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A first: sigma(Z) with b-jets at the Tevatron! December 8, 2007

Posted by dorigo in news, personal, physics, science.

The final piece of a long process has been placed yesterday, with the blessing of the cross section of Z production times branching fraction to b-quark pairs at 1.96 TeV by CDF. Julien, my colleague in Padova, took the burden of bringing to a completion the analysis we produced of Z \to b \bar b decays, by producing for the first time a measurement of \sigma(Z) \times B(Z\to b \bar b) in hadronic collisions. The signal is shown in the plot below.

In the plot you see the data (black points) fit as the sum of QCD background (green) and a small signal (red) sitting a bit below 90 GeV (b-jets lose energy to leptons, as I explain below). In the inset you see the background-subtracted signal, amounting to about 6500 events.

In our long-lasting analysis of Z decays, our main goal has always been to demonstrate the possibility of extracting from the Z \to b \bar b signal a precise number for the b-jet energy scale, the ratio between energy measured by the CDF detector for real and simulated hadronic jets produced by b-quark fragmentation. That number is a calibration which is in principle needed by all analyses aiming at measuring precisely the top quark mass by kinematical fitting of jet and lepton four-vectors. In principle -yes. Because it took us a long time to obtain a precise number for the b-JES, in the meantime top mass fitting techniques have become so fantastically precise that they now would not gain very much by including that input.

Well, I realize the above paragraph is a bit too handwaving for anybody’s taste, so let us see a bit more quantitatively what we are talking about here. In general, the jet energy scale is set for generic jets by studying the energy measurement in QCD two-jet events. The methods are very refined, and they allow to determine the systematic uncertainty on the jet energy measurement with high precision. CDF has currently an uncertainty of about 2.5% on the generic JES. That number, however, does not directly apply to b-jets. That is because b-quarks are quite special:

  • They have a large mass (of the order of 5 GeV), which implies that the jet hadronization products receive more energy transversely to the jet direction than other lighter partons impart to their products;
  • They have a hard fragmentation, which implies that the decay products have a momentum spectrum different from that of light parton jets. That, in turn, may cause a different energy response in the calorimeter, due to a non-linearity in the latter’s reponse to low and high momentum hadrons;
  • They produce leptons in their decay: b-quarks produce 12% of the times an electron and 12% of the times a muon. Then, most of the times the charm quark that the b has decayed into also decays producing electrons and muons. Overall, about a third of b-jets contain an electron or a muon. The calorimeter responds too much to electrons (if they are mistaken for hadrons, which surely happens unless one explicitly searches for them) and far too little to muons; but most importantly, together with the charged lepton the b-jet will originate neutrinos, which will carry away all of their momentum, producing a deficit in the estimated parton energy;
  • b-quarks are also special because of their color-connection to the top quark in top decay. That is the rule in QCD interactions, but on the contrary hadronic W decays, which are used to check or help set the scale of jets in single lepton top pair decays, have no color connection to the initial state.

All in all, b-jets are genuinely special. One can estimate that all these effects overall cause only a minor systematic uncertainty on the jet energy, but an estimate based on simulations cannot be trusted completely. So, a real measurement of the b-jet energy scale, independent from other determinations, is an important input in top mass measurements.

Jet energy scale systematics in CDF are shown in the (slightly outdated, but I could not find a more updated version) plot below. As you can see, for 30-40 GeV jets the total systematic uncertainty is largish, due to the combination of several effects. 

The black line is the total uncertainty, obtained from the sum in quadrature of all the other effects – among which the largest at low jet Pt is the out-of-cone uncertainty, due to the insufficient knowledge of soft effects of final state radiation.

Let us compare the above situation with the most precise top mass result by CDF, which now uses 1.8/fb of data: m_t = 172.7 \pm 1.3 \pm 1.2 GeV \pm…, where the first uncertainty is statistical and the second is the JES systematic uncertainty resulting from a calibration using the W \to jj signal in the same top decays used to extract the mass measurement. To that 1.2 GeV, one must add in quadrature the residual scale uncertainty and the systematic due to the unknown difference with b-jets, which amount respectively to 0.5 and 0.4 GeV. These numbers have collectively an impact of less than 1% on the top mass measurement by now!

A precise b-JES determination cannot help much the measurement of top quark mass in the single lepton final state, because there the W \to jj decay is good enough for the purpose. But in dilepton final states no W bosons decay to jets, and there are only b-jets to determine there. The best dilepton measurement in CDF obtains currently m_t=170.4 \pm 3.1 \pm 3.0 GeV, where the first uncertainty is statistical and the second is systematic. To the latter the JES contributes for a hefty 2.6 GeV: there is room of improvement there, from a precise b-JES determination. 

Now, let me discuss what we found with the analysis of Z boson decays. We measured a b-JES k = 0.974^{+0.020}_{-0.018} using about 6000 Z \to b \bar b decays selected by a tight kinematical selection and double secodary vertex tagging, in 584/pb of Run II data. That means an error of less than 2% on the b-JES, which could indeed help the dilepton top mass decays.

UPDATE: for lack of time, in my first publication of this post I could not include an additional information. The 2.6 GeV systematic uncertainty due to the JES in the dilepton top mass measurement quoted above must be interpreted as a roughly 2.6% contribution from jet energy scale (my own estimate). That is because in the top mass measurement the jet energy scale typically accounts for 1 GeV uncertainty for each 1% in JES uncertainty. So, a 2% error from the Z \to b \bar b signal fit would indeed help reducing significantly that uncertainty. A back of the envelope calculation (beware of them!) would predict that combining a determination with 2% error and one with 2.6% would correspond to one of \frac{1}{1/2^2+1/2.6^2}^{0.5} = 1.6\%, or 1.6 GeV on the top mass – a reduction of 1 GeV. Despite its inaccurate nature, this computation shows that it is indeed useful to calibrate b-jets with the Z peak. In our case, the 2% uncertainty on b-JES was extracted with less than 600/pb, a dataset three times smaller in luminosity than those which produced the mentioned top mass measurements.

Yesteday Julien presented for approval, and obtained blessing for, a complementary measurement obtained from the same data sample: the cross section for Z production. Of course this is simply a check, since we know very well the Z cross section from measurements involving the background-free Z \to ee, Z \to \mu \mu decays. However, it is a very nice check at that, and technically it indeed is a first-timer: nobody measured the cross section of Z bosons in hadronic collisions before – the UA2 collaboration in 1987 produced a combined W/Z signal to hadronic jets, but did not disentangle the two.

So what is our measurement ? We find \sigma(Z) B(Z \to b \bar b) = 1578 \pm 123 \pm 312 +541-236 pb  (the first uncertainty is statistical, the second systematic, and the third is due to the background modeling), in agreement with NLO calculations (A.D.Martin et al.), predicting 1129 \pm 22 pb.

A paper is going to be submitted to NIM quite soon… Congratulations to Julien, and of course to all the other members of our group:  K. Hatakeyama, M.Shochet, S.Kwang, C.Neu, T.Tomura, D.Whiteson – plus, of course, myself.


1. goffredo - December 8, 2007

well done!

2. Fred - December 10, 2007

“A paper is going to be submitted to NIM quite soon… Congratulations to Julien, and…”

T., for those of us not in the know, what is the purpose of submitting a paper to NIM? What is NIM? What is the standard procedure and what is the criteria for acceptance or rejection? What benefits do you achieve from this?


3. dorigo - December 10, 2007

Hello Fred,

NIM == Nuclear Instruments and Methods. It is a scientific periodical which collects articles in nuclear and particle physics, leaned towards methods and instruments, duh.

The procedure for a NIM submission in CDF is a bit easier than for papers going to PRL and PRD, because to NIM CDF authors can submit without all the signatures of the collaborators. Our paper does not have 500 authors, only nine. And it does not really discuss a physics measurement, because the focus is on the calibration method. So we could publish it alone.

One paper with 9 signatures is better than one with 500… because it is more “yours” than the others…


4. Michael Schmitt - December 24, 2007

Congratulations, Tommaso. You were modest and neglected to point out that you yourself paved the way for this particular analysis using data from CDF Run I. Will you attempt this at CMS?

5. dorigo - December 25, 2007

Hi Michael,

thank you… I am not always modest. In fact, in the past at least in one occasion I neglected to give recognition to a colleague, and he did point it out to me… With time one learns to be careful on these matters.

As for CMS, I think it is forbidding. The irreducible QCD b \bar b background is at least ten times larger in the Z region – I guess x50 or so. I think I will not fiddle with the Z->bb. However, a more interesting thing to do is searching for Z->bb plus a high-Et photon. That signature is more background-free because the photon cannot come from initial state gluons producing the QCD b-pair, thus cutting it at least tenfold. And the photon is measured with the crystals, so one gets the energy scale by just looking at the b-pair angle!


6. Michael Schmitt - December 26, 2007

Ah, Tommaso, now that is a very good idea! I was thinking that the Z production rate is so huge, and that particle flow should be (eventually) so performant, that one could beat the huge QCD background by accumulating super-large samples.

But tagging the initial state with an isolated photon is a **much** better idea. In fact, why not go all the way and ask for a second weakly decaying boson, such as W or Z decaying to leptons?

Seeing a clean Z peak in the bbbar sample would mean at least as much at CMS as it means at CDF. And you and your team are certainly the right ones to do it…😉

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