Measuring the Mass of the Top Quark

An Educational Resource from Fermilab, where the top quark was discovered in 1995.

(This is basically what the LHC at CERN will try to do to detect the Higg’s boson, only the particles will be moving even faster.)

In 1995 Fermilab detected the 6th and heaviest quark - the top quark - by smashing protons and antiprotons together. Top quarks decay very rapidly, so mass was measured by examining the decay products.

1) Is mass conserved in these collisions?

a) Yes, mass is always conserved

b) Yes, top quarks and protons have equal mass

c) No, kinetic energy of the protons is turned into the mass of the top quarks

2) Is momentum conserved in the collision?

The top quarks decay into a large variety of other particles which will be detected. Many things can happen, but momentum will always be conserved.

The particles move off in three dimensions and are detected in

the D-Zero detector.

The side view looks like this.

3) This is the cylinder of the data rolled onto a flat sheet. The heights represent the amount of energy found at that spot. Is this a two or three-dimensional collision?

The end view looks like this and we are going to assume that all the momentum is in this plane.

4) This arrow represents a momentum of 95.5 GeV/c. ….Sketch arrows for the other five momenta.

5) Carefully add all the vectors together.

What do you get?

6) Why didn’t the momenta add to zero?

a) Momentum isn’t conserved at these speeds.

b) We haven’t included the momentum of the neutrino

c) This really wasn’t a 2-D collision

d) Our measurements have limited accuracy.

The physicists at Fermilab use different units for energy, momentum and mass than we do. For energy they use GeV.

7) What is a GeV? Why do they use such strange units?

Energy is measured in GeV because joules are way too big.

Energy is converted to mass using m = E/c2. Rather than dividing by 9 x 1016 m2/s2 all the time, they just measure mass in GeV/c2.

Similarily, momentum is measured in GeV/c. This means that a particle with a momentum of 53.9 GeV/c has a mass of 53.9 GeV/c2.

The energy that came from the two top quarks that were formed is equal to the numerical sum of all the momenta discovered in the collision.

8) What is the mass of the top quark?

The mass of the top quark is 170.9 +/- 1.8 GeV/c2. This isn’t even close. What happened?

The mass of all the decay particles was95.5 + 54.8 + 17.0 + 58.6 + 61.2 + 7.3 + 53.9 = 348.3 GeV/c2

The decay products were from a top-antitop pair. Our calculations yield a top quark mass of 174.2 GeV/c2.