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Determining Mass

Top Home - Find the Mass

More Advanced Background Energy, Mass and Momentum Calculations:
To find the mass of the top quark, you need to understand that the discovery of the missing momentum of the neutrino is crucial. This value gives you all you need to find the mass of the top quark. The following discussion is beyond the scope of high school physics (and many college courses as well), but the leap is not so great that you cannot do it. Perhaps a bit of faith is needed here.

A common relation in high-energy physics is the following:

E2 - p2 = m2

The reason energy, momentum and mass are shown as equal is actually due to the convention of choosing a system where the speed of light, c, is set equal to one. In this case, where particles are traveling with speeds of almost c, E = mc2 becomes E=m and p=mv becomes p=mc or p=m. This does change scale somewhat to be sure, but it allows for a simpler conversion between energy, mass and momentum.

In this case, it follows that you should write energy and momentum in terms of the mass of the top quark:

E2 - p2 = (2mt)2

Observing that the net momentum in a plane perpendicular to the beam direction before the collision is the same as the momentum after and that value is zero, means:

E2 = (2mt)2

or, taking the square root of both sides,

E = 2mt

Because almost all of the energy of the collision is the result of top and antitop decay, simply add the energies of the four jets, the soft muon, the muon and the neutrino before dividing by the two tops (actually a top and an antitop quark) to obtain the mass of the most recently discovered quark.