The most you can know

The matrix element method strives to extract the most information possible from every event in the data set. Print "Squeezing Water from a Rock" by Rebecca Gilbert

The matrix element method strives to extract the most information possible from every event in the data set. Print “Squeezing Water from a Rock” by Rebecca Gilbert

Suppose you went looking for the top quark, and you had only one Tevatron event that looked like it was the result of a top quark decay.  Say the decay particles included one electron with lots of momentum and an opposite-charge muon with lots of momentum, and their trajectories aren’t back-to-back. That looks just like a top quark and a top antiquark decaying in what we call the dilepton channel. What can you learn from this one event? What is the most you can possibly learn?

Such was the situation back in 1992, when there was only one top event candidate in the world, and it came from the CDF collaboration. Richard Dalitz and Gary Goldstein analyzed that event pretty darned carefully! To estimate the mass of the top quark, Dalitz and Goldstein used a formula to determine the probability that you would get the event they actually got, assuming that it came from the decay of top quarks of any particular mass. That probability is found by computing something called a matrix element, which depends on the direction and speed of all the incoming and outgoing particles.

Maryna Borysova (Taras Shevchenko National University of Kiev and Kiev Institute for Nuclear Research, Kiev, Ukraine) and Viatchelsav Shary (CEA Saclay/Irfu/SPP, Gif-Sur-Yvette, France) are the primary analysts for this measurement.

Maryna Borysova (Taras Shevchenko National University of Kiev and Kiev Institute for Nuclear Research, Kiev, Ukraine) and Viatchelsav Shary (CEA Saclay/Irfu/SPP, Gif-Sur-Yvette, France) are the primary analysts for this measurement.

Dalitz and Goldstein concluded that the mass of the top was somewhere between 120 and 153 GeV. A short time later, Kunitaka Kondo and his colleagues at the University of Tsukuba, conducting a similar analysis, concluded that it was somewhere between 124 and 136 GeV. Actually, we have since learned that the mass of the top quark is more like 173 GeV. So that 1992 event probably didn’t have top quarks in it after all; it was what we call background. It was the result of some other process that just happened to look like a dilepton top quark event.

Notwithstanding, the matrix element technique of estimating the mass of the top was a big step forward. In a world where we understand our detectors and the structure of protons perfectly, the matrix element tells you the maximum amount that can ever be learned from given dilepton top event. In the real world, it is still the best way to extract the most information from each event.

Now it is 2016 and DZero has 545 dilepton top events, although 11.5 percent of them are, like the 1992 event, not actually the events we are looking for. The matrix element method has been developed over the years and still has the best expected precision of all the possible methods of analyzing this data. DZero used the matrix element method, with some refinements, to find the mass of the top quark from those events. One of those refinements allows for the fact that there is background. The result is that our top quark mass measurement — 173.93 ± 1.84 GeV — is consistent with all the other measurements of the top quark mass and has a precision of about 1 percent. For further information, you may click here or here, as you choose.