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Today: particle physics with some examples relevant to the final exam (practice applying QM and special relativity)
Friday Dec 16th: 12:00-2pm
Overview of final exam:
Problem 1: Interference Problem 2: Heisenberg Uncertainty Principle (Particles and/or Waves) Problem 3: QM I: Wave Functions (be ready for tunneling) Problem 4: QM II: Atomic Structure Problem 5: Molecules/Solid State Problem 6: Nuclear Physics (rest mass energy is important)
8 problems, 2 of which are short answer/conceptual questions (including chapter 44). The last two problems will include some questions about energy and momentum in special relativity

2. Two particle “resonances” (J/ψ and ϕ)
“Tune the radio dial to the right QM frequency” in a particle accelerator.

3. Heisenberg Uncertainty Principle Example (particle physics)
What is the energy width of the J/ψ particle (c-anti c bound state) if its mean lifetime is 7.6 x s ?
What is the lifetime of the ϕ particle (s sbar bound state), which has a mass of MeV/c2 and measured energy width of 4.4 MeV/c2

4. Special relativity in particle physics
What is the minimum energy required to produce an anti-proton in a collision with a stationary proton ?
Question: Why not a single anti-proton by itself ?
Ans: Need to conserve charge and “baryon number”
Question: How much available energy is needed ?
Ans: 4mpc2

5. Special relativity applied to particle physics
A proton (rest mass 938 MeV) with kinetic energy K collides with a proton at rest. Both protons survive the collision and a neutral pion (π0, rest energy 135 MeV) is produced. What is the threshold energy (minimum value of K) for this process ?
Need to have the “available” center of mass energy be greater or equal to twice the rest mass of a proton plus the rest mass of a neutral pion

6. Special relativity applied to particle physics
A proton (rest energy 938 MeV) with kinetic energy K collides with a proton at rest. Both protons survive the collision and a neutral pion (π0, rest energy 135 MeV) is produced. What is the threshold energy (minimum value of K) for this process ?
Note mp=938 MeV

7. Leptons
Leptons do not experience the strong interaction.
Table 44.2 summarizes the characteristics of the six leptons.

8. Clicker question on lepton number conservation
Electrons and neutrinos have lepton number +1, while positrons and antineutrinos have lepton number –1. If particle A decays to particle B, it could not at the same time emit
A. an electron and an antineutrino.
B. a positron and an antineutrino.
C. an electron and a positron.
D. Misleading question—any of these combinations could be emitted.
Answer: B

9. Clicker question on lepton number conservation
Electrons and neutrinos have lepton number +1, while positrons and antineutrinos have lepton number –1. If particle A decays to particle B, it could not at the same time emit
A. an electron and an antineutrino. (total lepton #=0)
B. a positron and an antineutrino. (total lepton #=-2)
C. an electron and a positron. (total lepton#=0)
D. Misleading question—any of these combinations could be emitted.
Answer: B

10. Hadrons experience the strong interaction.
Mesons and baryons are subclasses of hadrons.
Table 44.3 lists some hadrons and their properties.
The total baryon number is conserved in all interactions.
However, hadrons or particles containing strange (s) quarks have some “additional quantum numbers” called strangeness. This quantum number is conserved in the strong interaction.

11. Some hadrons and their properties

12. Strangeness
Murray Gell-Mann invented strangeness and discovered the SU(3) symmetry of the quark model
However, strangeness is violated in weak interaction decays
Question: Does these reactions conserve strangeness ?
How about this one ?

13. The figure (right) shows the quark content of four different hadrons.
Quarks
Hadrons are composed of quarks (fractionally charged point-like entities)
The figure (right) shows the quark content of four different hadrons.

14. Practice problem for the final.
Ans: p=uud; n=udd;
Let’s check the charges 2/3+2/3-1/3=1; 2/3-1/3-1/3=0
Ans: The proton has a lifetime of 1034years or more; the neutron decays by the weak interaction in about 15 minutes (881±1.5) s

15. The eightfold way (a brilliant discovery about symmetry)
The quark model and the eightfold way, using Figures (top) and (bottom).
Spin and angular momentum are quantized again in the quark model

16. Properties of the six quarks

17. Example of spin in the quark model
Bound state of a b and an anti-d or u quark
As in atomic transitions , the photon has an energy corresponding to the differences in energy levels
Question: What is a famous spin-flip transition in atomic physics ?
Remember 21cm or 5.9 x eV

18. E. In fact, all of these quantities are always conserved.
Which of the following properties is not conserved in certain particle physics experiments?
A. baryon number
B. lepton number
C. strangeness
D. electric charge
E. In fact, all of these quantities are always conserved.
Answer: C

19. A44.3
Which of the following properties is not conserved in certain particle physics experiments?
A. baryon number
B. lepton number
C. Strangeness (only in the strong interaction and EM interaction, not in the weak interaction).
D. electric charge
E. In fact, all of these quantities are always conserved.

20. Clicker question on a problem with the quark model
A baryon called the Δ++ is composed of three u quarks, each of which has the same spin component. Why does this not violate the Pauli exclusion principle, which forbids more than one fermion from being in the same quantum-mechanical state?
Quarks cannot be removed from a baryon, so the Pauli exclusion principle does not apply.
B. Quarks have an additional property called color, and each quark has a different color.
C. The quarks within the Δ++ are continually being created and annihilated.
D. more than one of the above
Answer: B

21. ”Freebie” short answer question for the final exam
A baryon called the Δ++ is composed of three u quarks, each of which has the same spin component. Why does this not violate the Pauli exclusion principle, which forbids more than one fermion from being in the same quantum-mechanical state?
Quarks cannot be removed from a baryon, so the Pauli exclusion principle does not apply.
B. Quarks have an additional property called color, and each quark has a different color.
C. The quarks within the Δ++ are continually being created and annihilated.
D. more than one of the above
Answer: B
Pauli exclusion principle is ok !

22. The standard model
Introduce the color quantum number and the theory of the strong interaction called “quantum chromodynamics” or QCD.
The weak interaction and electromagnetic interaction have been unified in the electroweak interaction (including the photon, W, and Z force mediator particles)
Is there a theory that unifies everything into a single fundamental force ?

23. The expanding universe
There is a red shift in the light from distant galaxies.
Hubble’s law: The recession speed of a galaxy is proportional to its distance r from us: v = H0r.
The graph in Figure (right) illustrates Hubble’s law.
Follow Example 44.8.
Follow Example 44.9.

24. The Big Bang
Hubble’s law suggests that at one time all the matter in the universe was extremely concentrated and was then blown apart by the Big Bang.
The red shift of galaxies is caused by the expansion of space itself. We live in an expanding universe.
Figure (right) shows an analogy for the expanding universe.

25. The future of the universe
If the average density of the universe is less than the critical density, the universe should expand forever. If it is greater, the universe should stop expanding and then contract. (See the figure on the right.)
Most of the matter in the universe is mysterious nonluminous dark matter.
Invisible dark energy is causing the expansion of the universe to speed up (or accelerate)

26. The beginning of time The early universe was extremely dense and hot.
Follow the text discussion of temperatures, uncoupling of interactions, and the standard model of the history of the universe, using Figure below.

27. Nucleosynthesis Follow the text discussion of nucleosynthesis.
Figure (right) shows the Veil Nebula, a supernova remnant.

28. Background radiation
3K “black-body radiation”. Non-uniformities determine the structure of the universe.