Chapter 31

1. Chapter 31 Particle Physics

2. 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

3. Discovery of New Particles • New particles • Beginning in 1945, many new particles were discovered in experiments involving high-energy collisions • Characteristically unstable with short lifetimes • Over 300 have been cataloged • A pattern was needed to understand all these new particles

4. 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 • Protons and neutrons are not truly elementary, but are systems of tightly bound quarks

5. Fundamental Forces • All particles in nature are subject to four fundamental forces • Strong force • Electromagnetic force • Weak force • Gravitational force • This list is in order of decreasing strength

6. Nuclear Force • Holds nucleons together • Strongest of all the fundamental forces • Very short-ranged • Less than 10-15 m • Negligible for separations greater than this

7. 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

8. 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 manifestions of a single interaction, the electroweak force

9. 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 10-41 times the strength of the nuclear force • Weakest of the four fundamental forces

10. Explanation of Forces • Forces between particles are often described in terms of the actions of field particles or exchange particles • The force is mediated, or carried, by the field particles

11. Forces and Mediating Particles

12. Paul Adrian Maurice Dirac • 1902 – 1984 • Understanding of antimatter • Unification of quantum mechanics and relativity • Contributions of quantum physics and cosmology • Nobel Prize in 1933

13. Antiparticles • Every particle has a corresponding antiparticle • From Dirac’s version of quantum mechanics that incorporated special relativity • An antiparticle has the same mass as the particle, but the opposite charge • The positron (electron’s antiparticle) was discovered by Anderson in 1932 • 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

14. 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

15. 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

16. 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

17. 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

18. 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 1.022 MeV • The excess energy appears as kinetic energy of the two particles

19. 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+® 2g

20. Antimatter, final • In 1955 a team produced antiprotons and antineutrons • This established the certainty of the existence of antiparticles • Every particle has a corresponding antiparticle with • equal mass and spin • equal magnitude and opposite sign of charge, magnetic moment and strangeness • The neutral photon, pion and eta are their own antiparticles

21. 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

22. 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

23. 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 made by studying cosmic rays in the late 1930’s • Actually discovered multiple particles • Pi meson (pion) • Muon • Not a meson

24. Pion • There are three varieties of pions • + and - • Mass of 139.6 MeV/c2 • 0 • Mass of 135.0 MeV/c2 • Pions are very unstable • For example, the - decays into a muon and an antineutrino with a lifetime of about 2.6 x10-8 s

25. 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

26. Richard Feynman • 1918 – 1988 • Developed quantum electrodynamics • Shared the Noble Prize in 1965 • Worked on Challenger investigation and demonstrated the effects of cold temperatures on the rubber O-rings used

27. 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

28. 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

29. 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 ΔE » / 2Δt

30. 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 100 MeV / c2 • This is in close agreement with experimental results

31. 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 cDt • Using these pieces of information, the rest energy of the pion is about 100 MeV

32. 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

33. Nuclear Force • The interactions previously described used the pion as the particles that mediate the nuclear force • Current understanding indicate that the nuclear force is more fundamentally described as an average or residual effect of the force between quarks

34. 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

35. 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

36. Hadrons • Interact through the strong force • Two subclasses distinguished by masses and spins • Mesons • Decay finally into electrons, positrons, neutrinos and photons • Integer spins (0 or 1) • Baryons • 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

37. Leptons • Do not interact through strong force • Do participate in electromagnetic (if charged) and weak interactions • All have spin of ½ • Leptons appear truly elementary • No substructure • Point-like particles

38. Leptons, cont • Scientists currently believe only six leptons exist, along with their antiparticles • Electron and electron neutrino • Muon and its neutrino • Tau and its neutrino • Neutrinos may have a small, but nonzero, mass

39. 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

40. 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 • Conservation of Baryon Number states: the sum of the baryon numbers before a reaction or a decay must equal the sum of baryon numbers after the process

41. 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

42. 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

43. Conservation of Lepton Number • There are three conservation laws, one for each variety of lepton • 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

44. 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

45. 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

46. Strange Particles • Some particles discovered in the 1950’s 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

47. Strangeness • To explain these unusual properties, a new quantum number, S, called strangeness, was introduced • A new law, the conservation of strangeness, was also needed • It states that whenever a reaction or decay occurs via the strong force, the sum of strangeness numbers before the process 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

48. Bubble ChamberExample of Strange Particles • The dashed lines represent neutral particles • At the bottom, - + p  Λ0 + K0 Then Λ0  - + p and

49. 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

50. 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 particles’ 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