A Quantum Diaries Survivor

Ok, I vowed a more varied reporting of physics results here in the last post. So why not show one I was unaware of, from my own collaboration, which is also quite interesting and new ?

Toronto University physicists in CDF have studied observable quantities showing a dependence on the production mechanism of top quark pairs at the Tevatron. They have found that when top quark pairs are produced by gluon fusion, there is a higher number of soft tracks in the interaction, ultimately due (or so I guess) to the higher color charge of the initial state, and the resulting higher probability of soft gluon radiation.

They studied soft tracks in several high-Pt processes and concluded that they could indeed extract a measurement of the fraction of top quark pairs due to gluon fusion processes.

Their fit is shown in the plot below. They find a fraction sigma(gg–>tt)/sigma(tt) of 0.25+-0.24+-0.10, when QCD predicts this fraction to be 15% at the Tevatron energy (will be 85% at the LHC). Quite interesting, isn’t it ?

If you want more information on this measurement, please visit the web site of the analysis:

http://www-cdf.fnal.gov/physics/new/top/2005/topProp/ttProduction/public.html

A mail message by Patrizia, who asks me about a plot I put together for a conference a while ago, stimulates me into reproducing it here. It represents a huge amount of information, so let’s try to discuss it bottoms up.

First of all, this plot has not been updated since 2004 - so the latest measurements of the top quark mass have not been inserted. They are not needed though, because by now the precision on the mass measurements make it impossible to see the error bars on a plot such as this.

The plot represent, indeed, 10 years of searches for the top quark and of theoretical estimates for its mass, as well as ten years of direct measurements. The horizontal scale goes from year 1987 to 2005, and the vertical scale from 0 to 300 GeV of mass.

In dark blue, the area shows the region excluded by direct searches at electron-positron colliders: a business ended in the early nineties, when LEP found no evidence, and set a limit of the top mass at half the Z mass value (if Mt<MZ/2, the Z could decay to two top quarks, and indeed they would have found it).

In light blue is the region excluded by proton-antiproton colliders - basically, the Tevatron, which sought it with more and more statistics and until 1994 could not find it, and only exclude its existence for low mass - a low mass would have implied a high production rate, and they would have not missed it.

The upper green region is instead picturing theoretical upper limits on the top quark mass, extracted from the combination of theoretical arguments and experimental evidence in other areas of particle physics (for instance, B mixing results).

The yellow area is the most intriguing: it shows theoretical determinations of the top quark mass as a function of time, based on dozens of different studies, which incorporated theory and the latest measurements of electroweak physics observables to infer the most probable mass of the top quark - in case it existed. Notice how the red line (the most probable value by these theoretical arguments) bounces around until the CDF evidence in 1994, when all at once the indirect evidence by LEP started to be a whole lot more compelling… Hmmm.

Finally, the points with error bars show the direct measurements by CDF and D0 until 1995. Having been in CDF for 14 years, I cannot help pointing out here that our very first evidence had a mass measurement which was right on the money, from the very start! Instead, theoretical estimates seemed to follow the experimental lower limits in an ascending trend.

Quite an informative plot, if you ask me!

In a comment to a post of a few days ago (http://dorigo.wordpress.com/2006/08/24/new-z-bb-signal-from-d0/), Markk writes:

“A kind of dumb question from a non-particle physics person. I see Pb-1 all over and understand it as an area, I even understand using it as luminosity but what is the top unit? I always see, say, L = 333 Pb-1 which makes sense as a luminosity if say energy is the “top” value. Or as you say above something like “700 pb-1 of data”, I don’t get it. What is the default value assumed that I am missing to make more sense of this stuff.”

I think I wrote about this in the past, but I will try to do my homework again here. Let me start by saying that particle fluxes are naturally computed as a number divided by area and time: N = [cm^(-2)][s^(-1)] is the way we write such a thing. These are the units of instantaneous luminosity. If you integrate over time (i.e., sum over a period of time) an instantaneous luminosity, you get what is called integrated luminosity: L = [cm^(-2)].

For instance, you could have a flux of a billion protons per square micron per second, and if you wanted to count the integrated flux per unit area in a minute you would do:

L = 1,000,000,000 * (100,000,000/cm^(2)) / s * (60 s) = 6*10^(18) cm^(-2).

That is beacuse there are 100 million squared microns in a squared cm, and you have multiplied the instantaneous luminosity by the total time (60s). Physicists readily use cm^(-2) s^(-1) as units for instantaneous luminosity, but when they time-integrate, they find out it is much less cumbersome to use a tiny fraction of the square cm as a reference area.

A picobarn is equal to 10^(-36) cm^2: a square of 10^(-18) cm across. By using picobarns, integrated luminosities take on much more manageable forms, as the following example shows.

A collider provides a luminosity of 1.055*10^(31) cm^(-2) s^(-1) and runs for a year. What is the integrated luminosity ? How many events of a kind that has a cross section of 10 pb were produced ?

A year is 86400×365.26 = 31,558,464 seconds. A cm^(-2) is 10^(36) picobarns. So,

L = 31,558,464 s * 1.055*10^(32) / (10^(36) pb s) = 333 pb^(-1).

To find how many events are produced of a process that has a cross section of 10 pb, just multiply:

N = sigma * L = 10 pb * 333 pb^(-1) = 3330.

What is, then, a ”cross section” ? It is something with area units. Picture a proton and imagine another particle (say, as at the Tevatron, an antiproton) coming towards it. They will collide if the axis of motion of the antiproton lies within a certain area, centered on the proton. That is the total proton cross section: about a tenth of a barn, or 10^(-25) cm^2.

When a proton and an antiproton collide, the energy released can produce many different results. Most of the times the two bounce off one another, but very rarely (with an increasing likelihood as the collision energy increases) they give rise to rare processes when massive particles are produced. For instance, only once every 10 million times at the Tevatron energy the collision gives rise to a Z boson. A simple measure of the probability of producing a Z is therefore the total proton cross section divided by this 10 million factor: 0.1 barns divided by 10 million makes 10 nanobarns (or 10,000 picobarns if you prefer). So we say that Z production at the Tevatron has a cross section of 10 nb.

Then, specifically for the case of Z->bb production in CDF (the plot this discussion originated from), the Z decays to a bb pair only 15% of the times, and then our selection cuts accept only one event every 150: that is why the “effective” cross section turns out to be 10 pb: 3330 events in 333 pb^(-1).