Pc Chapter 46
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Chapter 46 Particle Physics and Cosmology
Atoms as Elementary Particles
Atoms
From the Greek for “indivisible” Were once thought to be the elementary particles
Atom constituents
Proton, neutron, and electron After 1932 these were viewed as elementary All matter was made up of these particles
Discovery of New Particles
New particles
Beginning in the 1940s, many new particles were discovered in experiments involving high-energy collisions Characteristically unstable with short lifetimes Over 300 have been catalogued
A pattern was needed to understand all these new particles
Elementary Particles – Quarks
Physicists recognize that most particles are made up of quarks
Exceptions include photons, electrons and a few others
The quark model has reduced the array of particles to a manageable few The quark model has successfully predicted new quark combinations that were subsequently found in many experiments
Fundamental Forces
All particles in nature are subject to four fundamental forces:
Nuclear force Electromagnetic force Weak force Gravitational force
This list is in order of decreasing strength
Nuclear Force
Attractive force between nucleons Strongest of all the fundamental forces Very short-ranged
Less than 10-15 m Negligible for separations greater than this
Electromagnetic Force
Is responsible for the binding of atoms and molecules About 10-2 times the strength of the nuclear force A long-range force that decreases in strength as the inverse square of the separation between interacting particles
Weak Force
Is responsible for instability in certain nuclei
Is responsible for decay processes
Its strength is about 10-5 times that of the strong force Scientists now believe the weak and electromagnetic forces are two manifestations of a single force, the electroweak force
Gravitational Force
A familiar force that holds the planets, stars and galaxies together Its effect on elementary particles is negligible A long-range force It is about 10-39 times the strength of the strong force
Weakest of the four fundamental forces
Explanation of Forces
Forces between particles are often described in terms of the actions of field particles or exchange particles
Field particles are also called gauge bosons The interacting particles continually emit and absorb field particles The emission of a field particle by one particle and its absorption by another manifests itself as a force between the two interacting particles The force is mediated, or carried, by the field particles
Forces and Mediating Particles
Paul Adrien Maurice Dirac
1902 – 1984 Understanding of antimatter Unification of quantum mechanics and relativity Contributions of quantum physics and cosmology Nobel Prize in 1933
Antiparticles
For every particle, there is an antiparticle
An antiparticle has the same mass as the particle, but the opposite charge The positron (electron’s antiparticle) was discovered by Anderson in 1932
From Dirac’s version of quantum mechanics that incorporated special relativity
Since then, it has been observed in numerous experiments
Practically every known elementary particle has a distinct antiparticle
Among the exceptions are the photon and the neutral pi particles
Dirac’s Explanation
The solutions to the relativistic quantum mechanic equations required negative energy states Dirac postulated that all negative energy states were filled
These electrons are collectively called the Dirac sea
Electrons in the Dirac sea are not directly observable because the exclusion principle does not let them react to external forces
Dirac’s Explanation, cont.
An interaction may cause the electron to be excited to a positive energy state This would leave behind a hole in the Dirac sea The hole can react to external forces and is observable
Dirac’s Explanation, final
The hole reacts in a way similar to the electron, except that it has a positive charge The hole is the antiparticle of the electron
The electron’s antiparticle is now called a positron
Pair Production
A common source of positrons is pair production A gamma-ray photon with sufficient energy interacts with a nucleus and an electron-positron pair is created from the photon The photon must have a minimum energy equal to 2mec2 to create the pair
Pair Production, cont.
A photograph of pair production produced by 300 MeV gamma rays striking a lead sheet The minimum energy to create the pair is 1.02 MeV The excess energy appears as kinetic energy of the two particles
Annihilation
The reverse of pair production can also occur Under the proper conditions, an electron and a positron can annihilate each other to produce two gamma ray photons e- + e+ → 2γ
Hideki Yukawa
1907 – 1981 Nobel Prize in 1949 for predicting the existence of mesons Developed the first theory to explain the nature of the nuclear force
Mesons
Developed from a theory to explain the nuclear force Yukawa used the idea of forces being mediated by particles to explain the nuclear force A new particle was introduced whose exchange between nucleons causes the nuclear force
It was called a meson
Mesons, cont.
The proposed particle would have a mass about 200 times that of the electron Efforts to establish the existence of the particle were done by studying cosmic rays in the 1930s Actually discovered multiple particles
pi meson (pion) muon
Not a meson
Pion
There are three varieties of pions
Muons
Two muons exist
µ- and its antiparticle µ+
The muon is unstable
It has a mean lifetime of 2.2 µs It decays into an electron, a neutrino, and an antineutrino
Richard Feynman
1918 – 1988 Developed quantum electrodynamics Shared the Nobel Prize in 1965 Worked on Challenger investigation and demonstrated the effects of cold temperatures on the rubber O-rings used
Feynman Diagrams
A graphical representation of the interaction between two particles
Feynman diagrams are named for Richard Feynman who developed them
A Feynman diagram is a qualitative graph of time on the vertical axis and space on the horizontal axis
Actual values of time and space are not important The actual paths of the particles are not shown
Feynman Diagram – Two Electrons
The photon is the field particle that mediates the interaction The photon transfers energy and momentum from one electron to the other The photon is called a virtual photon
It can never be detected directly because it is absorbed by the second electron very shortly after being emitted by the first electron
The Virtual Photon
The existence of the virtual photon seems to violate the law of conservation of energy
But, due to the uncertainty principle and its very short lifetime, the photon’s excess energy is less than the uncertainty in its energy The virtual photon can exist for short time intervals, such that ∆E ≈ h / 2 ∆t
Feynman Diagram – Proton and Neutron (Yukawa’s Model)
The exchange is via the nuclear force The existence of the pion is allowed in spite of conservation of energy if this energy is surrendered in a short enough time Analysis predicts the rest energy of the pion to be 130 MeV / c2
This is in close agreement with experimental results
Nucleon Interaction – More About Yukawa’s Model
The time interval required for the pion to transfer from one nucleon to the other is
The distance the pion could travel is c∆t Using these pieces of information, the rest energy of the pion is about 100 MeV
Nucleon Interaction, final
This concept says that a system of two nucleons can change into two nucleons plus a pion as long as it returns to its original state in a very short time interval It is often said that the nucleon undergoes fluctuations as it emits and absorbs field particles
These fluctuations are a consequence of quantum mechanics and special relativity
Feynman Diagram – Weak Interaction
An electron and a neutrino are interacting via the weak force The Z0 is the mediating particle
The weak force can also be mediated by the W± The W± and Z0 were discovered in 1983 at CERN
Classification of Particles
Two broad categories Classified by interactions
hadrons – interact through strong force leptons – interact through weak force
Note on terminology
The strong force is reserved for the force between quarks The nuclear force is reserved for the force between nucleons
The nuclear force is a secondary result of the strong force
Hadrons
Interact through the strong force Two subclasses distinguished by masses and spins
Mesons
Baryons
Decay finally into electrons, positrons, neutrinos and photons Integer spins (0 or 1) Masses equal to or greater than a proton Half integer spin values (1/2 or 3/2) Decay into end products that include a proton (except for the proton)
Not elementary, but composed of quarks
Leptons
Do not interact through strong force All have spin of 1/2 Leptons appear truly elementary
No substructure Point-like particles
Scientists currently believe only six leptons exist, along with their antiparticles
Electron and electron neutrino Muon and its neutrino Tau and its neutrino
Conservation Laws
A number of conservation laws are important in the study of elementary particles Already have seen conservation of
Energy Linear momentum Angular momentum Electric charge
Two additional laws are
Conservation of Baryon Number Conservation of Lepton Number
Conservation of Baryon Number
Whenever a baryon is created in a reaction or a decay, an antibaryon is also created B is the baryon number
B = +1 for baryons B = -1 for antibaryons B = 0 for all other particles
The sum of the baryon numbers before a reaction or a decay must equal the sum of baryon numbers after the process
Conservation of Baryon Number and Proton Stability
There is a debate over whether the proton decays or not If baryon number is absolutely conserved, the proton cannot decay Some recent theories predict the proton is unstable and so baryon number would not be absolutely conserved
For now, we can say that the proton has a half-life of at least 1033 years
Conservation of Baryon Number, Example
Is baryon number conserved in the following reaction?
Baryon numbers:
Before: 1 + 1 = 2 After: 1 + 1 + 1 + (-1) = 2
Baryon number is conserved The reaction can occur as long as energy is conserved
Conservation of Lepton Number
There are three conservation laws, one for each variety of lepton The law of conservation of electron lepton number states that the sum of electron lepton numbers before the process must equal the sum of the electron lepton number after the process
The process can be a reaction or a decay
Conservation of Lepton Number, cont.
Assigning electron lepton numbers
Le = 1 for the electron and the electron neutrino Le = -1 for the positron and the electron antineutrino Le = 0 for all other particles
Similarly, when a process involves muons, muon lepton number must be conserved and when a process involves tau particles, tau lepton numbers must be conserved
Muon and tau lepton numbers are assigned similarly to electron lepton numbers
Conservation of Lepton Number, Example
Is lepton number conserved in the following reaction?
Check electron lepton numbers:
Before: Le = 0 After: Le = 1 + (-1) + 0 = 0 Electron lepton number is conserved
Check muon lepton numbers:
Before: Lµ = 1 After: Lµ = 0 + 0 + 1 = 1 Muon lepton number is conserved
Strange Particles
Some particles discovered in the 1950s were found to exhibit unusual properties in their production and decay and were given the name strange particles Peculiar features include:
Always produced in pairs Although produced by the strong interaction, they do not decay into particles that interact via the strong interaction, but instead into particles that interact via weak interactions
They decay much more slowly than particles decaying via strong interactions
Strangeness
To explain these unusual properties, a new quantum number S, called strangeness, was introduced A new law, the law of conservation of strangeness was also needed
It states that the sum of strangeness numbers before a reaction or a decay must equal the sum of the strangeness numbers after the process
Strong and electromagnetic interactions obey the law of conservation of strangeness, but the weak interaction does not
Bubble Chamber Example of Strange Particles
The dashed lines represent neutral particles At the bottom, π - + p → K0 + Λ0 Then Λ0 → π - + p and K0 → π + µ- + νµ
Creating Particles
Most elementary particles are unstable and are created in nature only rarely, in cosmic ray showers In the laboratory, great numbers of particles can be created in controlled collisions between high-energy particles and a suitable target
Measuring Properties of Particles
A magnetic field causes the charged particles to curve
This allows measurement of their charge and linear momentum
If the mass and momentum of the incident particle are known, the product particle’s mass, kinetic energy, and speed can usually be calculated The particle’s lifetime can be calculated from the length of its track and its speed
Resonance Particles
Short-lived particles are known as resonance particles
They exist for times around 10-20 s
They cannot be detected directly Their properties can be inferred from data on their decay products
Experimental Evidence
The location of the peak tells us the mass of the particle
The smaller peaks indicate the presence of two other resonance particles
The width of the peak can be used to infer the lifetime of the particle
Murray Gell-Mann
1929 – Studies dealing with subatomic particles
Named quarks Developed pattern known as eightfold way
Nobel Prize in 1969
The Eightfold Way
Many classification schemes have been proposed to group particles into families
The eightfold way is a symmetric pattern proposed by Gell-Mann and Ne’eman
These schemes are based on spin, baryon number, strangeness, etc.
There are many symmetrical patterns that can be developed
The patterns of the eightfold way have much in common with the periodic table
Including predicting missing particles
An Eightfold Way for Baryons
A hexagonal pattern for the eight spin 1/2 baryons Stangeness vs. charge is plotted on a sloping coordinate system Six of the baryons form a hexagon with the other two particles at its center
An Eightfold Way for Mesons
The mesons with spins of 0 can be plotted Strangeness vs. charge on a sloping coordinate system is plotted A hexagonal pattern emerges The particles and their antiparticles are on opposite sides on the perimeter of the hexagon The remaining three mesons are at the center
Eightfold Way for Spin 3/2 Baryons
The nine particles known at the time were arranged as shown An empty spot occurred Gell-Mann predicted the missing particle and its properties About three years later, the particle was found and all its predicted properties were confirmed
Quarks
Hadrons are complex particles with size and structure Hadrons decay into other hadrons There are many different hadrons Quarks are proposed as the elementary particles that constitute the hadrons
Originally proposed independently by GellMann and Zweig
Original Quark Model
Three types or flavors
Associated with each quark is an antiquark
The antiquark has opposite charge, baryon number and strangeness
Quarks have fractional electrical charges
u – up d – down s – strange
+1/3 e and –2/3 e
All ordinary matter consists of just u and d quarks
Original Quark Model – Rules
All the hadrons at the time of the original proposal were explained by three rules
Mesons consist of one quark and one antiquark
This gives them a baryon number of 0
Baryons consist of three quarks Antibaryons consist of three antiquarks
Quark Composition of Particles – Examples
Mesons are quarkantiquark pairs Baryons are quark triplets
Active Figure 46.12
(SLIDESHOW MODE ONLY)
Additions to the Original Quark Model – Charm
Another quark was needed to account for some discrepancies between predictions of the model and experimental results A new quantum number, C, was assigned to the property of charm Charm would be conserved in strong and electromagnetic interactions, but not in weak interactions In 1974, a new meson, the J/Ψ, was discovered that was shown to be a charm quark and charm antiquark pair
More Additions – Top and Bottom
Discovery led to the need for a more elaborate quark model This need led to the proposal of two new quarks
t – top (or truth) b – bottom (or beauty)
Added quantum numbers of topness and bottomness Verification
b quark was found in a Y- meson in 1977 t quark was found in 1995 at Fermilab
Numbers of Particles
At the present, physicists believe the “building blocks” of matter are complete
Six quarks with their antiparticles Six leptons with their antiparticles
Particle Properties
More About Quarks
No isolated quark has ever been observed It is believed that at ordinary temperatures, quarks are permanently confined inside ordinary particles due to the strong force Current efforts are underway to form a quarkgluon plasma where quarks would be freed from neutrons and protons
Color
It was noted that certain particles had quark compositions that violated the exclusion principle
Quarks are fermions, with half-integer spins and so should obey the exclusion principle
The explanation is an additional property called color charge
The color has nothing to do with the visual sensation from light, it is simply a name
Colored Quarks
Color “charge” occurs in red, blue, or green
Antiquarks have colors of antired, antiblue, or antigreen These are the quantum “numbers” of color charge
Color obeys the exclusion principle A combination of quarks of each color produces white (or colorless) Baryons and mesons are always colorless
Quantum Chromodynamics (QCD)
QCD gave a new theory of how quarks interact with each other by means of color charge The strong force between quarks is often called the color force The strong force between quarks is mediated by gluons
Gluons are massless particles
When a quark emits or absorbs a gluon, its color may change
More About Color Charge
Particles with like colors repel and those with opposite colors attract
Different colors attract, but not as strongly as a color and its anticolor
The color force between color-neutral hadrons is negligible at large separations
The strong color force between the constituent quarks does not exactly cancel at small separations This residual strong force is the nuclear force that binds the protons and neutrons to form nuclei
Quark Structure of a Meson
A green quark is attracted to an antigreen quark The quark – antiquark pair forms a meson The resulting meson is colorless
Quark Structure of a Baryon
Quarks of different colors attract each other The quark triplet forms a baryon Each baryon contains three quarks with three different colors The baryon is colorless
QCD Explanation of a Neutron-Proton Interaction
Each quark within the proton and neutron is continually emitting and absorbing gluons The energy of the gluon can result in the creation of quarkantiquark pairs When close enough, these gluons and quarks can be exchanged, producing the strong force
Elementary Particles – A Current View
Scientists now believe there are three classifications of truly elementary particles
Leptons Quarks Field particles
These three particles are further classified as fermions or bosons
Quarks and leptons are fermions Field particles are bosons
Weak Force
The weak force is believed to be mediated by the W+, W-, and Z0 bosons
These particles are said to have weak charge
Therefore, each elementary particle can have
Mass Electric charge Color charge Weak charge
Electroweak Theory
The electroweak theory unifies electromagnetic and weak interactions The theory postulates that the weak and electromagnetic interactions have the same strength when the particles involved have very high energies
Viewed as two different manifestations of a single unifying electroweak interaction
The Standard Model
A combination of the electroweak theory and QCD for the strong interaction form the Standard Model Essential ingredients of the Standard Model
The strong force, mediated by gluons, holds the quarks together to form composite particles Leptons participate only in electromagnetic and weak interactions The electromagnetic force is mediated by photons The weak force is mediated by W and Z bosons
The Standard Model does not actually yet include the gravitational force
The Standard Model – Chart
Mediator Masses
Why does the photon have no mass while the W and Z bosons do have mass?
Not answered by the Standard Model The difference in behavior between low and high energies is called symmetry breaking The Higgs boson has been proposed to account for the masses
Large colliders are necessary to achieve the energy needed to find the Higgs boson
In a collider, particles with equal masses and equal kinetic energies, traveling in opposite directions, collide head-on to produce the required reaction
Particle Paths After a Collision
Particle Paths After a Collision with a Gold Nucleus
The Big Bang
This theory states that the universe had a beginning, and that it was so cataclysmic that it is impossible to look back beyond it Also, during the first few minutes after the creation of the universe, all four interactions were unified
All matter was contained in a quark-gluon plasma
As time increased and temperature decreased, the forces broke apart
A Brief History of the Universe
Cosmic Background Radiation (CBR)
CBR represents the cosmic “glow” left over from the Big Bang The radiation had equal strengths in all directions The curve fits a black body at 2.7K There are small irregularities that allowed for the formation of galaxies and other objects
CBR, cont.
The COBE satellite found that the background radiation had irregularities that corresponded to temperature variations of 0.000 3 K Including other data, it was concluded that a peak in fluctuation intensity occurred 300 000 years after the Big Bang
Hubble’s Law
The Big Bang theory predicts that the universe is expanding Hubble claimed the whole universe is expanding Furthermore, the speeds at which galaxies are receding from the earth is directly proportional to their distance from us
This is called Hubble’s law
Hubble’s Law, cont.
Hubble’s law can be written as v = HR
H is called the Hubble constant H ≈ 17 x 10-3 m/s ly
Remaining Questions About the Universe
Will the universe expand forever?
Today, astronomers and physicists are trying to determine the rate of expansion It depends on the average mass density of the universe compared to a critical density
Missing mass in the universe
The amount of non-luminous (dark) matter seems to be much greater than what we can see Various particles have been proposed to make up this dark matter
Another Remaining Question About the Universe
Is there mysterious energy in the universe?
Observations have led to the idea that the expansion of the universe is accelerating To explain this acceleration, dark energy has been proposed The dark energy results in an effective repulsive force that causes the expansion rate to increase
Some Questions in Particle Physics
Why so little antimatter in the Universe? Is it possible to unify electroweak and strong forces? Why do quarks and leptons form similar but distinct families? Are muons the same as electrons apart from their difference in mass? Why are some particles charged and others not? Why do quarks carry fractional charge? What determines the masses of fundamental particles? Can isolated quarks exist?
A New Perspective – String Theory
String theory is one current effort at answering some of the previous questions It is an effort to unify the four fundamental forces by modeling all particles as various vibrational modes of an incredibly small string
String Theory, cont.
The typical length of a string is 10-35 m
This is called the Planck length
According to the string theory, each quantized mode of vibration of the string corresponds to a different elementary particle in the Standard Model
Complications of the String Theory
It requires space-time to have ten dimensions
Four of the ten dimensions are visible to us, the other six are compactified (curled)
Another complication is that it is difficult for theorists to guide experimentalists as to what to look for in an experiment
Direct experimentation on strings is impossible
String Theory Prediction – SUSY
One prediction of string theory is supersymmetry (SUSY)
It suggests that every elementary particle has a superpartner that has not yet been observed Supersymmetry is a broken symmetry and the masses of the superpartners are above our current capabilities to detect
Another Perspective – M-Theory
M-theory is an eleven-dimensional theory based on membranes rather than strings M-theory is claimed to reduce to string theory if one compactifies from the eleven dimensions to ten
Atoms as Elementary Particles
Atoms
From the Greek for “indivisible” Were once thought to be the elementary particles
Atom constituents
Proton, neutron, and electron After 1932 these were viewed as elementary All matter was made up of these particles
Discovery of New Particles
New particles
Beginning in the 1940s, many new particles were discovered in experiments involving high-energy collisions Characteristically unstable with short lifetimes Over 300 have been catalogued
A pattern was needed to understand all these new particles
Elementary Particles – Quarks
Physicists recognize that most particles are made up of quarks
Exceptions include photons, electrons and a few others
The quark model has reduced the array of particles to a manageable few The quark model has successfully predicted new quark combinations that were subsequently found in many experiments
Fundamental Forces
All particles in nature are subject to four fundamental forces:
Nuclear force Electromagnetic force Weak force Gravitational force
This list is in order of decreasing strength
Nuclear Force
Attractive force between nucleons Strongest of all the fundamental forces Very short-ranged
Less than 10-15 m Negligible for separations greater than this
Electromagnetic Force
Is responsible for the binding of atoms and molecules About 10-2 times the strength of the nuclear force A long-range force that decreases in strength as the inverse square of the separation between interacting particles
Weak Force
Is responsible for instability in certain nuclei
Is responsible for decay processes
Its strength is about 10-5 times that of the strong force Scientists now believe the weak and electromagnetic forces are two manifestations of a single force, the electroweak force
Gravitational Force
A familiar force that holds the planets, stars and galaxies together Its effect on elementary particles is negligible A long-range force It is about 10-39 times the strength of the strong force
Weakest of the four fundamental forces
Explanation of Forces
Forces between particles are often described in terms of the actions of field particles or exchange particles
Field particles are also called gauge bosons The interacting particles continually emit and absorb field particles The emission of a field particle by one particle and its absorption by another manifests itself as a force between the two interacting particles The force is mediated, or carried, by the field particles
Forces and Mediating Particles
Paul Adrien Maurice Dirac
1902 – 1984 Understanding of antimatter Unification of quantum mechanics and relativity Contributions of quantum physics and cosmology Nobel Prize in 1933
Antiparticles
For every particle, there is an antiparticle
An antiparticle has the same mass as the particle, but the opposite charge The positron (electron’s antiparticle) was discovered by Anderson in 1932
From Dirac’s version of quantum mechanics that incorporated special relativity
Since then, it has been observed in numerous experiments
Practically every known elementary particle has a distinct antiparticle
Among the exceptions are the photon and the neutral pi particles
Dirac’s Explanation
The solutions to the relativistic quantum mechanic equations required negative energy states Dirac postulated that all negative energy states were filled
These electrons are collectively called the Dirac sea
Electrons in the Dirac sea are not directly observable because the exclusion principle does not let them react to external forces
Dirac’s Explanation, cont.
An interaction may cause the electron to be excited to a positive energy state This would leave behind a hole in the Dirac sea The hole can react to external forces and is observable
Dirac’s Explanation, final
The hole reacts in a way similar to the electron, except that it has a positive charge The hole is the antiparticle of the electron
The electron’s antiparticle is now called a positron
Pair Production
A common source of positrons is pair production A gamma-ray photon with sufficient energy interacts with a nucleus and an electron-positron pair is created from the photon The photon must have a minimum energy equal to 2mec2 to create the pair
Pair Production, cont.
A photograph of pair production produced by 300 MeV gamma rays striking a lead sheet The minimum energy to create the pair is 1.02 MeV The excess energy appears as kinetic energy of the two particles
Annihilation
The reverse of pair production can also occur Under the proper conditions, an electron and a positron can annihilate each other to produce two gamma ray photons e- + e+ → 2γ
Hideki Yukawa
1907 – 1981 Nobel Prize in 1949 for predicting the existence of mesons Developed the first theory to explain the nature of the nuclear force
Mesons
Developed from a theory to explain the nuclear force Yukawa used the idea of forces being mediated by particles to explain the nuclear force A new particle was introduced whose exchange between nucleons causes the nuclear force
It was called a meson
Mesons, cont.
The proposed particle would have a mass about 200 times that of the electron Efforts to establish the existence of the particle were done by studying cosmic rays in the 1930s Actually discovered multiple particles
pi meson (pion) muon
Not a meson
Pion
There are three varieties of pions
Muons
Two muons exist
µ- and its antiparticle µ+
The muon is unstable
It has a mean lifetime of 2.2 µs It decays into an electron, a neutrino, and an antineutrino
Richard Feynman
1918 – 1988 Developed quantum electrodynamics Shared the Nobel Prize in 1965 Worked on Challenger investigation and demonstrated the effects of cold temperatures on the rubber O-rings used
Feynman Diagrams
A graphical representation of the interaction between two particles
Feynman diagrams are named for Richard Feynman who developed them
A Feynman diagram is a qualitative graph of time on the vertical axis and space on the horizontal axis
Actual values of time and space are not important The actual paths of the particles are not shown
Feynman Diagram – Two Electrons
The photon is the field particle that mediates the interaction The photon transfers energy and momentum from one electron to the other The photon is called a virtual photon
It can never be detected directly because it is absorbed by the second electron very shortly after being emitted by the first electron
The Virtual Photon
The existence of the virtual photon seems to violate the law of conservation of energy
But, due to the uncertainty principle and its very short lifetime, the photon’s excess energy is less than the uncertainty in its energy The virtual photon can exist for short time intervals, such that ∆E ≈ h / 2 ∆t
Feynman Diagram – Proton and Neutron (Yukawa’s Model)
The exchange is via the nuclear force The existence of the pion is allowed in spite of conservation of energy if this energy is surrendered in a short enough time Analysis predicts the rest energy of the pion to be 130 MeV / c2
This is in close agreement with experimental results
Nucleon Interaction – More About Yukawa’s Model
The time interval required for the pion to transfer from one nucleon to the other is
The distance the pion could travel is c∆t Using these pieces of information, the rest energy of the pion is about 100 MeV
Nucleon Interaction, final
This concept says that a system of two nucleons can change into two nucleons plus a pion as long as it returns to its original state in a very short time interval It is often said that the nucleon undergoes fluctuations as it emits and absorbs field particles
These fluctuations are a consequence of quantum mechanics and special relativity
Feynman Diagram – Weak Interaction
An electron and a neutrino are interacting via the weak force The Z0 is the mediating particle
The weak force can also be mediated by the W± The W± and Z0 were discovered in 1983 at CERN
Classification of Particles
Two broad categories Classified by interactions
hadrons – interact through strong force leptons – interact through weak force
Note on terminology
The strong force is reserved for the force between quarks The nuclear force is reserved for the force between nucleons
The nuclear force is a secondary result of the strong force
Hadrons
Interact through the strong force Two subclasses distinguished by masses and spins
Mesons
Baryons
Decay finally into electrons, positrons, neutrinos and photons Integer spins (0 or 1) Masses equal to or greater than a proton Half integer spin values (1/2 or 3/2) Decay into end products that include a proton (except for the proton)
Not elementary, but composed of quarks
Leptons
Do not interact through strong force All have spin of 1/2 Leptons appear truly elementary
No substructure Point-like particles
Scientists currently believe only six leptons exist, along with their antiparticles
Electron and electron neutrino Muon and its neutrino Tau and its neutrino
Conservation Laws
A number of conservation laws are important in the study of elementary particles Already have seen conservation of
Energy Linear momentum Angular momentum Electric charge
Two additional laws are
Conservation of Baryon Number Conservation of Lepton Number
Conservation of Baryon Number
Whenever a baryon is created in a reaction or a decay, an antibaryon is also created B is the baryon number
B = +1 for baryons B = -1 for antibaryons B = 0 for all other particles
The sum of the baryon numbers before a reaction or a decay must equal the sum of baryon numbers after the process
Conservation of Baryon Number and Proton Stability
There is a debate over whether the proton decays or not If baryon number is absolutely conserved, the proton cannot decay Some recent theories predict the proton is unstable and so baryon number would not be absolutely conserved
For now, we can say that the proton has a half-life of at least 1033 years
Conservation of Baryon Number, Example
Is baryon number conserved in the following reaction?
Baryon numbers:
Before: 1 + 1 = 2 After: 1 + 1 + 1 + (-1) = 2
Baryon number is conserved The reaction can occur as long as energy is conserved
Conservation of Lepton Number
There are three conservation laws, one for each variety of lepton The law of conservation of electron lepton number states that the sum of electron lepton numbers before the process must equal the sum of the electron lepton number after the process
The process can be a reaction or a decay
Conservation of Lepton Number, cont.
Assigning electron lepton numbers
Le = 1 for the electron and the electron neutrino Le = -1 for the positron and the electron antineutrino Le = 0 for all other particles
Similarly, when a process involves muons, muon lepton number must be conserved and when a process involves tau particles, tau lepton numbers must be conserved
Muon and tau lepton numbers are assigned similarly to electron lepton numbers
Conservation of Lepton Number, Example
Is lepton number conserved in the following reaction?
Check electron lepton numbers:
Before: Le = 0 After: Le = 1 + (-1) + 0 = 0 Electron lepton number is conserved
Check muon lepton numbers:
Before: Lµ = 1 After: Lµ = 0 + 0 + 1 = 1 Muon lepton number is conserved
Strange Particles
Some particles discovered in the 1950s were found to exhibit unusual properties in their production and decay and were given the name strange particles Peculiar features include:
Always produced in pairs Although produced by the strong interaction, they do not decay into particles that interact via the strong interaction, but instead into particles that interact via weak interactions
They decay much more slowly than particles decaying via strong interactions
Strangeness
To explain these unusual properties, a new quantum number S, called strangeness, was introduced A new law, the law of conservation of strangeness was also needed
It states that the sum of strangeness numbers before a reaction or a decay must equal the sum of the strangeness numbers after the process
Strong and electromagnetic interactions obey the law of conservation of strangeness, but the weak interaction does not
Bubble Chamber Example of Strange Particles
The dashed lines represent neutral particles At the bottom, π - + p → K0 + Λ0 Then Λ0 → π - + p and K0 → π + µ- + νµ
Creating Particles
Most elementary particles are unstable and are created in nature only rarely, in cosmic ray showers In the laboratory, great numbers of particles can be created in controlled collisions between high-energy particles and a suitable target
Measuring Properties of Particles
A magnetic field causes the charged particles to curve
This allows measurement of their charge and linear momentum
If the mass and momentum of the incident particle are known, the product particle’s mass, kinetic energy, and speed can usually be calculated The particle’s lifetime can be calculated from the length of its track and its speed
Resonance Particles
Short-lived particles are known as resonance particles
They exist for times around 10-20 s
They cannot be detected directly Their properties can be inferred from data on their decay products
Experimental Evidence
The location of the peak tells us the mass of the particle
The smaller peaks indicate the presence of two other resonance particles
The width of the peak can be used to infer the lifetime of the particle
Murray Gell-Mann
1929 – Studies dealing with subatomic particles
Named quarks Developed pattern known as eightfold way
Nobel Prize in 1969
The Eightfold Way
Many classification schemes have been proposed to group particles into families
The eightfold way is a symmetric pattern proposed by Gell-Mann and Ne’eman
These schemes are based on spin, baryon number, strangeness, etc.
There are many symmetrical patterns that can be developed
The patterns of the eightfold way have much in common with the periodic table
Including predicting missing particles
An Eightfold Way for Baryons
A hexagonal pattern for the eight spin 1/2 baryons Stangeness vs. charge is plotted on a sloping coordinate system Six of the baryons form a hexagon with the other two particles at its center
An Eightfold Way for Mesons
The mesons with spins of 0 can be plotted Strangeness vs. charge on a sloping coordinate system is plotted A hexagonal pattern emerges The particles and their antiparticles are on opposite sides on the perimeter of the hexagon The remaining three mesons are at the center
Eightfold Way for Spin 3/2 Baryons
The nine particles known at the time were arranged as shown An empty spot occurred Gell-Mann predicted the missing particle and its properties About three years later, the particle was found and all its predicted properties were confirmed
Quarks
Hadrons are complex particles with size and structure Hadrons decay into other hadrons There are many different hadrons Quarks are proposed as the elementary particles that constitute the hadrons
Originally proposed independently by GellMann and Zweig
Original Quark Model
Three types or flavors
Associated with each quark is an antiquark
The antiquark has opposite charge, baryon number and strangeness
Quarks have fractional electrical charges
u – up d – down s – strange
+1/3 e and –2/3 e
All ordinary matter consists of just u and d quarks
Original Quark Model – Rules
All the hadrons at the time of the original proposal were explained by three rules
Mesons consist of one quark and one antiquark
This gives them a baryon number of 0
Baryons consist of three quarks Antibaryons consist of three antiquarks
Quark Composition of Particles – Examples
Mesons are quarkantiquark pairs Baryons are quark triplets
Active Figure 46.12
(SLIDESHOW MODE ONLY)
Additions to the Original Quark Model – Charm
Another quark was needed to account for some discrepancies between predictions of the model and experimental results A new quantum number, C, was assigned to the property of charm Charm would be conserved in strong and electromagnetic interactions, but not in weak interactions In 1974, a new meson, the J/Ψ, was discovered that was shown to be a charm quark and charm antiquark pair
More Additions – Top and Bottom
Discovery led to the need for a more elaborate quark model This need led to the proposal of two new quarks
t – top (or truth) b – bottom (or beauty)
Added quantum numbers of topness and bottomness Verification
b quark was found in a Y- meson in 1977 t quark was found in 1995 at Fermilab
Numbers of Particles
At the present, physicists believe the “building blocks” of matter are complete
Six quarks with their antiparticles Six leptons with their antiparticles
Particle Properties
More About Quarks
No isolated quark has ever been observed It is believed that at ordinary temperatures, quarks are permanently confined inside ordinary particles due to the strong force Current efforts are underway to form a quarkgluon plasma where quarks would be freed from neutrons and protons
Color
It was noted that certain particles had quark compositions that violated the exclusion principle
Quarks are fermions, with half-integer spins and so should obey the exclusion principle
The explanation is an additional property called color charge
The color has nothing to do with the visual sensation from light, it is simply a name
Colored Quarks
Color “charge” occurs in red, blue, or green
Antiquarks have colors of antired, antiblue, or antigreen These are the quantum “numbers” of color charge
Color obeys the exclusion principle A combination of quarks of each color produces white (or colorless) Baryons and mesons are always colorless
Quantum Chromodynamics (QCD)
QCD gave a new theory of how quarks interact with each other by means of color charge The strong force between quarks is often called the color force The strong force between quarks is mediated by gluons
Gluons are massless particles
When a quark emits or absorbs a gluon, its color may change
More About Color Charge
Particles with like colors repel and those with opposite colors attract
Different colors attract, but not as strongly as a color and its anticolor
The color force between color-neutral hadrons is negligible at large separations
The strong color force between the constituent quarks does not exactly cancel at small separations This residual strong force is the nuclear force that binds the protons and neutrons to form nuclei
Quark Structure of a Meson
A green quark is attracted to an antigreen quark The quark – antiquark pair forms a meson The resulting meson is colorless
Quark Structure of a Baryon
Quarks of different colors attract each other The quark triplet forms a baryon Each baryon contains three quarks with three different colors The baryon is colorless
QCD Explanation of a Neutron-Proton Interaction
Each quark within the proton and neutron is continually emitting and absorbing gluons The energy of the gluon can result in the creation of quarkantiquark pairs When close enough, these gluons and quarks can be exchanged, producing the strong force
Elementary Particles – A Current View
Scientists now believe there are three classifications of truly elementary particles
Leptons Quarks Field particles
These three particles are further classified as fermions or bosons
Quarks and leptons are fermions Field particles are bosons
Weak Force
The weak force is believed to be mediated by the W+, W-, and Z0 bosons
These particles are said to have weak charge
Therefore, each elementary particle can have
Mass Electric charge Color charge Weak charge
Electroweak Theory
The electroweak theory unifies electromagnetic and weak interactions The theory postulates that the weak and electromagnetic interactions have the same strength when the particles involved have very high energies
Viewed as two different manifestations of a single unifying electroweak interaction
The Standard Model
A combination of the electroweak theory and QCD for the strong interaction form the Standard Model Essential ingredients of the Standard Model
The strong force, mediated by gluons, holds the quarks together to form composite particles Leptons participate only in electromagnetic and weak interactions The electromagnetic force is mediated by photons The weak force is mediated by W and Z bosons
The Standard Model does not actually yet include the gravitational force
The Standard Model – Chart
Mediator Masses
Why does the photon have no mass while the W and Z bosons do have mass?
Not answered by the Standard Model The difference in behavior between low and high energies is called symmetry breaking The Higgs boson has been proposed to account for the masses
Large colliders are necessary to achieve the energy needed to find the Higgs boson
In a collider, particles with equal masses and equal kinetic energies, traveling in opposite directions, collide head-on to produce the required reaction
Particle Paths After a Collision
Particle Paths After a Collision with a Gold Nucleus
The Big Bang
This theory states that the universe had a beginning, and that it was so cataclysmic that it is impossible to look back beyond it Also, during the first few minutes after the creation of the universe, all four interactions were unified
All matter was contained in a quark-gluon plasma
As time increased and temperature decreased, the forces broke apart
A Brief History of the Universe
Cosmic Background Radiation (CBR)
CBR represents the cosmic “glow” left over from the Big Bang The radiation had equal strengths in all directions The curve fits a black body at 2.7K There are small irregularities that allowed for the formation of galaxies and other objects
CBR, cont.
The COBE satellite found that the background radiation had irregularities that corresponded to temperature variations of 0.000 3 K Including other data, it was concluded that a peak in fluctuation intensity occurred 300 000 years after the Big Bang
Hubble’s Law
The Big Bang theory predicts that the universe is expanding Hubble claimed the whole universe is expanding Furthermore, the speeds at which galaxies are receding from the earth is directly proportional to their distance from us
This is called Hubble’s law
Hubble’s Law, cont.
Hubble’s law can be written as v = HR
H is called the Hubble constant H ≈ 17 x 10-3 m/s ly
Remaining Questions About the Universe
Will the universe expand forever?
Today, astronomers and physicists are trying to determine the rate of expansion It depends on the average mass density of the universe compared to a critical density
Missing mass in the universe
The amount of non-luminous (dark) matter seems to be much greater than what we can see Various particles have been proposed to make up this dark matter
Another Remaining Question About the Universe
Is there mysterious energy in the universe?
Observations have led to the idea that the expansion of the universe is accelerating To explain this acceleration, dark energy has been proposed The dark energy results in an effective repulsive force that causes the expansion rate to increase
Some Questions in Particle Physics
Why so little antimatter in the Universe? Is it possible to unify electroweak and strong forces? Why do quarks and leptons form similar but distinct families? Are muons the same as electrons apart from their difference in mass? Why are some particles charged and others not? Why do quarks carry fractional charge? What determines the masses of fundamental particles? Can isolated quarks exist?
A New Perspective – String Theory
String theory is one current effort at answering some of the previous questions It is an effort to unify the four fundamental forces by modeling all particles as various vibrational modes of an incredibly small string
String Theory, cont.
The typical length of a string is 10-35 m
This is called the Planck length
According to the string theory, each quantized mode of vibration of the string corresponds to a different elementary particle in the Standard Model
Complications of the String Theory
It requires space-time to have ten dimensions
Four of the ten dimensions are visible to us, the other six are compactified (curled)
Another complication is that it is difficult for theorists to guide experimentalists as to what to look for in an experiment
Direct experimentation on strings is impossible
String Theory Prediction – SUSY
One prediction of string theory is supersymmetry (SUSY)
It suggests that every elementary particle has a superpartner that has not yet been observed Supersymmetry is a broken symmetry and the masses of the superpartners are above our current capabilities to detect
Another Perspective – M-Theory
M-theory is an eleven-dimensional theory based on membranes rather than strings M-theory is claimed to reduce to string theory if one compactifies from the eleven dimensions to ten
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