Problem Set 1

Problem 5

Masses of particles:

mproton =  .9383mneutron =  .9396mW  =  80.22

Define the laboratory energy of the beam proton:

Eprotlab = Sqrt[pprot^2 + mproton^2]

Define the necessary center of mass energy:

Ecm = mproton + mneutron + mW

Since sqrt of 4-momentum is invariant, calculate for both center of mass and laboratory and equate to calculate beam momentum:

eq1  =  Ecm^2  ==  (Eprotlab + mproton)^2  - pprot^2

Solve[eq1, pprot]

Answer for fixed target production:  proton momentum must be 3.59 TeV.

Now calculate for a colliding beam experiment:

eq2  =  Ecm^2  ==  (2 Eprotlab)^2

Solve[eq2, pprot]

Thus for a colliding beam experiment, each beam needs to have at least 41 GeV/c momentum to produce W's almost a factor of 100 less than for fixed target production.

S is just the square of E_cm and thus = 6740. GeV^2.