PHYC4008 High Energy Particle Physics Problem Sheet 4
(Hand up solutions to Q. 2,3,4 by Nov 16th)
1. Explain whyη →ππ is forbidden for both the strong and electromagnetic interaction.
What can it decay to electromagnetically? Draw the Feynman diagram.
2. The colourless vector mesons have the following flavour composition:
= (uu − dd ) = (uu + dd ) = ss 0 0 , 0
2
, 1
2
1
ρ ω φ .
Show that the partial decay widths to electrons are in the ratio ( 0 ) : ( 0 ) : ( 0 ) 9 :1: 2 Γ ρ Γ ω Γ φ =
How do these compare to the partial decay widths to muons?
How do these compare to the partial decay widths to quarks?
Which quarks decays are possible? Draw the Feynman diagrams.
3. Considering the masses, spins, parity and quark composition of the lightest hadrons, write down
all possible strong decays of the ρ ,φ 0 + and − Ω . Discuss the lifetimes of the particles.
4. Work out the ratios for the partial decay widths ( 0 + − ), ( / + − ), ( + − ) Γ φ →e e Γ J ψ →e e Γ Ψ→e e .
Check your answers against the data values in the PDF: http://pdg.lbl.gov/
Explain why the lifetimes (full widths) for 0 , / ,Ψ φ J ψ are very different. Roughly what sizes are
they?
Why is the corresponding decay + − 0 →e e π not observed?
5. The proton is a uud state with JP=1/2+. The ‘excited’ proton is called Δ+ and has JP=3/2+
What will Δ+ the decay to? Check the quantum numbers for spin, parity and flavour work. Draw
the Feynman diagram for the decay.

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