Issued Wed Apr 23 Due Wed May 7

This is a "take home final homework set". You should treat it more as a take home final than a regular homework. It will count roughly as much as the first exam did. Please do not work together in study groups on this one - however, you may as usual come ask me questions about it. (I will be a little more careful than usual about just telling you the answers, of course, but will try to help where I can!) Throughout this assignment, feel free to use F+H, and Data Tables (everything you need should be found in Appendix 3 of F+H)

This is "open book, open note". Each question is worth 20 points.

1) Either F+H 5.43, or F+H 6.11, it's your choice. (Please don't do both!)

2) F+H 6.36

3a) State (briefly) the rules regarding conservation of isospin and strangeness for strong, weak, and EM interactions.

b) Why are mesons equal mass, but baryons are not?

c) The lifetime of the is 2.6*10^-8 sec, but that of the is 8.4*10^-17 sec. Why do members of an isospin triplet have radically different lifetimes?

d) Why has no one ever seen , at any energy?

e) The data tables don't show the decay .

Could this reaction possibly occur by a strong interaction? (Why/why not?)

4) A J/ particle is a bound state of a "c" (quark) and a " " (antiquark). A so-called spectroscopic notation for this particle is . The leading 1 tells you the "principle" (or radial) quantum number, i.e. it's in the lowest radial state. The "S" tell you that the quarks are in an orbital l=0 state. (S, P, D, F etc.) The upper "3" superscript is by convention 2J+1. (So this "3" says J=1, which tells you the total angular momentum of the system, J=L+S) The lower "1" subscript tells you what the combined spin, S is of the quarks.

a) Deduce the parity of the J/ . (Explain how you get it) Check your answer. Deduce the C quantum number (charge conjugation) of the J/ ? Again, explain and check. When the J/ decays, could it decay into a single photon? 2 photons? 3, 4? (Briefly, explain) What is the isospin of the J/ (why?)

b) There is another particle, the , slightly lighter than the J/ . Its spectroscopic notation is . Deduce its parity, and C number (check)

How many photons does the produce if it decays into only photons?

c) Can you deduce any basic property(ies?) of the strong force between quarks, based on the simple fact that the is lighter than the J/ ?

d) Can a J/ decay into an by emitting an electric dipole (E1) photon? Why/why not? How about by emitting a meson?

e) The baryon has isospin 3/2 and J=3/2. It's composed of 3 quarks. What specific quarks are they? This particle is a ground state, so all relative orbital l=0 (for any pair of quarks in it) Thus, J arises purely from the spins of the quarks. Figure out what the symmetry is under interchange of any pair of quarks in the . What should it be? (Your answer should bug you, it bugged theorists a lot in the 1960's! To resolve it, people invented color, a new additional quantum number, kind of vaguely like isospin)

5a) Why would detection of the process automatically demonstrate the existence of weak neutral currents, while detecting would not.? Can you make an argument as to which of these two cross sections is likely to be larger? (State your reasoning)

b)

In class we drew these 2 Feynman diagrams for Bhabha scattering, each of which is of order : Now draw all the next higher order diagrams which contribute to Bhabha scattering at order , for example:

Hint: I count at least 18 diagrams! But it's not that bad: try to organize them. E.g., with the one example I've given, you could then just say: "+ 3 more, with photon loop on other 3 legs" (rather than drawing those 3 more very similar diagrams...)

6a) F+H 11.9

Hint: Assume the matrix elements for these two reactions are the same, and neglect any Coulomb corrections. (Look at the start of section11.2) Don't forget, the Sigma hyperons don't have equal masses! Think phase space...

b) Check your answer using the lifetimes in Appendix 3. Note: This is tricky! App. 3 gives the mean life, but that's primarily due to other decay channels! You will need to take into account the "fraction" column (in App 3) which tells you what fraction of the decays are due to which process. Show your logic carefully; your answers to a and b should agree fairly nicely.

c) The weak charge changing interaction is mediated by and bosons, which are particle and antiparticle. Would it be meaningful to introduce linear combinations, W1 and W2, similar to what we did in the Kaon system? (Briefly, explain)