Particle physics file prepared by muzammal from hyperphyiscs site

7/31/2019 Particle physics file prepared by muzammal from hyperphyiscs site

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Sourse of this file is:-

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/parcon.html

Contants:Quarks --------------------------------------------------------------------------------------------03Why "Quark"? -----------------------------------------------------------------------------------03

Up and Down Quarks----------------------------------------------------------------------------04The Strange Quark--------------------------------------------------------------------------------04

The Top Quark------------------------------------------------------------------------------------05

Confinement of Quarks--------------------------------------------------------------------------05

The Bottom Quark-------------------------------------------------------------------------------06

Leptons--------------------------------------------------------------------------------------------06

Electron and Positron---------------------------------------------------------------------------07

Muon-----------------------------------------------------------------------------------------------07

Tau-------------------------------------------------------------------------------------------------08

Positron Annihilation----------------------------------------------------------------------------08

Electron-Positron Pair Production-------------------------------------------------------------08

Properties of the Leptons-----------------------------------------------------------------------09

Mesons--------------------------------------------------------------------------------------------09Pion------------------------------------------------------------------------------------------------09

The psi/J Particle---------------------------------------------------------------------------------11

The Upsilon Particle-----------------------------------------------------------------------------11

Hadrons--------------------------------------------------------------------------------------------11Baryons--------------------------------------------------------------------------------------------11

Hideki Yukawa and the Pion--------------------------------------------------------------------12

The Eta Meson------------------------------------------------------------------------------------12

The Rho Meson-----------------------------------------------------------------------------------13

The Phi Meson------------------------------------------------------------------------------------13

Color-----------------------------------------------------------------------------------------------13

Color Force---------------------------------------------------------------------------------------14

Transformation of Quark Flavors by the Weak Interaction---------------------------------14

Quark Transformations---------------------------------------------------------------------------15

The Lambda Baryon------------------------------------------------------------------------------16

The Omega-Minus Baryon----------------------------------------------------------------------17

Spin Classification--------------------------------------------------------------------------------18

Fermions--------------------------------------------------------------------------------------------19

Bosons----------------------------------------------------------------------------------------------19

Bose-Einstein Condensation---------------------------------------------------------------------19

D Meson--------------------------------------------------------------------------------------------20

Bag Model of Quark Confinement--------------------------------------------------------------21

Asymptotic Freedom------------------------------------------------------------------------------22Electron Neutrinos and Antineutrinos----------------------------------------------------------22

Detection of Neutrinos---------------------------------------------------------------------------23

Sudbury Neutrino Observatory-----------------------------------------------------------------23

The Solar Neutrino Telescope-------------------------------------------------------------------24

Detection of Supernova Neutrinos--------------------------------------------------------------25

Neutrino Mass?------------------------------------------------------------------------------------25

Some Neutrino History---------------------------------------------------------------------------25

Fundamental Forces------------------------------------------------------------------------------26

The Strong Force----------------------------------------------------------------------------------26

The Electromagnetic Force---------------------------------------------------------------------27

The Weak Force---------------------------------------------------------------------------------28

Feynman Diagrams for Weak Force----------------------------------------------------------28

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Super-Kamiokande Neutrino Detector-------------------------------------------------------30

Electron, Muon, and Tau Neutrinos----------------------------------------------------------31

Cerenkov Radiation-----------------------------------------------------------------------------31Cerenkov Applications-------------------------------------------------------------------------32

Particle Interactions and Conservation Laws------------------------------------------------33

Conservation of Baryon Number--------------------------------------------------------------34

Conservation of Lepton Number--------------------------------------------------------------34

Parity----------------------------------------------------------------------------------------------35

Isospin---------------------------------------------------------------------------------------------35

Crossing Symmetry------------------------------------------------------------------------------36

Totalitarian Principle----------------------------------------------------------------------------37

CPT Invariance-----------------------------------------------------------------------------------38

Charge Conjugation-----------------------------------------------------------------------------38

Time Reversal------------------------------------------------------------------------------------39

CP Invariance------------------------------------------------------------------------------------40

Kaons----------------------------------------------------------------------------------------------40

Gluons----------------------------------------------------------------------------------------------42Feynman Diagrams-------------------------------------------------------------------------------42

Intermediate Vector Bosons---------------------------------------------------------------------44

Properties of W and Z----------------------------------------------------------------------------44

Photon-----------------------------------------------------------------------------------------------45Graviton---------------------------------------------------------------------------------------------45

Parity------------------------------------------------------------------------------------------------46

Non-conservation of Parity-----------------------------------------------------------------------46

Cronin and Fitch Experiment with Kaons------------------------------------------------------47

CP Violation in Kaon Decay---------------------------------------------------------------------48

Left-Handed Neutrinos----------------------------------------------------------------------------48

Cowan and Reines Neutrino Experiment--------------------------------------------------------49

Electroweak Unification---------------------------------------------------------------------------50

Spontaneous Symmetry Breaking----------------------------------------------------------------50

Symmetry Breaking: Analogies------------------------------------------------------------------50

Magnetic Symmetry Breaking--------------------------------------------------------------------51

Grand Unification-----------------------------------------------------------------------------------51Neutrino Cross Section-----------------------------------------------------------------------------51

The Higgs Boson-----------------------------------------------------------------------------------53Unification of Gravity-----------------------------------------------------------------------------54

meson diagram--------------------------------------------------------------------------------------55

Table of mesons-------------------------------------------------------------------------------------56

Table of Baryons------------------------------------------------------------------------------------58

The Eta Meson--------------------------------------------------------------------------------------59

The Rho Meson-------------------------------------------------------------------------------------59

The Phi Meson--------------------------------------------------------------------------------------60

The B Meson----------------------------------------------------------------------------------------60

The Mystery of Quark Mass----------------------------------------------------------------------60

The Delta Baryon----------------------------------------------------------------------------------61The Xi Baryon--------------------------------------------------------------------------------------61

The Omega-Minus Baryon------------------------------------------------------------------------63

The Lambda Baryon-------------------------------------------------------------------------------64

The Sigma Baryon----------------------------------------------------------------------------------65

Neutral Currents and the 0Z ---------------------------------------------------------------------65

The Azimuthal Equation--------------------------------------------------------------------------66

The Magnetic Quantum Number---------------------------------------------------------------67

Selection Rules for Electronic Transitions--------------------------------------------67

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Up and Down QuarksThe up and down quarks are the most common and least massive quarks, being the

constituents of protons and neutrons and thus of most ordinary matter.

The fact that the free neutron decays

and nuclei decay by beta decay in processes like

is thought to be the result of a more fundamental quark process

The Strange QuarkIn 1947 during a study of cosmic ray interactions, a product of a proton collision with a

nucleus was found to live for much longer time than expected: 10-10 seconds instead of theexpected 10-23 seconds! This particle was named the lambda particle (0) and the

property which caused it to live so long was dubbed "strangeness" and that name stuck to

be the name of one of the quarks from which the lambda particle is constructed. Thelambda is a baryon which is made up of three quarks: an up, a down and a strange quark.

The shorter lifetime of 10-23 seconds was expected because the lambda as a baryonparticipates in the strong interaction, and that usually leads to such very short lifetimes. The

long observed lifetime helped develop a new conservation law for such decays called the

"conservation of strangeness". The presence of a strange quark in a particle is denoted by a

quantum number S=-1. Particle decay by the strong or electromagnetic interactionspreserve the strangeness quantum number. The decay process for the lambda particle must

violate that rule, since there is no lighter particle which contains a strange quark - so the

strange quark must be transformed to another quark in the process. That can only occur bythe weak interaction, and that leads to a much longer lifetime. The decay processes show

that strangeness is not conserved:

The quark transformations necessary to accomplish these decay processes can be visualized

with the help of Feynmann diagrams.

The omega-minus, a baryon composed of three strange quarks, is a classic example of the

need for the property called "color" in describing particles. Since quarks are fermions withspin 1/2, they must obey the Pauli exclusion principle and cannot exist in identical states.

So with three strange quarks, the property which distinguishes them must be capable of at

least three distinct values.

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Conservation of strangeness is not in fact an independent conservation law, but can be

viewed as a combination of the conservation of charge, isospin, and baryon number. It is

often expressed in terms of hypercharge Y, defined by:

Isospin and either hypercharge or strangeness are the quantum numbers often used to draw

particle diagrams for the hadrons.weak interaction in order for it to decay.

One baryon with a charm quark is a called a lambda with symbol c+

. It has a

composition udc and a mass of 2281 MeV/c2.

The Top QuarkConvincing evidence for the observation of the top quark was reported by Fermilab 'sTevatron facility in April 1995. The evidence was found in the collision products of 0.9

TeV protons with equally energetic antiprotons in the proton-antiproton collider. Theevidence involved analysis of trillions of 1.8 TeV proton-antiproton collisions. The

Collider Detector Facility group had found 56 top candidates over a predicted background

of 23 and the D0 group found 17 events over a predicted background of 3.8. The value forthe top quark mass from the combined data of the two groups after the completion of the

run was 174.3 +/- 5.1 GeV. This is over 180 times the mass of a proton and about twice the

mass of the next heaviest fundamental particle, the Z0 vector boson at about 93 GeV.

The interaction is envisioned as follows:

Confinement of QuarksHow can one be so confident of the quark model when no one has ever seen an isolatedquark? There are good reasons for the lack of direct observation. Apparently the color force

does not drop off with distance like the other observed forces. It is postutated that it mayactually increase with distance at the rate of about 1 GeV per fermi. A free quark is notobserved because by the time the separation is on an observable scale, the energy is far

above the pair production energy for quark-antiquark pairs. For the U and D quarks the

masses are 10s of MeV so pair production would occur for distances much less than afermi. You would expect a lot of mesons (quark-antiquark pairs) in very high energy

collision experiments and that is what is observed.

Basically, you can't see an isolated quark because the color force does not let them go,and the energy required to separate them produces quark-antiquark pairs long before they

are far enough apart to observe separately.

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One kind of visualization of quark confinement is called the "bag model". Onevisualizes the quarks as contained in an elastic bag which allows the quarks to move freely

around, as long as you don't try to pull them further apart. But if you try to pull a quark out,

the bag stretches and resists.Another way of looking at quark confinement is expressed by Rohlf. "When we try

to pull a quark out of a proton, for example by striking the quark with another energetic

particle, the quark experiences a potential energy barrier from the strong interaction that

increases with distance." As the example of alpha decay demonstrates, having a barrierhigher than the particle energy does not prevent the escape of the particle - quantum

mechanical tunneling gives a finite probability for a 6 MeV alpha particle to get through a

30 MeV high energy barrier. But the energy barrier for the alpha particle is thin enough fortunneling to be effective. In the case of the barrier facing the quark, the energy barrier does

not drop off with distance, but in fact increases.

The Bottom Quarkn 1977, an experimental group at Fermilab led by Leon Lederman discovered a new

resonance at 9.4 GeV/c^2 which was interpreted as a bottom-antibottom quark pair andcalled the Upsilon meson. From this experiment, the mass of the bottom quark is implied to

be about 5 GeV/c 2. The reaction being studied was

where N was a copper or platinum nucleus. The spectrometer had a muon-pair massresolution of about 2%, which allowed them to measure an excess of events at 9.4

GeV/c^2. This resonance has been subsequently studied at other accelerators with a

detailed investigation of the bound states of the bottom-antibottom meson.

LeptonsLeptons and quarks are the basic building blocks of matter, i.e., they are seen as the

"elementary particles". There are six leptons in the present structure, the electron, muon,and tau particles and their associated neutrinos. The different varieties of the elementary

particles are commonly called "flavors", and the neutrinos here are considered to havedistinctly different flavor.

Important principles for all particle interactions are the conservation of lepton number and

the the conservation of baryon number.

Now that we have experimental evidence for six leptons, a relevant question is "Are

there more?". The present standard model assumes that there are no more than threegenerations. One of the pieces of experimental evidence for that is the measured

hydrogen/helium abundance ratio in the universe. When the process of nucleosynthesis

from the big bang is modeled, the number of types of neutrinos affects the abundance ofhelium. The observed abundance agrees with three types of neutrinos.

Electron and Positron

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As one of the leptons, the electron is viewed as one of the fundamental particles. It is afermion of spin 1/2 and therefore constrained by the Pauli exclusion principle, a fact that

has key implications for the building up of the periodic table of elements.

The electron's antiparticle, the positron, is identical in mass but has a positive charge. If an

electron and a positron encounter each other,they will annihilate with the production of two

gamma-rays. On the other hand, one of the mechanisms for the interaction of radiation with

matter is the pair production of an electron-positron pair. Associated with the electron is athe electron neutrino.

MuonThe muon is a lepton which decays to form an electron or positron.

The fact that the above decay is a three-particle decay is an example of the conservation of

lepton number; there must be one electron neutrino and one muon neutrino or antineutrinoin the decay.

The lifetime of the muon is 2.20 microseconds. The muon is produced in the upper

atmosphere by the decay of pions produced by cosmic rays:

Measuring the flux of muons of cosmic ray origin at different heights above the earth is animportant time dilation experiment in relativity.

Muons make up more than half of the cosmic radiation at sea level, the remainder

being mostly electrons, positrons and photons from cascade events.(Richtmyer) The

average sea level muon flux is about 1 muon per square centimeter per minute

Tau

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The tau is the most massive of the leptons, having a rest mass some 3490 times the massof the electron, also a lepton. Its mass is some 17 times that of the muon, the other massive

lepton

Positron AnnihilationThe positron is the antiparticle of the electron, and when a positron enters any normal

matter, it will find an abundant supply of electrons with which to annihilate. The energyreleased by the annihilation forms two highly energetic gamma rays, and if one assumes

that the momenta of the positron and electron before the annihilation, the two gamma ray

photons must travel in opposite directions in order to conserve momentum.

These coincident gamma rays at 180 degrees provide a useful analysis tool. For one thing,eliminating all gamma events which are not coincident at 180 degrees improves the signal-

to-noise ratio of experiments using positron annihilation. Another interesting application isthe use of the coincident gammas to locate the source by back projecting. This is used in

medical PET scans.

Electron-Positron Pair ProductionWhen a photon has quantum energy higher than the rest mass energy of an electron plus a

positron, one of the ways that such a photon interacts with matter is by producing and

electron-positron pair.

The rest mass energy of the electron is 0.511 MeV, so for photon energy above 1.022MeV,

pair production is possible. For photon energies far above this threshold, pair production

becomes the dominant mode for the interaction of x-rays and gamma-rays with matter.

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Properties of the Leptons

MesonsMesons are intermediate mass particles which are made up of a quark-antiquark pair.

Three quark combinations are called baryons. Mesons are bosons, while the baryons arefermions. Recent experimental evidence shows the existence of five-quark combinations

which are being called pentaquarks.

Pion

The neutral pion decays to an electron, positron, and gamma ray by the electromagnetic

interaction on a time scale of about -1610 seconds. The positive and negative pions have

longer lifetimes of about 2.6 x -810 s.

The negative pion decays into a muon and a muon antineutrino as illustrated below. Thisdecay is puzzling upon first examination because the decay into an electron plus an

electron antineutrino yields much more energy. Usually the pathway with the greatest

energy yield is the preferred pathway. This suggests that some symmetry is acting to inhibitthe electron decay pathway.

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The symmetry which suppresses the electron pathway is that of angular momentum, as

described by Griffiths. Since the negative pion has spin zero, the electron and antineutrino

must be emitted with opposite spins to preserve net zero spin. But the antineutrino isalways right-handed, so this implies that the electron must be emitted with spin in the

direction of its linear momentum (i.e., also right-handed). But if the electron were massless,

it would (like the neutrino) only exist as a left-handed particle, and the electron pathwaywould be completely prohibited. So the suppression of the electron pathway is attributed to

the fact that the electron's small mass greatly favors the left-handed symmetry, thus

inhibiting the decay. Weak interaction theory predicts that the fraction of muons decayinginto electrons should be 1.28 x 10-4 and the measured branching ratio is 1.23 +/- 0.02 x 10-

4.

The pion, being the lightest meson, can be used to predict the maximum range ofthe strong interaction. The strong interaction properties of the three pions are identical. The

connection between pions and the strong force was proposed by Hideki Yukawa. Yukawa

worked out a potential for the force and predicted its mass based on the uncertainty

principle from measurements of the apparent range of the strong force in nuclei.Being composed of an up and an antidown quark, the positive pion would be

expected to have a mass about 2/3 that of a proton, yet it's mass is only about 1/6 of that of

the proton! This is an example of how hadron masses depend upon the dynamics inside theparticle, and not just upon the quarks contained. The pion is a meson. The + is considered

to be made up of an up and an anti-down quark. The neutral pion is considered to be a

combination

Pions interact with nuclei and transform a neutron to a proton or vice versa:

The pions + and - have spin zero and negative intrinsic parity

The psi/J Particle

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The psi/J particle is a meson which was discovered in 1974 by experimenters at Stanford

(Richter) and Brookhaven National Laboratory (Ting). Slightly more than three times asmassive as the proton, this particle decayed slowly and didn't fit into the framework of the

up, down, and strange quarks. It is considered to be a charm-anticharm quark pair and wasthe first firm experimental evidence for the fourth quark. Richter and Ting shared the 1976

Nobel Prize for their discovery.

The Upsilon Particle

The upsilon particle is a meson which was discovered at Fermilab in 1977. It appeared asanother long-lived particle which didn't fit into the framework of the first four quarks, the

up,down, strange, and charm quarks. It is taken as a botton-antibottom quark pair and was

the first experimental evidence of the fifth quark.

HadronsParticles that interact by the strong interaction are called hadrons. This general

classification includes mesons and baryons but specifically excludes leptons, which do notinteract by the strong force. The weak interaction acts on both hadrons and leptons.

Hadrons are viewed as being composed of quarks, either as quark-antiquark pairs (mesons)or as three quarks (baryons). There is much more to the picture than this, however, because

the constituent quarks are surrounded by a cloud of gluons, the exchange particles for the

color force.

Recent experimental evidence shows the existence of five-quark combinations whichare being called pentaquarks

BaryonsBaryons are massive particles which are made up of three quarks in the standard model.

This class of particles includes the proton and neutron. Other baryons are the lambda,

sigma, xi, and omega particles. Baryons are distinct from mesons in that mesons are

composed of only two quarks. Baryons and mesons are included in the overall class knownas hadrons, the particles which interact by the strong force. Baryons are fermions, while the

mesons are bosons. Besides charge and spin (1/2 for the baryons), two other quantum

numbers are assigned to these particles: baryon number (B=1) and strangeness (S), whichin the chart can be seen to be equal to -1 times the number of strange quarks included.

The conservation of baryon number is an important rule for interactions and decays ofbaryons. No known interactions violate conservation of baryon number.

Recent experimental evidence shows the existence of five-quark combinations which

are being called pentaquarks. The pentaquark would be included in the classification of

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baryons, albeit an "exotic" one. The pentaquark is composed of four quarks and anantiquark, like a combination of an ordinary baryon plus a meson.

Hideki Yukawa and the PionOnce quantum electrodyamics had produced the picture of the electromagnetic force as a

process of exchanging photons, the question of whether or not the other forces were also

exchange forces was a natural one. In 1935, Hideki Yukawa reasoned that the

electromagnetic force was infinite in range because the exchange particle was massless. Heproposed that the short range strong force came about from the exchange of a massive

particle which he called a meson. By observing that the effective range of the nuclear force

was on the order of a fermi, a mass for the exchange particle could be predicted using theuncertainty principle. The predicted particle mass was about 100 MeV. It did not receive

immediate attention since no one knew of a particle which fit that description.

In 1937 a particle of mass close to Yukawa's prediction was discovered in cosmicrays by Anderson & Neddermeyer and by Street & Stevenson in independent experiments.

This particle, the muon, turned out not to interact by the strong interaction. Hans Bethe and

Robert Marshak predicted that the muon could be a decay product of the particle sought. In1947, Lattes, Muirhead, Occhialini and Powell conducted a high altitude experiment, flying

photographic emulsions at 3000 meters. These emulsions revealed the pion, which met allthe requirements of the Yukawa particle.

We now know that the pion is a meson, a composite particle, and the currentview is that the strong interaction is an interaction between quarks, but the Yukawa theory

stimulated a major advance in the understanding of the strong interaction.

The Eta Meson

2* The neutral eta meson is considered to be a quark combination

The Rho Meson

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The rho meson has the same quark composition as the pion and can be considered to be an

excited state of the pion. The fact that its mass is five and one half times the mass of the

pion illustrates the difficulties of assigning mass to the quarks. Hadron masses depend uponthe dynamics inside the particle, and not just upon the quarks contained. The quark

modeling of the pion and rho classifies the pion as a pseudoscalar meson with zero angular

momentum. The quarks have spin 1/2 and the spins are "paired" or anti-aligned. In the rhomeson, a vector meson, the angular momentum is j=1, indicating parallel spins. Under the

influence of the strong color force, the state with spins aligned has a higher energy whichshows up as a larger mass energy. The analogy to the higher energy of aligned spins in amagnetic field (Zeeman effect) is instructive, but this difference in energy associated with

the color force is enormous.

Georgi comments "There is good reason to believe that most of the mass of the quark that

we 'see' in the mass of the proton or the rho is a dynamical effect of quark confinement,

that the u and d quarks in the underlying QCD theory actually have masses much smallerthan 1/3 the mass of the proton."

The omega meson is grouped here with the rho mesons because of similar mass and

the same constituent quarks.

The Phi Meson

ColorColor is the strong interaction analog to charge in the electromagnetic force. The term

"color" was introduced to label a property of the quarks which allowed apparentlyidentical quarks to reside in the same particle, for example, two "up" quarks in the proton.

To allow three particles to coexist and satisfy the Pauli exclusion principle, a property with

three values was needed. The idea of three primary colors like red, green, and blue makingwhite light was attractive, and language about "colorless" particles sprang up. It has

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nothing whatever to do with real color, but provides three distinct quantum states. Theproperty can be considered something like a "color charge" with three distinct values, with

only color neutral particles allowed. The terms "color force" and even "quantum

chromodynamics" have been used, extending the identification with color terms. Theantiquarks have anti-colors, so the mesons can be colorless by having a red and an "anti-

red" quark. The idea of color is supported by the fact that all commonly observed particles

have either three quarks (baryons) or two (mesons), the combinations which can be

"colorless" or "color neutral" with the three values of color. This does not exclude "di-baryons" with 6 quarks and other combinations of more than three. The only experimental

indication of the presence of such particles is recent evidence for a penta-quark particle.

The rationale for the concept of color can be highlighted with the case of the omega-minus,

a baryon composed of three strange quarks. Since quarks are fermions with spin 1/2, they

must obey the Pauli exclusion principle and cannot exist in identical states. So with three

strange quarks, the property which distinguishes them must be capable of at least threedistinct values.

Color ForceA property of quarks labeled color is an essential part of the quark model. The force

between quarks is called the color force. Since quarks make up the baryons, and the stronginteraction takes place between baryons, you could say that the color force is the source of

the strong interaction, or that the strong interaction is like a residual color force which

extends beyond the proton or neutron to bind them together in a nucleus.

Inside a baryon, however, the color force has some extraordinary properties not seen in the

strong interaction between nucleons. The color force does not drop off with distance and isresponsible for the confinement of quarks. The color force involves the exhange of gluonsand is so strong that the quark-antiquark pair production energy is reached before quarks

can be separated. Another property of the color force is that it appears to exert little force at

short distances so that the quarks are like free particles within the confining boundary ofthe color force and only experience the strong confining force when they begin to get too

far apart. The term "asymptotic freedom" is sometimes invoked to describe this behavior of

the gluon interaction between quarks.

Transformation of Quark Flavors by the Weak

InteractionThe decay of hadrons by the weak interaction can be viewed as a process of decay of theirconstituent quarks. There is a pattern of these quark decays: a quark of charge +2/3 ( u,c,t)

is always transformed to a quark of charge -1/3 (d,s,b) and vice versa. This is because thetransformation proceeds by the exchange of charged W bosons, which must change the

charge by one unit. The general pattern is that the quarks will decay to the most massive

quark possible, leading the the pattern

t b c s u d The following table shows the usual pattern of quark transformation and gives examples ofsome hadron processes to which those quark transformations contribute.

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* The W bosons which are indicated as W* are virtual bosons, existing only within the

time frame allowed by the uncertainty principle. The positive W* decays to a positron andan electron neutrino, and the negative W* to an electron and antineutrino as can be seen in

the example reactions above.

The transformations shown are the most probable for the quarks, but there are other

possibilities. The c quark has about 5% probability of decaying into a d quark instead of ans quark.

The most common of the quark transformations are those of the up and down quarkswhich are the constituents of ordinary matter in the form of protons and neutrons.

The decay of the up quark above is important in the proton-proton cycle of nuclear fusion.The decay of the down quark is involved in the decay of the neutron and in beta decay in

general.

Quark TransformationsThe modes of quark flavor transformation by the weak interaction are shown in Feynman

diagrams. These diagrams are useful in analyzing decay processes to help keep track of

what is happening on the quark level. The most common transformations are listed in thequark transformation table. These transformations take place by means of the W vector

boson.

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The Lambda Baryon

In 1947 during a study of cosmic ray interactions, a product of a proton collision with a

nucleus was found to live for much longer time than expected: -1010 seconds instead of the

expected -2310 seconds! This particle was named the lambda particle ( 0 ) and the property

which caused it to live so long was dubbed "strangeness" and that name stuck to be the

name of one of the quarks from which the lambda particle is constructed. The lambda is a

baryon which is made up of three quarks: an up, a down and a strange quark.

The shorter lifetime of -2310 seconds was expected because the lambda as a baryon

participates in the strong interaction, and that usually leads to such very short lifetimes.

The long observed lifetime helped develop a new conservation law for such

decays called the "conservation of strangeness". The presence of a strange quark in a

particle is denoted by a quantum number S=-1. Particle decay by the strong or

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electromagnetic interactions preserve the strangeness quantum number. The decayprocess for the lambda particle must violate that rule, since there is no lighter particle

which contains a strange quark - so the strange quark must be transformed to another quark

in the process. That can only occur by the weak interaction, and that leads to a much longerlifetime. The decay processes show that strangeness is not conserved:

Another baryon which is also called a lambda with symbol c+

contains a charm quark. It

has a composition udc and a mass of 2281 MeV/c2.

The Omega-Minus Baryon

The omega-minus, a baryon composed of three strange quarks, is a classic example of the

need for the property called "color" in describing particles. Since quarks are fermions with

spin 1/2, they must obey the Pauli exclusion principle and cannot exist in identical states.So with three strange quarks, the property which distinguishes them must be capable of at

least three distinct values.The discovery of the omega baryon was a great triumph for the quark model of

baryons because it was searched for and found only after its existence, mass, and decay

modes were predicted by the quark model. It was discovered at Brookhaven in 1964. At

left is a sketch of the bubble chamber photograph in which the omega-minus baryon wasdiscovered.

The omega-minus was produced by a p

collision which produced the omega-minus

and two kaons.

Considering the particle conservation laws, this interaction conserves strangeness andtherefore proceeds by the strong interaction. The decays observed are as follows.

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Note that all three of these decays violate strangeness conservation and therefore canproceed only by the weak interaction. This gives them longer lifetimes, on the order of

1010 seconds.

Examining the decays of the omega-minus above, you see that a quark-antiquark pair

can be added on the right, provided the process satisfies conservation of energy. It isexpected that the strange quark will be transmuted to an up quark by a quark decay process

involving the W vector boson. This can produce an electron plus and antineutrino, but an

alternative Wprocess involves the production of an up plus an antiup-down (a p- meson).

It appears that alternative decay is operating here.In the decay of the Xi particle above, a lambda baryon and two gamma rays are shown as

the products. Actually, the primary decay of the Xi is to a lambda-zero and a pi-zero. It is

just that the 0 decays into two gammas with a lifetime of about 1610 seconds, so the two

gamma rays appear to come from the same point as the lambda.According to the Particle Data Book, the decays of the omega minus branch as

follows0 067.8% , 8.6%

Spin ClassificationOne essential parameter for classification of particles is their "spin" or intrinsic angular

momentum. Half-integer spin fermions are constrained by the Pauli exclusion principlewhereas integer spin bosons are not. The electron is a fermion with electron spin 1/2.

The spin classification of particles determines the nature of the energy distribution ina collection of the particles. Particles of integer spin obey Bose-Einstein statistics, whereas

those of half-integer spin behave according to Fermi-Dirac statistics

Fermions

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Fermions are particles which have half-integer spin and therefore are constrained by thePauli exclusion principle. Particles with integer spin are called bosons. Fermions include

electrons, protons, neutrons. The wavefunction which describes a collection of fermions

must be antisymmetric with respect to the exchange of identical particles, while thewavefunction for a collection of bosons is symmetric.

The fact that electrons are fermions is foundational to the buildup of the

periodic table of the elements since there can be only one electron for each state in an atom

(only one electron for each possible set of quantum numbers). The fermion nature ofelectrons also governs the behavior of electrons in a metal where at low temperatures all

the low energy states are filled up to a level called the Fermi energy. This filling of states is

described by Fermi-Dirac statistics.

BosonsBosons are particles which have integer spin and which therefore are not constrained by thePauli exclusion principle like the half-integer spin fermions. The energy distribution of

bosons is described by Bose-Einstein statistics. The wavefunction which describes a

collection of bosons must be symmetric with respect to the exchange of identical particles,while the wavefunction for a collection of fermions is antisymmetric.

At low temperatures, bosons can behave very differently than fermions because anunlimited number of them can collect into the same energy state. The collection into a

single state is called condensation, or Bose-Einstein condensation. It is responsible for thephenomenon of superfluidity in liquid helium. Coupled particles can also act effectively as

bosons. In the BCS Theory of superconductivity, coupled pairs of electrons act like bosons

and condense into a state which demonstrates zero electrical resistance.Bosons include photons and the characterization of photons as particles with

frequency-dependent energy given by the Planck relationship allowed Planck to apply

Bose-Einstein statistics to explain the thermal radiation from a hot cavity.

Bose-Einstein Condensation

n 1924 Einstein pointed out that bosons could "condense" in unlimited numbers into asingle ground state since they are governed by Bose-Einstein statistics and not constrainedby the Pauli exclusion principle. Little notice was taken of this curious possibility until the

anomalous behavior of liquid helium at low temperatures was studied carefully.

When helium is cooled to a critical temperature of 2.17 K, a remarkable discontinuity in

heat capacity occurs, the liquid density drops, and a fraction of the liquid becomes a zero

viscosity "superfluid". Superfluidity arises from the fraction of helium atoms which hascondensed to the lowest possible energy.

A condensation effect is also credited with producing superconductivity. In the

BCS Theory, pairs of electrons are coupled by lattice interactions, and the pairs (called

Cooper pairs) act like bosons and can condense into a state of zero electrical resistance.The conditions for achieving a Bose-Einstein condensate are quite extreme. The

participating particles must be considered to be identical, and this is a condition that is

difficult to achieve for whole atoms. The condition of indistinguishability requires that thedeBroglie wavelengths of the particles overlap significantly. This requires extremely low

temperatures so that the deBroglie wavelengths will be long, but also requires a fairly high

particle density to narrow the gap between the particles.Since the 1990s there has been a surge of research into Bose-Einstein condensation

since it was discovered that Bose-Einstein condensates could be formed with ultra-cold

atoms. The use of laser cooling and the trapping of ultra-cold atoms with magnetic traps

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has produced temperatures in the nanokelvin range. Cornell and Wieman along withKetterle of MIT received the 2001 Nobel Prize in Physics "for the achievement of Bose-

Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of

the properties of the condensates". Cornell and Wieman led an active group at theUniversity of Colorado, Boulder which has produced Bose-Einstein condensates with

rubidium atoms. Other groups at MIT, Harvard and Rice have been very active in this

rapidly advancing field.

D MesonThe D Meson is the lightest particle which contains a charm quark, and therefore is a goodexample for the study of decay by quark transformation by the weak interaction.

An interesting example of a particle interaction which involves the D meson was observedin a bubble chamber at SLAC in 1982 (K. Abe et al., Phys. Rev. Lett. 48,1526 (1982)).

Photons at about 20 GeV were produced by Compton scattering of radiation from a YAGlaser from energetic electrons from the linear accelerator. The interaction is sketched from

the bubble chamber photograph. The presumption is that the photon interacted with a

proton, producing the D mesons indicated. The reaction which produced these productswould appear to be the following.

The reaction can be analyzed by examining the quark content of the products, and is seen

to involve the production of a charm-anticharm quark pair. From the bubble chambertracks, it can be seen that the neutral D meson decays into two products and the positive D

meson decays into three. While the specific products can not be identified with just thisphotograph, it is interesting to propose possibilities for this process. The decays shown

below are one possibility.

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Since the D meson is the lightest meson which contains a charm quark, it must change that

charm quark to some other quark in order to decay. Transmutations of quarks occurs by the

weak interaction, which changes the charm quark to a strange quark with a W particle. Thisweak interaction process is indicated in both of the decays above. For the particular decay

proposed for the positive D meson, an up-antiup quark pair is also required.

There are many possible decay processes for the D meson because it has a lot ofexcess mass energy. These all involve the weak interaction to change the charm quark, and

the variety of W decays provide many paths for the process.

2011 reports from the Beauty detector of the Large Hadron Collider suggest thatD-mesons seem to decay slightly differently from their antiparticles. The LHCb team

reported a difference of about 0.8 percent - a significant difference that, if true, could

herald the first "new physics" to be found at the LHC.

Bag Model of Quark ConfinementIn dealing with the nature of quark confinement, one visualization is that of an elastic bag

which allows the quarks to move freely around, as long as you don't try to pull them furtherapart. But if you try to pull a quark out, the bag stretches and resists.

The models of quark confinement help in understanding why we have not seen isolated

quarks. If one of the constituent quarks of a particle is given enough energy, it can create ajet of mesons as the energy imparted to the quark is used to produce quark-antiquark pairs.

Experiments show that the forces containing the quarks get weaker as the quarks get

closer together, so that within the confines of a baryon or hadron, they are essentially free

to move about. This condition is referred to as "asymptotic freedom".

Asymptotic Freedom

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As the quarks within a meson or baryon get closer together, the force of containmentgets weaker so that it asymptotically approaches zero for close confinement. The

implication is that the quarks in close confinement are completely free to move about. Part

of the nature of quark confinement is that the further you try to force the quarks apart, thegreater the force of containment. This is often visualized in terms of the "bag model" of

quark confinement.

A potential function which has been successfully used to describe some quark systems is ofthe form:

The quark-quark coupling strength decreases for small values of r, and Rohlf describes thisqualitatively as resulting from the penetration of the gluon cloud surrounding the quarks.

The gluons carry "color charge" and therefore the penetration of the cloud would reduce

the effective color charge of the quark.

Another approach to asymptotic freedom is to use a variable strong force coupling constantwhich depends upon the wavelength of the quark. An expression which comes from

quantum chromodynamics is:

The nature of this relationship is that it gives a value of about 1 for the coupling constant atthe radius of a proton, and this is the value conventionally used to describe the strength of

the strong interaction within nuclei. When the proton is penetrated to a radius

corresponding to an energy of 1 TeV, the coupling constant is down to about 0.1, anothermanifestation of asymptotic freedom.

Electron Neutrinos and AntineutrinosThe history of a particle that appeared to have no charge and no mass is an interesting one.The electron neutrino (a lepton) was first postulated in 1930 by Wolfgang Pauli to explain

why the electrons in beta decay were not emitted with the full reaction energy of the

nuclear transition. The apparent violation of conservation of energy and momentum wasmost easily avoided by postulating another particle. Enrico Fermi called the particle a

neutrino and developed a theory of beta decay based on it, but it was not experimentally

observed until 1956. This elusive particle, with no charge and almost no mass, couldpenetrate vast thicknesses of material without interaction. The mean free path of a neutrino

in water would be on the order of 10x the distance from the Earth to the Sun. In thestandard Big Bang model, the neutrinos left over from the creation of the universe are the

most abundant particles in the universe. This remnant neutrino density is put at 100 percubic centimeter at an effective temperature of 2K (Simpson). The background temperature

for neutrinos is lower than that for the microwave background (2.7K) because the neutrino

transparency point came earlier. The sun emits vast numbers of neutrinos which can passthrough the earth with little or no interaction. This leads to the statement "Solar neutrinos

shine down on us during the day, and shine up on us during the night!" . Bahcall's modeling

of the solar neutrino flux led to the prediction of about 5 x 106 neutrinos/cm2s.

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A remarkable opportunity for observing neutrinos came with Supernova 1987Awhen the Japanese observing team detected neutrinos almost coincident with the discovery

of the light from the supernova.

Neutrinos interact only by the weak interaction. Their interactions are usuallyrepresented in terms of Feynman diagrams.

Detection of NeutrinosThe first experimental observation of the neutrino interacting with matter was made byFrederick Reines, Clyde Cowan, Jr, and collaborators in 1956 at the Savannah River Plant

in South Carolina. Their neutrino source was a nuclear reactor (it actually produced

antineutrinos from beta decay). Modern neutrino detectors at IMB in Ohio andKamiokande in Japan detected neutrinos from Supernova 1987A. A new neutrino detector

at Sudbury, Ontario began collecting data in October of 1999. Another Japanese neutrino

detector called Super Kamiokande became operational in April 1996.

An early set of experiments with a facility called the solar neutrino telescope, measured the

rate of neutrino emission from the sun at only one third of the expected flux. Often referredto as the Solar Neutrino Problem, this deficiency of neutrinos has been difficult to explain.

Recent results from the Sudbury Neutrino Observatory suggest that a fraction of theelectron neutrinos produced by the sun are transformed into muon neutrinos on the way to

the earth. The observations at Sudbury are consistent with the solar models of neutrino flux

assuming that this "neutrino oscillation" is responsible for observation of neutrinos otherthan electron neutrinos.

Sudbury Neutrino ObservatoryThe new Sudbury Neutrino Observatory (SNO) consists of a 1000 metric ton bottle ofheavy water suspended in a larger tank of light water. The apparatus is located in Sudbury,

Ontario, Canada at a depth of about 2 km down in a nickel mine. A 18 m diameter geodesicarray of 9,500 photomultiplier tubes surrounds the heavy water to detect Cerenkovradiation from the neutrino interaction which dissociates deuterium:

The distinctive characteristic of the heavy water observatory is that it can measure both the

electron neutrino flux and the total neutrino flux (electron, muon and tau neutrinos). It

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should allow them to determine whether neutrinos change flavors. If so, it could explainthe solar neutrino problem and would show that the neutrinos have mass.

SNO began operating in production mode in October, 1999, and as of Summer

2000 had collected a sizable number of neutrino events both from the sun (the main focusof the experiment) and from atmospheric events with pions and muons. The Cerenkov

cones of the solar neutrinos center about the direction opposite the sun, showing about the

same flux at night as during the day. This was an expected result, since the mean free path

of a neutrino in matter is about 22 lightyears in lead and having the earth in the path makeslittle difference. A sizable number of the atmospheric neutrino events come from below,

having traveled all the way through the earth and forming the Cerenkov cone in the

photomultiplier tubes at the top of the spherical heavy-water ball. These Cerenkov conesare scattered all around the sphere, while the solar ones of course show a precise anti-solar

direction.

The depth of the detector protects it from the intense bombardment of cosmicray muons which reaches the earth's surface. The detector measures only about 70 muon

events per day, and they are easily distinguished from neutrino events since the muon

interacts by the electromagnetic interaction and produces a much larger signal in thedetector array.

In order to detect the ring of light which is the signature of Cerenkov radiation,the responses of all the photomultiplier tubes (PMTs) are monitored with a very short time

scale. In order to be counted as an "event" in the detector, at least 20 PMTs must betriggered within an interval of 100 nanoseconds.

The Solar Neutrino TelescopeRaymond Davis of Brookhaven National Laboratory constructed a neutrino detector 1.6 km

underground in the Homestake Gold Mine in Lead, South Dakota. The detector consists of

a 378,000 liter tank of perchloroethylene, which is further isolated by being submerged inwater. Theoretical expections were about one neutrino-chlorine interaction per day, but the

measured solar neutrino events were about a third of that, raising serious questions about

the abundance of solar neutrinos (the Solar Neutrino Problem).The detection of neutrinos by this instrument was based on the interaction of

neutrinos with chlorine nuclei to produce argon. The argon can be removed from the tank

and measured so that the number of neutrinos captured in a given time interval can be

determined.

The argon decays back to the chlorine isotope from which it was created by the process of

electron capture. The detection of this transition is aided by the definite energy of the x-rayemitted during the electron capture process. This mine experiment was able to detect about

15 argon atoms a month, according to Simpson.

Perchloroethylene is ordinary dry-cleaning fluid, but 400,000 gallons is a lot of cleaningfluid. Davis denies the story that he was besieged by wire coat-hanger salesmen after the

large purchase.

Detection of Supernova Neutrinos

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ince the neutrino can pass through the entire Earth without interaction, it takesspecialized techniques to detect one. After being postulated by Fermi in 1930 to explain

anomalies in beta decay, they were not actually detected until 1953 by Reines and Cowan.

Detection of neutrinos is now well developed and a classic opportunity for neutrino

detection occurred with Supernova 1987A. A burst of ten neutrinos was detected within a

time interval of about 15 seconds at a neutrino detector deep in a mine in Japan. They had

to penetrate the Earth to get to the detector.

Neutrino Mass?No definite mass has been measured for the neutrino, and the standard comment aboutmost experiments is "the results are consistent with zero mass for the neutrino". But this

raises certain theoretical problems and there have been many attempts to set a range for the

mass of the neutrino. Since its mass is evidently very small, if non-zero, the mass is usuallystated in terms of its energy equivalent in electron volts. Most experiments conclude that

the mass equivalent of the neutrino is less than 50 eV.

One of the recent pieces of information about neutrino mass came from theneutrinos observed from Supernova 1987A. Ten neutrinos arrived within 15 seconds of

each other after traveling 180,000 light years, and they differed by a up to factor of three in

energy. This limits the neutrino rest mass energy to less than about 30 eV (Rohlf).New experimental evidence from the Super-Kamiokande neutrino detector in

Japan represents the strongest evidence to date that the mass of the neutrino is non-zero.Models of atmospheric cosmic ray interactions suggest twice as many muon neutrinos as

electron neutrinos, but the measured ratio was only 1.3:1. The interpretation of the datasuggested a mass difference between electron and muon neutrinos of 0.03 to 0.1 eV.

Presuming that the muon neutrino would be much more massive than the electron neutrino,

then this implies a muon neutrino mass upper bound of about 0.1 eV.The recent neutrino measurements at the Sudbury Neutrino Observatory are

consistent with the modeled total neutrino flux and add evidence for neutrino oscillation, a

process which can only occur if the neutrinos have mass.

Some Neutrino HistoryThe electron neutrino (a lepton) was first postulated in 1930 by Wolfgang Pauli to explainwhy the electrons in beta decay were not emitted with the full reaction energy of thenuclear transition. The apparent violation of conservation of energy and momentum was

most easily avoided by postulating another particle. Enrico Fermi called the particle a

neutrino and developed a theory of beta decay based on it, but it was not experimentallyobserved until 1956.

Wolfgang Pauli introduced the neutrino to the world of physics in 1930 with a famousletter to "Liebe Radioacktive Damen und Herren" (Dear radioactive ladies and gentlemen)

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at the Tubingen meeting of radioactivity researchers. Pauli's first public discussion of theneutrino was at the 7th Solvay Conference in Brussels in 1933.

Fundamental Forces

The Strong Force

A force which can hold a nucleus together against the enormous forces of repulsion of the

protons is strong indeed. However, it is not an inverse square force like the electromagnetic

force and it has a very short range. Yukawa modeled the strong force as an exchange forcein which the exchange particles are pions and other heavier particles. The range of a

particle exchange force is limited by the uncertainty principle. It is the strongest of the four

fundamental forcesSince the protons and neutrons which make up the nucleus are themselves

considered to be made up of quarks, and the quarks are considered to be held together by

the color force, the strong force between nucleons may be considered to be a residual color

force. In the standard model, therefore, the basic exchange particle is the gluon which

mediates the forces between quarks. Since the individual gluons and quarks are containedwithin the proton or neutron, the masses attributed to them cannot be used in the range

relationship to predict the range of the force. When something is viewed as emerging froma proton or neutron, then it must be at least a quark-antiquark pair, so it is then plausible

that the pion as the lightest meson should serve as a predictor of the maximum range of the

strong force between nucleons.

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The sketch is an attempt to show one of many forms the gluon interaction between

nucleons could take, this one involving up-antiup pair production and annililation andproducing a - bridging the nucleons.

The Electromagnetic Force

One of the four fundamental forces, the electromagnetic force manifests itself through the

forces between charges (Coulomb's Law) and the magnetic force, both of which are

summarized in the Lorentz force law. Fundamentally, both magnetic and electric forces aremanifestations of an exchange force involving the exchange of photons . The quantum

approach to the electromagnetic force is called quantum electrodynamics or QED. The

electromagnetic force is a force of infinite range which obeys the inverse square law, and is

of the same form as the gravity force.

The electromagnetic force holds atoms and molecules together. In fact, the forces of

electric attraction and repulsion of electric charges are so dominant over the other three

fundamental forces that they can be considered to be negligible as determiners of atomicand molecular structure. Even magnetic effects are usually apparent only at high

resolutions, and as small corrections.

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The Weak Force

One of the four fundamental forces, the weak interaction involves the exchange of the

intermediate vector bosons, the W and the Z. Since the mass of these particles is on the

order of 80 GeV, the uncertainty principle dictates a range of about 10-18 meters which isabout 0.1% of the diameter of a proton.

The weak interaction changes one flavor of quark into another. It is crucial to the structure

of the universe in that1. The sun would not burn without it since the weak interaction causes the

transmutation p n so that deuterium can form and deuterium fusion can take place.

2. It is necessary for the buildup of heavy nuclei.The role of the weak force in the transmutation of quarks makes it the interaction involved

in many decays of nuclear particles which require a change of a quark from one flavor toanother. It was in radioactive decay such as beta decay that the existence of the weak

interaction was first revealed. The weak interaction is the only process in which a quarkcan change to another quark, or a lepton to another lepton - the so-called "flavor changes".

The discovery of the W and Z particles in 1983 was hailed as a confirmation of the

theories which connect the weak force to the electromagnetic force in electroweakunification.

The weak interaction acts between both quarks and leptons, whereas the strong force doesnot act between leptons. "Leptons have no color, so they do not participate in the strong

interactions; neutrinos have no charge, so they experience no electromagnetic forces; but

all of them join in the weak interactions."(Griffiths)

Feynman Diagrams for Weak Force

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So it is seen that the quark changes its flavor when interacting via the W- or W+. As drawn,

this interaction cannot be observed because it implies the isolation of an up quark. Because

of quark confinement, isolated quarks are not observed. But rotating the Feynman diagram

gives an alternative interaction, shown below for both electron and muon products.

This suggests the weak interaction mechanism for the decay of the pion, which is observed

to happen by the muon pathway.

The weak interaction in the electron form at left above is responsible for the decay of the

neutron and for beta decay in general.

Super-Kamiokande Neutrino DetectorInside Mount Ikenoyama in Japan within an active zinc mine is a remarkable tank ofultrapure water which is the world's most sensitive neutrino detector as of 1999. The

50,000 tons of water in the tank detector is so pure and transparent that light passes 70meters before its intensity drops to half, compared to a few meters in a typical swimming

pool. The 11,000 hand-blown photomultiplier tubes are half a meter in diameter and coated

inside with a thin layer of alkali metal to detect the Cerenkov radiation from theinteractions of either electron neutrinos or muon neutrinos.

Kearns, Kajita and Totsuka report the detection of 5000 neutrino events in two

years of measurement. From the nature of the interactions of cosmic rays in the upperatmosphere, two muon neutrinos are expected for every electron neutrino, but they found a

ratio of only 1.3 to 1. Their interpretation of this result is that the deficiency is caused by

"neutrino oscillation" in which a number of muon neutrinos are transmuted into tauneutrinos which are undetectable. Neutrino oscillation has been hotly debated over the past

few years because its existence implies a mass for the neutrinos. Further detailed analysis

of this data from Super-Kamiokande is consistent with neutrino oscillation, so this is the

first clear experimental evidence supporting a non-zero mass for the neutrino.

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Electron, Muon, and Tau NeutrinosThe massive leptons are the electron, muon and tau, and each of them has an associated

neutrino. Most experiments involving neutrinos involve electron neutrinos which are muchmore common in our low-energy world, but some current neutrino detectors are sensitive to

the other two as well. The current generation of neutrino detectors such as the Super-

Kamiokande can detect and distinguish between electron and muon neutrinos. When amuon neutrino interacts with a nucleus, it can produce an energetic muon which travels

only a short distance, emitting a sharply outlined cone of Cerenkov radiation which can be

detected by photomultiplier tubes. An electron neutrino interaction can produce an

energetic electron, but the Cerenkov cone from this interaction differs significantly fromthat of the muon. The electron generates a shower of electrons and positrons, each with its

own Cerenkov cone. This smears out the circle of light which hits the detectors; the diffuse

circle at the photomultipliers is the signature of the electron neutrino. Tau neutrinos are notdetected by these detectors because the neutrino energies are not sufficient to produce tau

particles (which are about 3500 times the mass of an electron).

The first clear experimental evidence for the difference between electron and muon

neutrinos came from an experiment conducted at Brookhaven in 1962. The two reactionsindicated would have been equally probable if electron and muon neutrinos were the same.

G. Danby, et al.,Phys. Rev. Lett. 9,36 (1962) . Also see L. Lederman, Scientific American, (March 1963).

Since the electron and muon neutrinos are distinct, the second reaction above violates

conservation of lepton number.

Cerenkov RadiationWhen highly radioactive objects are observed under water, such as in "swimming pool"

reactors and in the underwater temporary spent fuel storage areas at nuclear reactors, theyare seen to be bathed in an intense blue light called Cerenkov radiation. It is caused by

particles entering the water at speeds greater than the speed of light in the water. As the

particles slow down to the local speed of light, they produce a cone of light roughlyanalogous to the bow wave of a boat which is moving through water at a speed greater than

the wave speed on the surface of the water. Another analogy statement is to say that the

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Cerenkov cone is like a sonic boom except that it is done with light. One of the valuableapplications of Cerenkov radiation is in the detection of neutrinos and distintinguishing

between different types of neutrinos. An energetic muon remains intact while slowing

down and its Cerenkov cone paints out a well-defined circular ring on the detector array. Ahigh energy electron on the other hand will produce a diffuse ring on the detectors because

it will produce a shower of electrons, each with its own Cerenkov cone.

Cerenkov ApplicationsCerenkov radiation can be used to detect the occurrence of certain nuclear interactions.

Such interactions can release large amounts of energy and eject particles at highly

relativistic speeds. If these interactions take place in water or another clear substance, thenthe Cerenkov radiation emitted as the reaction products travel through the water can be

detected by photomultiplier tubes. This kind of detection is to be used in the Sudbury

Neutrino Observatory to detect neutrino interactions.The Super-Kamiokande neutrino detector facility in Japan has 11,000

photomuliplier tubes in place to detect Cerenkov radiation and is able to detect anddistinguish electron and muon neutrinos.

Measurements of particle speeds can be made by measuring the angle of theCerenkov cone, like photographing ship wakes to measure ship speeds. A portion of the

light emitted by the decelerated particle is coherent and is emitted at a characteristic angle

The total amount of energy appearing in Cerenkov radiation is small compared to the total

energy loss by ionization as the particle enters the medium. According to Rohlf, a

relativistic particle near the speed of light will lose energy at the rate of about 200 MeV/m,

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The first reaction above (decay of the pion) is known to be a two-body decay by the fact

that a well-defined muon energy is observed from the decay. However, the decay of the

muon into an electron produces a distribution of electron energies, showing that it is at leasta three-body decay. In order for both electron lepton number and muon lepton number to

be conserved, then the other particles must be an electron anti-neutrino and a muon

neutrino.

ParityOne of the conservation laws which applies to particle interactions is associated withparity.

Quarks have an intrinsic parity which is defined to be +1 and for an antiquark parity = -1.

Nucleons are defined to have intrinsic parity +1. For a meson with quark and antiquark

with antiparallel spins (s=0), then the parity is given by

The meson parity is given by

The lowest energy states for quark-antiquark pairs (mesons) will have zero spin andnegative parity and are called pseudoscalar mesons. The nine pseudoscalar mesons can be

shown on a meson diagram. One kind of notation for these states indicates their angular

momentum and parity

Excited states of the mesons occur in which the quark spins are aligned, which with zero

orbital angular momentum gives j=1. Such states are called vector mesons.

The vector mesons have the same spin and parity as photons.

All neutrinos are found to be "left-handed", with an intrinsic parity of -1 while

antineutrinos are right-handed, parity =+1.

IsospinIsospin is a term introduced to describe groups of particles which have nearly the samemass, such as the proton and neutron. This doublet of particles is said to have isospin 1/2,

with projection +1/2 for the proton and -1/2 for the neutron. The three pions compose a

triplet, suggesting isospin 1. The projections are +1 for the positive, 0 and -1 for the neutral

and negative pions. Isospin is used as an axis in particle diagrams, with strangeness beingthe other axis. Isospin is not really spin, and doesn't have the units of angular momentum -

the spin term is tacked on because the addition of the isospins follows the same rules as

spin.Isospin is a dimensionless quantity associated with the fact that the strong interaction

is independent of electric charge. Any two members of the proton-neutron isospin doublet

experience the same strong interaction: proton-proton, proton-neutron, neutron-neutronhave the same strong force attraction.

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At the quark level, the up and down quarks form an isospin doublet (I=1/2) and the

projection 3I = +1/2 is assigned to the up quark and 3I =-1/2 to the down. (The subscript 3

is used here for the third component rather than the z used with spin and orbital angular

momentum because most of the literature does so.) The other quarks are assigned isospinI=0. Isospin is related to other quantum numbers for the particles by

This relationship is called the Gell Mann-Nishijima formula. Some references use T for

isospin, but it appears that most use I for isospin and T for weak isospin.Isospin is associated with a conservation law which requires strong interaction decays

to conserve isospin, as illustrated by the process

which does not involve any transmutation of quarks, so would be expected to decay bystrong interaction. However, it does not conserve isospin, and is observed to decay by the

electromagnetic interaction, but not by the strong interaction. The experimental

discrimination is made by the observation of its decay lifetime, presuming by thetotalitarian principle that if it could decay by the strong interaction, it would.

Crossing SymmetryIf a particle interaction

is observed to occur, then related interactions can be anticipated from the fact that any ofthe particles can be replaced by its antiparticle on the other side of the interaction. This is

commonly known as "crossing symmetry". The observation of the above interaction

implies the existence of the following interactions.

The overbar indicates the antiparticle. Crossing symmetry applies to all known particles,

including the photon which is its own antiparticle. One example of the crossing principle isthat of the relation between Compton scattering and electron-positron annihilation.

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Compton scattering: + e e +

Pair annihilation: e- + e+ +

By examination, it can be seen that these two interactions are related by crossing

symmetry. It could then be said that the observation of Compton scattering implies the

existence of pair annihilation and predicts that it will produce a pair of photons.Another example of crossing symmetry may have led Reines and Cowan to their

experiment for the detection of the neutrino. If you take the electron product from the

neutron decay reaction to the other side and convert it into a positron, then you have the

reaction which they used.

Totalitarian PrincipleFrom what we observe with massive particles, it would seem that any localized particle offinite mass should be unstable, since the decay into several smaller particles provides many

more ways to distribute the energy, and thus would have higher entropy. Some have

adopted the description "totalitarian principle" for this situation. It might be stated as"every process that is not forbidden must occur". From this point of view, any decay

process which is expected but not observed must be prevented from occuring by some

conservation law. This approach has been fruitful in helping to determine the rules for

particle decay.For example, with just conservation of energy and charge considered, one might

expect a proton to decay into a positive pion plus a gamma ray to take away excess energy

and conserve momentum:

The fact that neither this nor any other decay of the proton is observed suggests that thedecay of the proton is forbidden by a strong conservation principle. This principle is called

the conservation of baryon number, and no observed particle decays violate it. The proton

does not decay because it is the least massive baryon, and has nowhere to go.

Another decay which was expected on energy and charge grounds was the decay ofthe neutron into a proton and an electron. The decay of the neutron is observed, but the fact

that the electron does not have a definite energy implies that there is a third particle in the

decay, the antineutrino.

The fact that the first of these decays did not occur suggested a prohibiting conservation

law, which is called the conservation of lepton number.

Since the strengths of the interactions associated with particle decay descendin the order strong, electromagnetic and weak, it might be presumed that the strongest

interaction would lead to the shortest lifetime, and that is what is observed. From

experiments we can establish time regimes for the three types of interactions.

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In the spirit of the "totalitarian principle", if you observed a decay in the16

10

s range youmight guess that it is electromagnetic, and that some principle prevented it decay by the

strong interaction. A 1010 s decay suggests that both strong and electromagnetic are

somehow blocked.

CPT InvarianceMany of the profound ideas in nature manifest themselves as symmetries. A symmetry in a

physical experiment suggests that something is conserved, or remains constant, during the

experiment. So conservation laws and symmetries are strongly linked.

Three of the symmetries which usually, but not always, hold are those of chargeconjugation (C), parity (P), and time reversal (T):

Charge conjugation(C): reversing the electric charge and all the internal quantum numbers.Parity (P): space inversion; reversal of the space coordinates, but not the time.

Time reversal (T): replacing t by -t. This reverses time derivatives like momentum and

angular momentum.

Examples in nature can be cited for the violation of each of these symmetriesindividually. It was thought for a time that CP (parity transformation plus charge

conjugation) would always leave a system invariant, but the notable example of the neutral

kaons has shown a slight violation of CP symmetry.

We are left with the combination of all three, CPT, a profound symmetry consistentwith all known experimental observations.

On the theoretical side, CPT invariance has received a great deal of attention. Georg

Ludens, Wolfgang Pauli and Julian Schwinger independently showed that invariance underLorentz transformations implies CPT invariance. CPT invariance itself has implications

which are at the heart of our understanding of nature and which do not easily arise from

other types of considerations.Integer spin particles obey Bose-Einstein statistics and half-integer spin particles obey

Fermi-Dirac statistics. Operators with integer spins must be quantized using commutation

relations, while anticommutation relations must be used for operators with half integerspin.

Particles and antiparticles have identical masses and lifetimes. This arises from CPT

invariance of physical theories.

All the internal quantum numbers of antiparticles are opposite to those of the particles.

Charge ConjugationAssociated with the conservation laws which govern the behavior of physical particles,charge conjugation (C), parity (P) and time reversal (T) combine to constitute a

fundamental symmetry called CPT invariance.

Classically, charge conjugation may seem like a simple idea: just replace positive charges

by negative charges and vice versa. Since electric and magnetic fields have their origins in

charges, you also must reverse these fields.

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In quantum mechanical systems, charge conjugation has some furtherimplications. It also involves reversing all the internal quantum numbers like those for

lepton number, baryon number and strangeness. It does not affect mass, energy, momentum

or spin.Thinking of charge conjugation as an operator, C, then electromagnetic processes

are invariant under the C operation since Maxwell's equations are invariant under C. This

restricts some kinds of particle processes. Das and Ferbel proceed by defining a charge

parity of c ( ) 1 = for a photon since the C operation reverses the electric field. This

constrains the electromagnetic decay of a neutral particle like the 0. The decay of the 0

is:0

+

This implies that the charge parity or behavior under charge conjugation for a 0 is:0 2

c c c( ) ( ) ( ) ( 1) 1 = = +Charge conjugation symmetry would imply that the 0 will not decay by

0

which we already know because it can't conserve momentum, but the decay0

+ +can conserve momentum. This decay cannot happen because it would violate charge

conjugation symmetry.

While the strong and electromagnetic interactions obey charge conjugationsymmetry, the weak interaction does not. As an example, neutrinos are found to have

intrinsic parities: neutrinos have left-handed parity and antineutrinos right-handed. Since

charge conjugation would leave the spatial coordinates untouched, then if you operated on

a neutrino with the C operator, you would produce a left-handed antineutrino. But there isno experimental evidence for such a particle; all antineutrinos appear to be right-handed.

The combination of the parity operation P and the charge conjugation operation C on a

neutrino do produce a right-handed antineutrino, in accordance with observation. So it

appears that while beta decay does not obey parity or charge conjugation symmetryseparately, it is invariant under the combination CP.

Time ReversalAssociated with the conservation laws which govern the behavior of physical particles,

charge conjugation (C), parity (P) and time reversal combine to constitute a fundamental

symmetry called CPT invariance.In simple classical terms, time reversal just means replacing t by -t, inverting the

direction of the flow of time. Reversing time also reverses the time derivatives of spatial

quantities, so it reverses momentum and angular momentum.Newton's second law isquadratic in time and is invariant under time reversal. It's invariance under time reversal

holds for either gravitational or electromagnetic forces.Very sensitive experimental tests have been done to put upper bounds on anyviolation of time-reversal symmetry. One experiment described by Das and Ferbel is the

search for a dipole moment for the neutron. Even though the neutron is neutral, it is viewed

as made up of charged quarks and therefore could conceivably have a dipole moment.

Experimental evidence is consistent with zero dipole moment, so time reversal symmetryseems to hold in this case.

The small violation of CP symmetry suggests some departure from T symmetry in someweak interaction process since CPT invariance seems to be on very firm ground.

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CP InvarianceAssociated with the conservation laws which govern the behavior of physical particles,

charge conjugation (C), parity (P) and time reversal (T) combine to constitute afundamental symmetry called CPT invariance.

The strong and electromagnetic interactions leave systems invariant under any of the

three operations applied alone, but the weak interaction does not. The beta decay of cobalt-

60 established the violation of parity in 1957, and led to our understanding that the weakinteraction violates both charge conjugation and parity invariance. However, the weak

interaction does appear to leave systems invariant under the combination CP. Examination

of the case of the neutrino is instructive at this point. The parity operation on a neutrinowould leave its spin in the same direction while reversing space coordinates

L L

R R

CP n n

CP n n

Neither of these things is observed to happen in nature; neutrinos are always left-handed,

anti-neutrinos always right-handed. But if you add the charge conjugation operation, the

result of the combined operation gives you back the original particle

L L L

R R R

CP n C n n

CP n C n n

=

=

CP invariance was thought to be a general conservation principle until the details of theneutral kaon decay process were examined by Croni

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Particle physics file prepared by muzammal from hyperphyiscs site

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