Homework 4(26+8 bonus points) Name:
Problem 1 (1 point)
Why do -decays of different elements, although all due to the very same reaction occurring inside their nuclei n p e, have so different lifetimes ranging from a tiny fraction of a second to billions of years?
Problem 2 (9 points)
Which of three conservation laws would be violated if the following reactions were possible?
Angular momentum? / Lepton number? / Baryon number?n p e–e
n + e–
n +
n p + e+ +
n + e–e
– –
–p
– e–
– e–e
Problem 3 (2 points)
What are the two distinct methods that can be used in searching for resonances in -p-system?
Problem 4 (6 bonus points)
How would you search for a resonance in +n system, if its expected mass was 2 GeV and width—100 MeV? Sketch out your experimental setup that would make such discovery possible.
Problem 5 (3 points)
A. List all elementary fermions that can participate in electromagnetic interactions. (1 point)
B. List all elementary fermions that can participate in strong interactions. (1 point)
C. List all elementary fermions that can participate in weak interactions. (1 point)
Note: quarks of the same flavor but of different colors can be considered here as one fermion.
Problem 6 (3 points)
The main decay mode of a charged pion is ++ and its lifetime ~10-8 s.
The main decay mode of a neutral pion is 0 and its lifetime ~10-16 s.
Starting from the quark structure of both pions, draw Feynman diagrams for both decays. (2 points)
Why are the two lifetimes so different? (1 point)
Problem 7 (8+ 2 bonus points)
- Give the quark composition of ++ and - baryons. (1 point)
- What are their spins? (1 point)
- What are their masses? (1 point)
- Why are the two masses different? (1 points)
- Give one typical decay channel for each of them. (2 points)
- Starting from the quark structure of ++ and - baryons, draw Feynman diagrams these decay modes. (2 bonus points)
- What are their lifetimes? (1 point)
- Why are the lifetimes so drastically different? (1 points)