, 248-252 critical mass density of the universe 156 neutrino detector 145 cyclotron 127 D meson 47, 112-115 electrons 231 decay of 113 hadrons 232 dark matter 33, 144, 157, 214 muons 233 Dirac's theory of antimatter 32 shapes of detectors 103 decay(s) 54, 214 deuteron binding energy 270 alpha (0:) decay 19 dipole magnet and particles 119 beta (ß) decay 40 discoveries of particles, timeline 31 D meson decay 113 Doppler-shift in star spectra 151 decay law of radioactivity 273 down quark (d) 40, 59-64, 214 lepton decay 53 drift chamber 105, 226 neutron decay (hypothetical) 87 electric charge 214 rP -+ K+ + K- 113 of quarks 59 quark decay 69 electromagnetic calorimeter 100, 132, rates and strength of inter action 24 229-231 ZO -+ f-L+ + f-L- 116 electromagnetic force 252-267 DESY 75, 140, 224 electromagnetic interaction 42, 214 detector(s) 95-119, 214 force carrier of 73, 82 basic principle 98-100 unification of 80 bubble chamber 34, 50, 58, 78, 115 electron (e-) 16-18, 35, 37, 39, 51, 55, 214 cloud chamber 20-21, 29, 32, 55, 258 accelerators 27, 256 detector components 100-102 and beta (ß) decay 19, 24, 40, 48-49, calorimeter 101-102, 213 70,79 electromagnetic ~ 101, 132, 229-231 collider 96, 97, 136 hadron ~ 101, 231 diffraction of electron 247 drift chambers 105, 226-228 discovery of electron 45-46 muon chamber 102, 104 identification in detectors 231 proportional counters 225 linac 123-127, 256 scintillators 227 quantum number 89-91 silicon strips 227 scattering 65-66 tracking devices 223 spin (meson) 57 vertex detectors 221, 224 electron-positron collider 96, 97, 136 event pictures electronvolt (e V) 51, 125 computer generated ~ 105-107, 250 electrostatic accelerator 123 computer simulations 99 electroweak interaction 80, 171, 214 force carriers of 77 298 General Index

elements, abundances of 161-163 force(s) (cont'd) energy carrier particles 71-84 and mass 51, 242-244 due to fields 260 and uncertainty relation 282 electrical forces 22-23 at everyday scales 240 electramagnetic forces 252-254 conservation of energy fundamental forces 15-25, 50 in classical physics 239 in classical physics 237 relativistic description 241-245 residual forces 42, 219, 266 energy loss of particles 232 strang nuclear forces 22 energy of accelerated particles 254-267 weak forces 24-25 event 97, 214 force field 83, 105 event picture(s) 98, 105-107 fractional charges 59, 68 oftop decay 250-251 frames of reference 241 evolution of the universe 153 freeze out 162-163, 215 exchange of force carrier particles 73 fundamental building blocks exclusion principle 83, 215 of elements 11 experiments 12 of matter 15 basic technique 25 fundamental interaction (forces) 15, 50, 215 colliding-beam experiments 96, 134-136 between quarks and leptons 39 discovery of atomic nucleus 12 relative strength of 82 discovery of D meson 112-115 fundamental particle(s) 215 discovery of J /1/J 109-112 force carriers 71 discovery of rr particle 58 leptons 39 discovery of tau lepton (T) 108 quarks 36 discovery of top quark (t) 117, 248-252 fusion (nuclear) 270 discovery of Wand Z bosons 115 galaxy(ies) 15, 144, 216 electron scattering experiments 66 and dark matter 157 fixed-target experiments 134-135 formation of 148 Fermilab 139, 215 receding galaxies 150 (Fermi National Accelerator Lab) gamma ('Y) particle 73, 84 fermion 83-84, 215 from annihilation 97 ~n 2re gamma rays ('Y rays) 19, 24 field(s) 252-254 general relativity 149, 152-153,174-175, field !ines 253 181, 184, 216 fixed-target experiment 134, 215 generation 216 fiavor 45, 52, 62, 215 geometries of space 153-155 change of 79-80 glossary 211-221 FNAL (see Fermilab) gluon (g) 74, 84, 216 Tevatron 139 and experiments 75-76 force(s) radiation 76, 107 (see also interactions and carriers of force) spin 89 and decay rates 24 Grand Unified Theory (GUT) 165, 216 and nuclear structure 74-76 gravitational constant 186 and potential energy 261-265 in higher dimensions 186-187 between particles 258 General Index 299

gravitational interaction 41, 83, 216 LHC 98, 133, 140-141, 217 and electrostatic forces 23 (Large Hadron Collider, CERN) force carriers of 83-84 lifetime 54, 217 Newton's law of 39, 175 and decay law 54, 271-273 and spacetime 175-180 measurement 246 graviton (G) 83, 216 muon lifetime 272-273 gravity (see gravitational interaction) proton lifetime 166, 273 Greek alphabet 209 light year 217 hadron 35, 39, 60, 216 limiting factors in accelerator design 132 hadron calorimeter 101, 231 linac (linear accelerator) 123-127, 217, 256 half-life 216, 272 Mach cone 233 and interaction strength 41 magnetic field and particles 131, 133, 257 Higgs boson 171-173,216 magneto-optical elements 129-130 historical perspectives 189 mass 217 Hubble's law 150 binding energy and mass 267-270 interactions (see also forces) 22, 39-43, critical mass density of the universe 156 71-84, 216 deficit 267 definition of 22 determination of top quark mass 248-252 electromagnetic 39, 73 energy relationship 242-246 gravitational 41, 83, 216 of composite objects 267-268 of quarks and leptons 39 origin of 65, 171 relative strength of fundamental ~ 42 quark masses 68 residual 42, 219, 266-267 relativistic description 244 strong 39, 60 units of 51 weak 40, 77-79 matter-antimatter imbalance 33, 164 identification of particles matter waves 28, 246-248 electrons 231 meson(s) 35, 55-56, 218 hadrons 232 as colorless quark combinations 61 muons 233 B mesons 137 Intersecting 138 charmed mesons 110 (ISR, CERN) strange mesons 112 isotopes 21 microwave(s) 74, 218 J/1/J particle discovery 1-10, 100, 109-115 in accelerator technique 123 jet 76, 106, 119, 216, 249-250 radiation cosmic 157-160 K meson (see also kaon) 63, 112 moment um 58, 81, 90, 94 Kamiokande (super-neutrino detector) 145 and wavelength of a particle 28 kaon (K) 56, 63, 112, 114, 217 angular momentum 56, 211 (A) 53 in classical physics 240 LEP 105, 204 in colliding-beam experiments 134-136 (Large Electron-Positron Collider, CERN) of accelerated particles 125-126, 135 lepton 35, 39, 45-55, 217 measurement of a particles ~ 99, 223, 257 decay 53-54 relativistic description 126, 242 number conservation 88-91 table 51 300 General Index

muon (IL) 29-30, 47, 50-53, 218, 272 particle(s) (cont'd) 218 chamber 102, 104 types (see also corresponding keywords) discovery of 29 electron (e -), kaon (K), muon (IL), decay of 55, 91 neutrino (v), neutron (n), pion (7r), from collision events 105-107 positron (e+), proton (p), quarks from tau (T) decays 108-109 zoo 25, 36 from top (t) decays 118 periodic table of elements 11-12 from ZO decays 116 phi decay (cf; --+ K+ + K-) 113 lifetime 272-273 photon C'Y) 219 neutral 218 as force carrier 73 color neutral 61 pion (7r) 219 neutrino (v) 48, 218 discovery 29 detector 145 in 35 interactions 49 Planck's constant (h) 57 types 48, 51 plasma 219 neutron (n) 21, 218 potential energy decay of 24, 40, 79-80, 87 and force 82, 261-265 Newton's law of gravitation 23, 175 positron (e +) 32, 136, 219 23, 42, 269 discovery of 32-33 nuclear fusion 162, 270 proportional counters 102, 225-226 nuclear reactions, first observed 21 proton (p) 219 nucleon 21, 218 as building block of the nucleus 23 nucleosynthesis 148, 160-163, 218 collider 138 nucleus decay and lifetime 166, 273 and its building blocks 22-23 spin from quarks 279 discovery of 12-13 QCD () 201, 203 Omega-minus (~r) particle discovery57-58 QED (quantum electrodynamics) 197, 201 pair creation 34 quadrupole magnets 130 parity violation 94 quantum 57, 219 parsec (pc) 218 quantum chromodynamics (QCD) 201,203 particle(s) 218 quantum electrodynamics (QED) 197, 201 (see also corresponding keywords) quantum ideas 192 acceleration (see accelerators) quantum mechanics 219 baryons, discoveries; timeline of 31 quantum numbers 63, 85, 88 baryons, examples of 56 strangeness 63 baryons, patterns of 35, 63 quantum physics 57 detection of (see detectors) quarkes) 36, 59-70, 219 identification of and pattern of baryons 63 by measuring moment um 257 as fundamental building blocks 36 leptons 45-55, 90-91 confinement 65 mesons, examples of 56 experimental evidence 36, 65, 110-114, patterns of 35-36 248 size of 38 decay 69-70 mass 70 observation of 36, 65, 110-114, 248 General Index 301

quark(s) (cont 'd) 36, 59-70, 219 strangeness quantum number 63 properties, summary of 70 strength of fundamental interactions 82 quark-antiquark combinations 61 183-186 separation 66-68 strong interaction 39-60, 220 radioactivity carrier particles of 74 and decay law 273 charge of 39 discovery of 19 strong nuclear force 22, 42 radio frequency (RF) in accelerators 127 structure within the atom 11-23 red giant stars 147 modern view of 37 relativistic kinematics 242 subatomic particle 220 relativity superconducting magnets 133 general 149, 152-153, 174-175, 181, SuperKamiokande detector 145 184, 216 supernova 146, 220 special 135, 242-244 SN1987A 143-145 moment um in ~ 126, 135 symmetry residual interaction 42, 219, 266 and conservation laws 92-94 rest mass 219 symmetry breaking 171 rho (p) meson 39 synchrotron 127, 220 scattering experiments synchrotron radiation 132 electron 66 target 14,25 fundamental technique 13, 25 tau (1") lepton 47,220 Schwarzschild and black holes 182 decay of 91, 109 scintillation 219 discovery of 47, 108 silicon strip devices 227 Tevatron 139, 178, 220 size of particles 38 time SLAC 1-10,47,65,95-97, 109-111, 124, relativistic description of 245 137, 200, 202-204, 220, 256 timeline of particle discoveries 31 SLAC linac 123, 256 top quark (t) 64, 220 spatial dimensions discovery of 11 7-119 in modern theories 174-180 mass determination of 248-252 special relativity (see relativity) track 20, 220 spin 56, 89, 220 tracking detectors 20, 34, 223-227 and angular momentum 273-279 transrnutation of the elements 20 discovery of 277 TV tube as accelerator 27 neutrino spin from beta (ß) decay 278 U ncertainty principle 81, 194, 221, proton spin by its components 279 279-281 SPS 77 consequences of 281 (Super Proton Synchrotron, CERN) unification stable 220 of weak and electromag. interaction 80 Standard Model 11, 40, 65, 83, 220 units and conservation laws 89 of energy 255 status of 169 of mass 51 Stanford Linear Accelerator (see SLAC) universe, accelerating 151-153 Stern-Gerlach experiment 277 up quark (u) 40, 59-64, 221 strange quark (8) 57, 59, 63, 220 vertex detector 221, 224 302 General Index

virtual particles 81, 221, 282 W± boson 221 search for 77-79 discovery of 79, 115 wavelength of particles 246 weak inter action 24-25, 42, 79, 221 carrier particles (table) 77 wire chamber 224, 227 (see also drift chamber) x rays 18 ZO ...... p,+ + p,- decay 116 ZO boson 77, 221 discovery 79, 115 search for 77-79