Issued Wed Feb 26 Note! Due Mon, Mar 10

Required reading: F+H Ch. 8 and 9

Reminder: First midterm, Thursday Mar 13. It will cover F+H Ch 1-8

Take a look at the Particle Data Tables, one of the most important compilations of particle physics information available. These are published every two years, the most recent is Phys. Rev D54 (1996) p.1. Feel free to use it to help answer the following questions, especially #1. (You will find lots of additional useful information in there - take a moment to browse through this journal)

1a) Give 3 experimental reasons why we know that the and (1.2 GeV) particles are not a particle/antiparticle pair.

b) Look at the 5 dominant decay modes of the (1.2 GeV), and classify them as strong, weak, or EM. (Give a brief reason).

c) Do the same for the (1.39 GeV). (Here, the branching ratios are not yet measured - just take a sensible guess, and give your reason).

d) What are the quantum numbers of the (1.39 GeV) (I, I3, Q, S, A, J, and parity?). Do any of these differ from the (1.2 GeV)? What do you think is the quark model makeup of these two particles? (Why?)

2a) F+H 7.11.

2b) F+H 7.14 (Note: This is chapter 7, so don't worry about isospin here)

3a) The nuclear fusion reaction has never been observed. Why not? (Note: here, you are expected to think about isospin!)

3b) The rho is a neutral isovector (I=1) meson. (We first met it in Ch. 5, when the invariant mass spectrum of pi production showed a peak at 765 MeV, indicating ) However, the rho is never observed to decay into . Why not? (Hint: Think isospin, and Clebsh-Gordon coefficients!)

3c) Estimate the ratio of strong interaction cross sections

Does your answer depend on energy? Why/why not?

(Hint: Isospin symmetry says that the strong force doesn't care about I_3)

3d) Strong pion-nucleon scattering occurs only through states of total combined isospin 1/2 and 3/2. How do I conclude this?

These "channels" each have their own strength -- at a CM energy of 1.232 GeV, there is a strong resonance, the "Delta". There are 4 observed resonant pi-N states at this energy, with charges -1, 0, +1, and +2.

Thus, the Delta has I=3/2 (how do I conclude this?)

The presence of such a strong resonance means that the I=3/2 channel completely dominates over the I=1/2 channel.

In this energy regime, estimate the ratio of cross sections .

(Hint: F+H talk about this problem in Ch. 14.2(!) in some detail, p. 403. You will need to find Clebsh-Gordon's for I=1 + I=1/2, because F+H didn't happen to give the particular case I chose for the denominator)

4) F+H 8.13. (In your answers, discuss the third component of isospin, and nuclear charges (Z), as well as the total isospin of nucleus A')

HINT: For He(3) and H(3), note that F+H Eq'n 8.34 tells you isospin of a nucleus in terms of Z and N. Here, the ground state of the He and H nuclei have the MINIMUM total isospin consistent with their I3.

5a) Use F+H Eq'n 8.30 to deduce the strangeness and charm content of the (2.28 GeV), an isosinglet baryon (not an antibaryon). (Note - it is too light to contain any bottom or top quarks) Guess the complete quark content of this baryon, and explain your reasoning. (use Table A3 in F+H, or the Particle Data Tables, to check your answer)

5b) Electron-positron annihilation shows a few very strong, narrow resonances. The first especially significant ones occur at CM energies of 1.020 GeV (the " "), and at 3.097 GeV. (the " ") Such a resonance indicates the threshold creation of a single new particle. In each case, there are no other states nearby with the same mass and quantum numbers (spin=1, parity=-1)

Use Eq'n 8.30 to deduce the net strangeness and charm content of these particles. (Again, they're too light to involve bottoms or tops)

Are they mesons or baryons? Why?

Make a reasonable guess as to the quark content of these particles.

Explain your reasoning. (Use Table A3 to check your answer.)

5c) Why do you think I consider these two particles to be so significant? (What is the name and mass of the next "significant" narrow resonance with these same quantum numbers?)