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New paper on RS Gravitons out January 4, 2008

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

Publishing a scientific paper is very satisfying accomplishment. In experimental high energy physics, an article describing the results of a measurement or a search is usually the result of a huge amount of work by dozens of physicists, as well as engineers, technicians, computer scientists. And reviewers.

In CDF, the internal review process of a scientific result aiming for a publication starts after the analysis of the data is “blessed” in a physics group meeting. That prerequisite is by itself the result of a rather lengthy procedure.

To be blessed, a result has to be documented in detail in one, or more usually a few, internal notes. After a series of presentations where progress in the analysis is reported by concentrating on particular aspects of the work and on specific details, the authors usually converge to a final result. They then present the results in front of their collaborators three additional times, when they take questions of all kinds and address the (usually, but not always, constructive) criticism.

The first presentation is a “full status report”, when a complete summary of the study is given; the second is called “preblessing”, and it is where the most heat is dissipated, when the nastiest questions are asked and where the analysis must be shown to be essentially foul-proof; the third, and last one, is the “blessing”, which usually runs much more smoothly – to reach that phase, you must have got your conveners to agree that things are in good shape. 

The above phase – obtaining a blessed result – is just a preliminary step in the crafting of a publication. After the blessing, a committee is formed to review and guide the publication process of the result. This “godparent committee” is usually formed with three members, who have no affiliation with the authors (i.e., they work for different institutions and have no direct involvement in the particular analysis under review), but have a specific expertise in the topic.

The godparents meet regularly with the authors, and they sometimes force a complete overhaul of the analysis. They can request any change, from the inclusion of more data, the exclusion of part of it, the modification of methods and tools. They can suggest checks that involve taking in consideration completely different datasets. They can ask for more plots, proofs of any kind, and they will question every bit of the work. In a word, they will usually be a real pain in the neck. But the real purpose of this harassment is to ensure that the godparents are really confident about the result proposed for publication: they are the warrantors of the scientific result.

Yes, godparents can be a pain. However, once they are satisfied with the quality of the result and the lack of any mistake, they become the authors’ best friends: they now push toward publication. Authors are encouraged to write a first draft of the paper, the draft is corrected by the godparents, and released to the collaboration for comments. Each member of the collaboration has now two weeks to send comments, request corrections, make questions and instill doubt in the result. They do so in written form. Authors then collect all this written criticism and address it line by line. Godparents endorse the authors’ answers. Occasionally, a deep question will cause some modification in the analysis; more rarely, concern from collaborators about the presentation of the results will cause a major re-analysis. The process can be time-consuming, but at this stage godparents are usually proactive in trying to solve the remaining knots and proceed steadily to a second draft.

The second draft is produced, reviewed, released again to the collaboration, and again there are two weeks during which new comments may be produced which require additional answers. After these last concerns are straightened out, a final draft is produced, and a paper seminar is scheduled with the consent of the godparent committee. The result is described by the authors at this final stage, in a meeting where usually godparents bring food to celebrate with authors and collaborators. Then, a submission to a scientific magazine is made by the authors. This concludes the internal process, and the paper has now to withstand additional scrutiny by external scientists. But that is another story.

Now, what about the RS Graviton search ?

A bit more than one year ago I was invited to be part of the review committee of a paper describing the search for a four-electron resonance in CDF data. That signature is a possible way to detect a Randall-Sundrum graviton, which can decay through the chain G \to ZZ \to e^+ e^- e^+ e^-.

The review process was not too painful, but was nonetheless lengthy, because of many concurring obligations by the authors of the search – Antonio Boveia, Benjamin Brau, and David Stuart, all physicists from the University of California at Santa Barbara. All in all, a bit more than a year from blessing to paper seminar: a bit longer than typical for CDF, but still within normal bounds.

The search is quite easy to describe, because of the very striking final state. As with any signature-based searches, limits are obtained on any narrow particle which can produce the studied final state: $latex X \to ZZ$. However, specific emphasis is given to the graviton which, in the Randall-Sundrum RS1 model, can exist at the TeV scale, and be produced in proton-antiproton collisions at the Tevatron with a cross section of some fractions of a picobarns: for a mass of 500 GeV and a ratio k/M_p = 0.1 (where k is a parameter called “warp factor” and M_p is the Planck mass) it is estimated that \sigma (p \bar p \to G \to Z Z ) = 290 fb

The tiny cross section implies that in the analyzed dataset of 1.1/fb only 0.37 events of the kind searched (four electrons from the decay of the two Z bosons) are expected, before detector acceptance and identification efficiencies are taken into account: that is because the branching probability of a Z boson into an electron-positron pair is only about 3%.

So is the search hopeless ? Well, no: it only means that the search does not have sensitivity for the particular model taken as a reference; surprises may be behind the corner, and in fact the signature-based nature of the search retains intact the possibility to detect anything that may contribute to the particularly clean signature studied.


And the signature is indeed spectacular: as the graph on the left shows, a simulated G decay into four electrons is very cleanly reconstructed in the CDF detector. The four high-energy electrons produce four charged tracks (the four pink lines) pointing to four well-contained calorimetric signals of electromagnetic showers (pink areas in the cutaway view of the electromagnetic calorimeter). Very little else is present in the detector, except very small momentum tracks, curling inside the strong axial magnetic field. In the graph below (called a “lego plot” by insiders), the calorimetric deposits are shown as bars in the “unrolled” cylinder where \eta is pseudorapidity – a function of the angle with respect to the beam axis- and \phi is the azimuthal angle in the plane orthogonal to the beam, the same one shown in the graph above. If you have trouble visualizing the coordinates, simply think at the CDF detector as a cylinder rolled around the beam axis: then if you cut it along its height on one side, you can unroll it on a plane. The cut line will be your pseudorapidity coordinate, and the unrolled circle (the cylinder circumference) will be the azimuthal angle.


Backgrounds in the search region – four-electron masses above 500 GeV, and a good fit to the ZZ hypothesis- are tiny: they are due to standard model production of two Z bosons or to fake electrons.

ZZ production in the SM is a process with a cross section of about 1.5 picobarns; larger than the reference signal, but the two Z almost always have a combined mass peaking at threshold, and they are thus basically excluded by the search, which focuses in the region of invariant masses above 500 GeV: there, SM ZZ production yields an estimated 0.008 \pm 0.006 events.

The fake electrons background is instead due to QCD multijet events where the jets are all mistaken for electrons – an exceedingly rare instance, which however is boosted by the large production of QCD four-jet events. This background is estimated from real data, where electron identification cuts are inverted or dropped for one, two, or three of the four electron candidates. This produces independent background samples which contain no real Z bosons, as can be checked by computing the invariant mass of one fiducial and one inverted-cuts electron (see plot below). With these samples, one can produce an estimate of the rate of four fake electrons in the data selected for the search, resulting in an estimate of 0.20 \pm 0.01 events.


The search actually produces no candidates with a four-electron mass above 500 GeV, so by accounting for systematic uncertainties and the total background of 0.28 events, it is easy to derive cross section limits for the graviton. The limit lies one to three orders of magnitude above the expected value for a RS1 graviton, which implies that that particle can still exist in the mass range studied, and have gone undetected by the insensitive search. However, the limit is directly convertible into one for any other resonance providing the studied final state of two Z bosons. In the picture below you can see, as a function of graviton mass, the cross section limit (full line)  in picobarns, compared to the graviton cross section (hatched line).


Below, a “lego plot” of a candidate ZZ event found by the search in the data. This event is excluded by the search because of the too low invariant mass of the four electrons. It is most likely a genuine standard model production of two Z bosons.

Finally, it only remains to express my congratulations to the authors, Ben, Antonio and David, for their nice analysis and their collaborative attitude in the review process. The paper is not public yet, but it will be in a few days – I will link it here when it is released.


1. Michael Schmitt - January 4, 2008

Hi Tommaso,

this is a nice description of the analysis. One obvious question: why weren’t muons used in addition to electrons? The number of produced signal events would be larger by a factor of four, and the number of selected events by nearly that factor (depending on the eta range of the electrons used by the Santa Barbara group). As you know well, CDF does a good job at reconstructing muons, too, and while the mass resolution would be poorer than for electrons, the rate of hadrons giving fake muons is much smaller than for electrons. Am I missing something?


2. dorigo - January 4, 2008

Hi Michael,

obviously you aren’t missing anything. The question was among the first posed to the authors by my committee. Indeed, muons multiply nominal acceptance by four in terms of branching fraction (ZZ->eemm, ZZ->mmee, ZZ->mmmm get added to ZZ->eeee). I am not sure whether the individual efficiency for muons can be made as high as (or higher than) that of the very loose identification criteria used by the UCSB group for electrons, but certainly should be not too different. Resolution should not be a concern since, once a fit of pairs of tracks to each Z is done, the resolution on the G is not too different for mmmm and eeee states. Fake rates are not a big concern since the analysis is statistically limited and backgrounds are small. So, yes. Muons would have made the sensitivity roughly four times higher – certainly more than double, for sure less than x10.

The answer of the authors was that they wanted to publish the search as it was, to later include those other final states, which would have required a lot of additional work. Since the result was not sensitive and a factor of 4 more would have made no big difference, their argument made sense – publish a first search first, then refine.

I do hope I will see a 3/fb search for G->ZZ which includes ee and mm states. And why not, also eejj, mmjj. I bet backgrounds can be handled well there too, since we are talking of very high mass stuff. And imagine the increase in acceptance: from B(ee)^2=0.0009 to 4B(ee)^2+4B(ee)B(jj)=0.0876… A net gain of a factor 100 in statistics!


3. Stefan Scherer - January 5, 2008

Hi Tommaso,

thanks a lot, that’s once more a very interesting and informative post!

I have a question about the lego plot: The height of the columns, is that transverse energy? And then, I would have naively expected that the four pseudorapidities (for electrons at that energy, that’s essentially the same as rapidity, right?) sum up to zero, but that seems not to be the case?

Best, Stefan

4. dorigo - January 5, 2008

Hello Stefan, and happy new year!

Yes, you guessed correctly, and indeed it is something I failed to explain in the post: the bars in the lego plot are proportional to the transverse energy deposited in that bin of azimuth-rapidity.

As for the other question. pseudorapidity is like rapidity but it assumes zero mass for the object. It is simply defined as - \log (\tan (\theta /2) ), where \theta is the polar angle (i.e. the angle the particle makes with the beam axis). In general, it has the good property of transforming additively for lorentz boosts along the beam, so that your guess is indeed well-founded. However, at proton-antiproton colliders the center of mass of the collision is not at rest: it depends on the unknown fraction of momentum carried by the two quarks or gluons participating in the hard scattering process. To put it in another way, we are not measuring the rapidity of the remainder of the two protons, which have escaped along the beam line.


5. Stefan Scherer - January 5, 2008

Hi Tommaso,

a Happy New Year also to you, and thanks for the explanation!

However, at proton-antiproton colliders the center of mass of the collision is not at rest…

Oh, yes, of course… it’s a bit surprising, if you haven’t heard about PDFs etc. before, but I could have known that ;-)…

Cheers, Stefan

6. Gravitons are heavier than 500 GeV! « A Quantum Diaries Survivor - December 23, 2008

[…] personal, physics, science. Tags: CDF, graviton, higgs, Z boson trackback About a year ago I reported here on a search performed by CDF for events featuring two Z bosons, both decaying to electron-positron […]

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