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calculating the centre-of-mass

 
1. For the following: (i) calculate the centre-of-mass; (ii) state what the most massive particle that
can be produced is; (iii) draw a Feynman diagram for the process.
a,m) an e+ e- collider where the energy of each beam is 1 GeV
b,n) an e+ e- collider where the energy of each beam is 1.6 GeV
c,o) an e+ e- collider where the energy of each beam is 4.8 GeV
d,p) an e+ e- collider where the energy of each beam is 45.6 GeV
e,q) a 100 keV X-ray incident on your body (medical X-ray)
f,r) a 4 MeV electron beam incident on your body (Electron beam therapy)
g,s) a 100 MeV proton beam incident on your body (Hadron therapy)
h,t) a proton fixed target experiment where the energy of the beam is 100 GeV
i,u) a proton-proton colliding beam experiment where the energy of each beam is 100 GeV
j,v) a proton-proton colliding beam (the LHC) where the energy of each beam is 6500 GeV
k) a proton-antiproton collider each beam having 270 GeV of energy (the SPS). What did the UA1
experiment at the SPS discover?
l) a proton-antiproton collider each beam having 1TeV of energy (Tevatron at Fermilab).
2. Neutrinos are produced at CERN with a 400 GeV proton beam incident on a fixed target. Some
of these neutrino are subsequently detected 700 km away by the presence of a muon created through
inverse beta decay. What is the maximum energy of this muon? If you wanted to produce a (real) W
boson, how energetic would the initial proton beam need to be?
3. Which of the following pair of processes are possible and which are forbidden. Draw the Feynman
diagram for the process that is possible and explain why the other is forbidden.
a,i,q) η → ππ;η → πππ
b,j,r) η → π0
π0
γ;η → π0
π0
γγ
c,k,s) η → π+
π−
µ+
µ−
;η → π+
π−
π+
π−
d,l,t) J /ψ →γγ; J /ψ →γγγ
e,m,u) ω → π+
π−
;ω → π0
π0
f,n,v) ω → π+
π−
π0
;ω → π0
π0
π0
g,o) ηc → KKπ;ηc → KK
h,p) η'(958)→ηππ;η'(958)→ωππ

 

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