## Top mass updates from CDF: 1 – the dilepton template method October 19, 2007

Posted by dorigo in news, physics, science.

A series of brand new results from CDF have been approved a month ago, and I feel enough time has passed to make it possible to describe the analyses here without hurting anybody’s feelings. I will be short here, and just give the updated results with a very quick and dirty description of the most important features of the measurements. These days I am a bit overburdened with deadlines, and this blog is the first to pay the price…

By the way, one thing to note. Among other things, I am presently spending some time browsing some textbooks for a course in particle physics I am to give next month: well, most books are from the early nineties, and they either report only lower limits on the top mass, or provide “indirect measurements” from electroweak fits which carry 30 GeV uncertainties. It is hard for me to escape from being awed at the contemplation of the giant steps forwards we have made with the Tevatron in measuring that quantity!

If I have time and energy (many, many units of $h / (4 \pi)$) I will complete this post with some commentary later on. For the time being, just enjoy the incredible precision CDF is obtaining in this once unknown parameter of the Standard Model.

The top quark mass determined from dilepton decays using mass template fits

This new result is a precision measurement based on the final state $t \bar t \rightarrow W^+ b W^- \bar b \rightarrow l^+ \nu_l b l^- \bar \nu_l \bar b$, and a total of 1.8 inverse femtobarns of proton-antiproton collisions provided by the Fermilab Tevatron collider. The so-called “dilepton” decay mode can be easily detected over backgrounds since “leptons” are defined as electrons or muons -objects the detector is optimized to detect efficiently and with high purity, while the tau lepton is much harder to isolate. Backgrounds are small because the presence of leptons removes all events due to strong interactions, which are the most frequent processes at a hadron collider: for the most part those are due to either electroweak pair production of two W bosons, with additional QCD radiation yielding the two jets; or to $Z \to \tau \tau$ decays with tau leptons yielding electrons or muons, with QCD initial state radiation again providing the extra two jets. $W + jets$ events where the W decays leptonically and one additional jet is mistaken for an electron or muon also constitute a significant, but still small, source of backgrounds.

The final state is clean, but rare: only 4/81, or about 5%, of all top-antitop decays feature the classic dilepton signature. This is something which is easy to determine. A W boson can decay to any of the following pairs with almost equal probability: $(e \nu_e)$, $(\mu \nu_\mu)$, $(\tau \nu_\tau)$, $3 \times (u \bar d)$, $3 \times (c \bar s)$. The “3” factors remind us that there are three species of each quark doublet, since these objects come in three different colors. Also, note that the $3 \times (t \bar b)$ final state is prohibited by energy conservation, since the top quark mass is way larger than the W boson mass. All in all, there are nine possible final states, all equally probable: they each get a probability of one ninth! And since W bosons cannot decay to anything else, each has a 11% branching ratio. Easy! But then, why 4/81 for the dilepton mode ? Well, just count: each W has to go to either an electron-neutrino or muon-neutrino pair, so a total of 2/9… Multiply probabilities to get composites, and you are done. The graph on the right explains the same concept pictorially – dilepton decays to electron or muons are represented by the green square at the lower right. [If you do not get it at a glance: Both the horizontal and vertical sides of the big square represent the possible W decay modes, and are divided into nine slices of equal width. The intersection of the slices represent areas proportional to the probability for a WW decay to yield any given final state. Oh, a further note: this plot is my own invention. I was probably not the first to cook it up, but I have indeed seen no instance of it in the literature before I started using it in presentations… If you saw it used before 1992, let me know.]

Now, not only is the clean dilepton final state rather rare – one such event is created in two hundred billion collisions: there is a further catch. This mode in fact features not one but two energetic neutrinos from W decay, and is thus unconstrained: we only measure the transverse component of the vector sum of the two neutrinos, so there is no kinematical closure. What that means is that the equality of top and antitop masses (1), the equality of the two W boson masses to 80.4 GeV (2,3), and the constraint that the total momentum transverse to the beam direction cancels (4,5: two components separately equal zero) provide in total five constraints, which are not enough to provide a unique solution for the undetermined six components of neutrino and antineutrino momenta: just as if you had five equations with six unknowns.

And then there is combinatorics: even if you had perfectly determined momentum for each of the six final state objects, you could match a lepton with a neutrino and a b-quark  in four different ways (plus four for the other top). In reality, however, there are experimental techniques by which we can pick the most likely assignment, reducing the possible combinations.

With hundreds of man-years of analysis we have refined those methods, and we can now obtain from the measured momentum of jets and leptons alone a quite precise estimate of top mass for each event. I will not attempt a description of the refined technique called “neutrino weighting method” which allows that result, but just mention that if you plot the “neutrino-weighted” estimated mass for a sample of simulated top quark pair decays to dileptons, you obtain the distributions shown in the plot on the right, where different histograms refer to increasing values of the simulated mass of the top quark, from 150 to 180 GeV. These distributions are broad: they are not just simple narrow gaussians centered at the true top mass value. However, they still allow some discrimination between different top mass values.

What next ? Well, just a few fits of the mass distribution of 124 selected real events to a sum of a background template -obtained by mixing the various expected contributions from background sources, totalling $35 \pm 7$ events- and each in turn of the top signal templates shown above. Each of the different fits provides a different interpretation of the data, with a varying degree of likelihood – see the result for a top mass of 172 GeV in the plot on the left. In the end, a plot of the obtained values of likelihood as a function of the top mass used for he template provides a measurement of the top quark mass, as shown below (the fit has the top mass as a continuous parameter, but that is a detail I am glad to skip).

The result is:

$m_t = 172.0^{+5.0}_{-4.9} (stat.) \pm 3.6 (syst.)$ GeV.

A surprisingly precise determination from a final state “unsuited” for top mass measurements!

More details are available in the public page of the analysis.

1. Matteo Martini - October 21, 2007

Comment completely unrelated to the post ( if I may.. ).
Tommaso, what is your opinion about the new law against blogs by Mr. Levi?
Are not you scared they may close your blog soon?

2. dorigo - October 21, 2007

Hi Matteo,

first two words about what you mention above, for those who have no access to italian news. Ricardo Levi, an aide of the italian premier Romano Prodi, has drafted a law on publishing, which partly modifies previous rules. In particular, in the tentative text there is a norm which would require blogs and other sites to register or be gone. The law received pre-approval from the government, then it was attacked for its dangerous lack of specification on which sites are required to register and what are the criteria to decide.

I think the contested article of the law is useless, confused, and dangerous. I am sure it will be changed. I am not too worried, although it represents a signal that there are attempts at reducing the freedom of the Internet.

Ricardo Levi is probably the first to regret the words he wrote at this time…

Cheers,
T.

3. Matteo Martini - October 21, 2007

Mm..
I may be wrong, but if someone from Berlusconi s side had proposed the same law that Mr. Levi ( Prodi s right hand ) put forward, you would be very angry and screaming all over because if this freedom-killer law.
Now that the left-party did it, you have more quiet words.
I may be wrong, and excuse me for being direct, but I think you are quite biased.
The more I think about it, the more I see little ( no ) difference between Berlusconi gang, and Prodi s ( Mastella, D Alema, Levi, and so on.. )
Again, sorry for being direct, I may be wrong.
And, sorry for posting two comments completely out of topic.
Keep up with the good work!!

4. dorigo - October 21, 2007

Matteo,

the only reason why I did not post on the topic is that I have been quite busy lately, with some deadlines. Other than that, I usually do not scream, and it takes much more than that to get me angry. Further, I think the proposed law is not too dangerous, because it will not pass the scrutiny of our bicameral system.

Sure, if Berlusconi had put a finger in drawing the lines of a law attempting at creating rules for the internet, I would have been more interested in the topic -and a bit more scared. The fact that it is a unknown lackey to write a law that is then publically criticized by members of the government (after reading it 😉 makes me much me more comfortable with it.

Of course, there are much more important things that the center-left promised they would do, and are still in the drawer. Too bad: retequattro is still there although illegal, the law on the conflict of interest is not mentioned any more, etc. etc. . We all read Grillo’s blog, but it is a fact that this government is weak and can only “pick its battles” very carefully, if you know the expression.

Cheers,
T.

5. Anonymous - October 21, 2007

Quote:
“Other than that, I usually do not scream, and it takes much more than that to get me angry”

Are you sure?

6. Thomas Larsson - October 21, 2007

Beppe Grillo’s post about Prodi-Levi attracted 10,000+ comments in two days. Now that’s what I call a comment thread.

7. Matteo Martini - October 22, 2007

And Grillo s blog has grown dramatically in popularity.
Number 9 in the world, it seems.
http://technorati.com/pop/blogs/

By the way, Prodi and Mastella have moved a prosecutor ( De Magistri ) who had found them guilty and wanted to put them on trial.
Nobody is out to help this guy.
http://www.gulf-times.com/site/topics/article.asp?cu_no=2&item_no=177029&version=1&template_id=39&parent_id=21
Prodi is not better than Berlusconi, IMHO

8. Matteo Martini - October 22, 2007

Errata corrige.
De Magistris and not De Magistri

9. jeff - October 22, 2007

Natural unit of action is h/2pi!

10. dorigo - October 22, 2007

Jeff, you are right – and you are wrong. What you say is perfectly right, but what you imply isn’t. The minimum value of the expectation value of DEDt is indeed (slashed h)/2, or h/4pi….

Cheers,
T.

11. dorigo - October 22, 2007

Matteo, Prodi is by definition better than Berlusconi, if only for the fact that if he performs illicit acts he tries to conceal them, rather than making them legitimate de facto, thus creating a situation when every other joe is led to believe it is normal and lawful to evade taxes, mix private and public interest, rape our society.

Cheers,
T.

12. dorigo - October 22, 2007

Anonymous, I am sure you do not mean to start a discussion on what makes me scream and what doesn’t…

Cheers,
T.

13. Matteo Martini - October 23, 2007

Tommaso,
just a comment..
Was Stalin better than Hitler?
Mm..
Maybe 🙂

14. dorigo - October 23, 2007

Matteo, Stalin was way better than Hitler of course! Both had a deranged mind, and both had obsessions – Hitler with racial issues and Stalin with conspiracy threats. Both caused atrocities and unheard of suffering…

But Stalin won the war!

Seriously, however: Stalin cannot be compared with Hitler. I will not defend him here, but there simply is no ruler on which you can put the two of them.

Cheers,
T.

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