The Higgs boson is a proposed elementary particle that should be observed in a f

Question

The Higgs boson is a proposed elementary particle that should be observed in a few
years, assuming it exists. One strategy for producing it in a high-energy particle ac-
celerator is to collide protons and antiprotons together. If the mass of a proton (and
antiproton) is m, and if the mass of the Higgs boson is about 100m, how much energy
must be supplied to the proton-antiproton system in order to produce a Higgs boson if:
(a) A moving proton collides with a stationary antiproton?
(b) A proton and antiproton have equal and opposite momenta?

Explanation / Answer

Etotal = Kproton + Kantiproton + mprotonc2 + mantiprotonc2

a) Etotal = Kproton + 2mc2 = 100mc2

Kproton = 98mc2 = 98(938.1 MeV) = 91.9 GeV

b) Etotal = 2Kproton + 2mc2 = 100mc2

Kproton = Kantiproton = 49mc2 = 45.95 GeV each

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