# Calculate the Top Quark Mass

#### E = mc2 Used in the Creation of the Most Massive Quark Yet Discovered! Analysis of DZero Data from Fermi National Accelerator Laboratory

Introduction: Today you will make use of Einstein's famous equation and actual experimental data collected in 1995 from a special event that is two-dimensional rather than three-dimensional to determine the mass of the top quark; this is the most massive quark ever discovered.
Procedure - Part One: You will be given a computer-generated plot of a collision between a proton and an antiproton. You will need to determine the momentum of each bit of debris that comes from the collision. Be sure to remember that momentum has direction! Your teacher may give you printed copies of the plots or you can look at the Events for Displaying on the Computer.

The diagram below shows the collision for the event labeled Run 92704 Event 14022. The other data plots can be represented by diagrams similar to this but may not have exactly the same debris, going in the directions shown here. While this event looks complex at first, it may be summarized by noting that a proton and antiproton collide to create a top-antitop pair that exists for a very short time. Almost immediately the very massive top and antitop decay into the constituents that are known to be their signature. These include four "jets" (large blasts of particles) that are the result of decays of W bosons and some less massive quarks. It is important to note that one of the jets will often contain a low-energy or "soft" muon. The soft muon helps identify the jet as a bottom quark jet. In addition, a muon and neutrino come out as debris from the collision. You can see it in the upper right part of the diagram. Check out the QuickTime event animation.

You will notice that there is no information given about the neutrino except the magenta tower indicating its direction on the color plot. While scientists can predict with confidence that it comes out of the collision, it cannot be detected very easily. Still, a careful consideration of the momenta before the collision and after the collision may give you a clue as to how much momentum this particle has!

Make a momentum vector diagram to determine the momentum of the neutrino. Be sure to remember that the total momentum of the system must be zero, so any "missing" momentum must belong to the muon neutrino.

Question 1. What is the momentum of the missing neutrino?

Procedure - Part Two: It turns out that if you are careful about your choice of units, it is possible to equate momentum and energy in a way that is similar to the way mass and energy are related. Specifically, it may be shown that the momentum you measured above is the same numerical value as the energy or mass of the particle. In other words,

E (in GeV) = p (in GeV) = m (in GeV)

This shows, then, that the total 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. Fill in all the momentum values from your color plot in the table below. Finally, add the measured value for the neutrino that you just determined at the end of this table.

Momentum,
Energy
or Mass
 Jet 1 Jet 2 Jet 3 Jet 4 Muon Soft Muon Neutrino

Question 2. What do you determine the mass of the top quark to be?

If this activity has stimulated your interest in learning more about high-energy physics, look at the Particle Adventure. To learn more about the top quark discovery, check out the Scientific American article on the top quark by Tony M. Liss and Paul L. Tipton in the September 1997 issue Included in the Revised Edition of Topics in Modern Physics, August, 1996, Fermilab.