1. START (Strategic Arms Reduction Treaty) was a bilateral treaty between the United States of America and the Union of Soviet Socialist Republics (USSR) on the reduction and limitation of strategic offensive arms. The treaty was signed on 31 July 1991 and entered into force on 5 December 1994.[1] The treaty barred its signatories from deploying more than 6,000 nuclear warheads atop a total of 1,600 inter-continental ballistic missiles (ICBMs) and bombers. START negotiated the largest and most complex arms control treaty in history, and its final implementation in late 2001 resulted in the removal of about 80 percent of all strategic nuclear weapons then in existence. Proposed by United States President Ronald Reagan, it was renamed START I after negotiations began on the second START treaty.
The START I treaty expired 5 December On 8 April 2010, the replacement New START treaty was signed in Prague by U.S. President Barack Obama and Russian President Dmitry Medvedev. Following ratification by the U.S. Senate and the Federal Assembly of Russia, it went into force on 26 January 2011.

2. Today’s plan Collect homework Return quizzes
Review Chapter 3 and 4 material
and prepare for Midterm

3. Isospin (review)
Masses are approximate equal and seem to behave in the same way in strong interaction processes.
Deep idea from Werner Heisenberg (1932): The proton and neutron can be considered to be different charge substates of one particle, “the Nucleon”.
Assign a new quantum number, isospin, conserved in the strong interaction (but not in the EM interaction)
A Nucleon is assigned isospin I=1/2

4. The mathematics (group theory) of isospin is the same as the mathematics of spin or angular momentum in QM
The sum of two isospins; the product of two representations; or the sum of two angular momenta in QM.
Question: What is the dimensionality of a representation with isospin I ? (i.e. how many IZ components are available ?)
Question: What is the dimensionality of a representation with angular momentum J ? (i.e. how many JZ components are available ?)
Ans: 2I + 1 for isospin or 2J +1 for angular momentum (2S+1) for spin.

5. The spin ½ baryons Question: What is the isospin I of the Σ ?
Gell-Mann/Nishijima relation
Hypercharge
Question: What is the isospin I of the nucleon (p, n) ?
Question: What is the isospin I of the Σ ?
Question: What is the isospin I of the Λ ?
Ans: ½ for nucleons, 1 for sigma’s and 0 for lambda’s. Count the number of charge states !!

6. The pseudoscaler mesons
Question: What is the isospin I of the pion ?
Question: What is the isospin I of the K0, K+ doublet ?
Question: Why are the K+ and K- not in the same isospin multiplet ?
Ans: I=1/2, multiplicity 2 I + 1 = 2;
Note that strangeness S for the K+ and K- as well as K0 and Kobar are opposite

7. Question: What would you find if I=2 or if I=1 dominated ?
Ans: ratio of rates is 1 if I=0

8. What is the isospin of a deuteron (p n) bound state ?
What is the isospin of a Helium-4 nucleon ?
What is the isospin of a neutral pion ?
Ans: No since it cannot proceed by the strong interaction. An EM interaction might occur.

9. Isospin review: Compare the rates of these four reactions
What is A3/2 ?
What is A1/2 ?

10. Question: If the I=3/2 channel dominates as is the case for the Δ(1232), what are the ratio of the the upper three rates ?
Answer: 1: 2/9: 1/9 or 9:2: 1
This is experimentally confirmed.
What is the resonance shape called ?
Ans: Breit-Wigner

11. Kinematics Review
Do you see why ? We are using the ultra-relativistic limit.

13. Cross-section review Remember 1 barn= 10-28m2
Now multiply by the number of seconds in a year

15. Review Example: Quantum Numbers
Consider positronium, an EM bound state of an electron and positron.
Determine the relationship that this condition imposes on the orbital angular momentum l, total spin s and charge conjugation C.
What is the minimum number of photons for ortho-positronium (3S1) and para-positronium (1S0) ?
Ans: the electron and positron are fermions, hence C=(-1)l+s
Ans: the electron and positron are spin ½ particles, hence the total spin can be 0 or 1 in a orbital angular momentum s-wave.
Ans: C=-1 for ortho, so it decays to (-1)n=-1 or n=3 photons while C=+1 for para positronium so it decays to (-1)n=1 or n=2 photons.

16. Question: How do the energy levels of charmonium and positronium compare ? How do the energy levels of positronium and hydrogen compare ?
Ans: they are almost the same with the following substitutions:
Question: What is the reduced mass μ ? Remember the hydrogen atom in QM

17. The reduced mass is defined as:

18. November Revolution 1974

19. SLAC
BNL
1974 November Revolution

20. Nobel Prize in Physics 1976
Sam Ting
Burton Richter

21. Question: How do the energy levels of bottomonium and positronium compare ?
Ans: they are almost the same with the following substitutions:
Question: What is the reduced mass μ ? Remember the hydrogen atom in QM