Question

In an experiment two beams of protons with the same energy are fired at each other. Particle detectors surround the interaction point. One unusual event is recorded which contains one electron and two muons. It is hypothesized that these could arise from the decay of a hitherto unknown particle, the 'X'. The energy and momentum components (E, Px, Py, Pz) of each muon and electron are measured and tabulated below (GeV) Px (GeV Particle electron First muon Pz (GeV 7.5 26.0 26.0 ne 10.6 45.0 0.0 26.0 26.0 26.0 26.0 Second muon |45.0 (i) Briefly describe how momentum and energy are measured experimentally. 2 marks] (ii) Calculate the invariant mass of the X particle 12 marks]

You may assume the proton mass = 1 GeV and the electron and muon masses are negligible.

I would appreciate an answer to part two!

Answer 1

i) Particle detectors are made such that the high energy particles are accelerated and they collide. when they collide new particles can be identified. Likewise, when the particles are accelerating in a circular chamber, they move with velocity. if their speed is more than that of light, then it emits Cherenkov radiation. now the angle with which it emits the radiation is noted, this angle gives the velocity of the particle. From velocity, we can find the momentum and hence the energy.

ii) since the electron and two muons are formed by the decay of the hitherto, the mass of all the three particles should be the mass of X.

mass of electron:

= |p|² - E²

=112.5 -112.36

= 0.14 GeV

muon

=2028 - 2025

=3 GeV

second muon :

= 3 GeV

total mass = 3 + 3 + 0.14

= 6.14 GeV