By Tommaso Dorigo

Reporting on scientific results to a broad audience is difficult, in my opinion, not so much because of the need to explain things in a simple way -which is easy and fun, once you master the matter- as for the self-discipline you are forced to stick to.

Things that are obvious to you, because you have seen them and studied them for years, are not obvious to others, not even to fellow scientist from the other door who practice a just slightly different sub-field of research, let alone to the larger pool of smart readers who are drawn to science readings but have never taken an advanced course on the matter. An alarm bell has to go off every time you hit on a concept which is likely unfamiliar to most: maintaining in good operation that alarm bell is by far the hardest part. At least, that is what my experience tells me.
 

So let me try and check how rusty that alarm bell is today, as I make an attempt at reporting in hopefully simple terms on a new particle physics search by the DZERO experiment (see right), one for a subatomic process that I find extremely interesting, and which, once found, will make manifest the hard core of our theory of electroweak symmetry breaking, a fundamental pillar of our current understanding of the subnuclear world. This process is the associated production in hadron collisions of three of the fanciest building blocks that Nature (the bitch, not the magazine) has provided our playground with: a top-antitop quark pair, and a Higgs boson.

This, by the way, is a good point for you to jump ahead by a couple of sections in this long post, if you are curious about the new DZERO result but know about, or are not interested in, some underlying basic facts about hadron collisions.

Some background on hadronic collisions

In the case of the result I report today the hadron collider at hand is not the LHC, the fast-asleep giant sitting underground below the border between Switzerland and France, but rather the quite awake Tevatron collider of Batavia, Illinois, which is traversed daily by a few micrograms worth of protons and antiprotons, all rigorously traveling at 99.9 and something percent of the speed of light.

As protons and antiprotons hit each other at that fantastic speed, they often just bounce off each other retaining their integrity: physicists call that process "elastic scattering", but they are not interested in it, because it tells them about as much on the inner structure of matter as a glance at a glass of wine can tell you about its tannins. 

In closer encounters the protons may break apart, but still nothing much happens. It is only in those rarer instances when one of the most energetic quarks or gluons making up a proton hit directly one of their kin from the antiproton that things become interesting. The collision is then hard enough that the two constituents -we call them "partons"- kick each other off their envelopes, the parent proton and antiproton: they then materialize in the form of streams of subatomic particles, energetic sprays that we call hadronic jets; in still rarer instances, their interaction instead gives rise directly to new states of matter.

(I have explained elsewhere why quarks can only be seen as jets, and I will avoid repeating myself here. Suffices to say that quarks cannot exist isolated, and they must "dress up" in the form of hadrons. Hadrons are composed of pairs or triplets of quarks: it is them, and not individually their constituent quarks, the particles that make up the jets we observe in energetic collisions.)

Doing business with a hadron collider -a proton-antiproton collider like the Tevatron, for instance- is a frustrating experience: you spend your money and wits to build a machine that accelerates those particles at incredibly high energies, and then as you turn it on would like to see that energy materialize into fantastically energetic jets, or even better, new exotic, massive particles that can only be produced by exchanging the projectiles' kinetic energy into mass. Instead, you have to accept the fact that most of the collisions you get release way less energy than the total theoretically available.

That is because what is colliding are not really the proton and antiproton that you launched one against the other -or more precisely, one each among a trillion of the former and a hundred billion of the latter. What really collides is a (anti)quark or a gluon inside one projectile and a (anti)quark or a gluon inside the other. And, since these constituents of the proton only carry a small fraction of the total kinetic energy of their parent "envelope", the total energy release is smaller than the sum of proton and antiproton kinetic energy. 
 

Particle physicists learn this fact in their playground years. Parton Distribution Functions(PDF) have been devised to describe what is the probability that a quark or a gluon is found with a given fraction of their envelope's total energy. The graph on the left shows their density as a function of the fraction x the partons carry, for different parton species: g labels gluons, u are up-type quarks, d are down-type quarks, etcetera. Needless to say, these functions get vanishingly small as the fraction approaches unity: at the Tevatron for instance you will never, ever, get a collision releasing 1.96 TeV, which is the sum of the proton and antiproton energies provided by the superconducting, 4-mile-long accelerator. The same, of course, goes for the LHC: 14 TeV will never be actually reached by that machine; nope: not even if its currently ongoing repairs exceed expectations!

How energetic can a collision be at the Tevatron, then ? That depends: the larger the number of collisions you observe, the higher is the chance to see a very energetic one. The most energetic collisions recorded by CDF and DZERO, the two experiments built around the points where the Tevatron proton and antiproton beams intersect, have a total energy release of about 1 TeV, but they are exceedingly rare. Below is a 2-D bar chart of the energy read out by the DZERO detector for two high-energy jets: the detector is like a cylinder surrounding the collision point, and it has been cut along one side and unrolled on the plane you see, to display the localized energy deposits of the streams of hadrons which hit it. Such events are spectacular: they are as close as you can get to actually "seeing" two quarks.
 

Enter the production process

Now, the above introduction served one important purpose besides sorting out the few of you who really want to get personal with elementary particles: it provides important input to figure out why the production of a top-antitop quark pair AND a Higgs boson is so rare and special. It is only a part of the whole story, but let me use the acquired knowledge at once. Top quarks are the heaviest ones in the lot of six we have figured out matter can be made of. They weigh about 173 GeV each, which is the total weight of about 184 hydrogen atoms! As for the Higgs boson, we may assume it weighs 120 GeV here for the sake of argument: existing experimental hints point to a value not too far from the one above.

Let us make a simple addition: two top quarks, plus a Higgs boson, already make a rest mass of 470 GeV. This is about a quarter of the total kinetic energy of a proton-antiproton pair at the Tevatron, and it is an energy which is only reached once in a million collisions or so. Those PDF are indeed functions steeply peaking when the fractional energy is close to zero, as I noted above. 
 

There is at least another important thing to consider. Not all collisions above 470 GeV produce a top, an antitop, and a Higgs boson! Quite on the contrary, that piece of magic is a rare occurrence regardless of the energy release. The rules for computing the probability of subatomic production processes like the one we are discussing are enshrined in Feynman diagrams, graphs which describe the space-time propagation of the colliding and produced particles. On the left you can see one such diagram: time is taken to flow from left to right here, and only one space dimension is drawn, on the vertical axis.

As you see, the way a  reaction occurs works by first producing a top-antitop pair, and then letting the duo (in the case shown) "radiate off" a Higgs particle. Such a feat is predicted to occur because the Higgs boson couples to any particle if the latter possesses a mass, and that is for sure something that top quarks are good at -they are the heaviest elementary bodies known to us. Just as a photon can be emitted by any electrically charged body, and it does so more readily if the charge of the latter is higher, a Higgs boson will happily be emitted by any mass-endowed particle. The difference, however, is that Higgs bosons are very heavy themselves, and you cannot produce mass out of nothing: the top quark originating the Higgs boson has better be very energetic to enable Higgs radiation.

Computing precisely the rate of tth production is beyond my decidedly experimental expertise, but from the few hints I provided above you can probably accept that such rate is seriously dampened by asking for a very specific way of spending the 500 or more GeV of energy we have already dearly paid for  (a one-in-a-million chance, give or take a cow or two). The easiest way to release that energy for a proton-antiproton collision would be to produce two 250-GeV jets like the ones pictured above: any quark pair would do, and even a pair of gluons would be a very probable solution. Asking for top quarks makes this much less probable because most of the energy has to go into the mass of the two fat guys; and asking that one top quark spits out a Higgs boson makes this a real rarity.

(If you need more detail, here is an important piece: the dampening in part comes from the narrowness of a thing called phase space. Given a fixed 500 GeV energy budget to materialize a pair of quarks, Nature way prefers light-mass ones, since almost all the initial energy may then be allocated to endowing quarks with large momenta, and large momenta translate in a larger span of allowed configurations. The more configurations, the more probable a process is! But in our case it is still worse: we need one of the top quarks to be produced with a mass much larger than its nominal 173 GeV, since we need the surplus to materialize the Higgs boson via radiation. Short-lived particles can indeed be created off-mass-shell, but the probability for this to happen rapidly decreases with the departure from their rest mass.)

From the above discussion you have certainly gathered that there are several factors making tth production a very rare process. Well, that is exactly true. And here is the final result: all in all, at the Tevatron one expects less than one in ten trillion collisions to give rise to a ttH final state. Once-in-ten-trillions is roughly as frequent as a total failure of the "save a parent" strategy some dads and moms adopt when they have to travel, taking different flights to reach the same destination: once in ten trillion times, both planes crash (I am purposedly neglecting correlated catastrophes such as 9/11 here, but you get the point). That is what I call pretty darn rare, what do you think ?

...And they still search for those!

Despite the rarity of associated production of a top-antitop pair and a Higgs boson -or maybe because of that!-, the CDF and DZERO experiments at the Tevatron have started to look for it. That does not mean the physicists in these collaborations are desperate: a search for a new physical process predicted by your theory is intrinsically interesting and worth pursuing even if you predict your experimental setting cannot reach the required sensitivity to observe the process, because of a couple of facts. 

One: particle theory -the so-called Standard Model- has reached a high level of refinement, but putting it to the test in new ways, such as searching for a process that is predicted to be unobservable in a particular environment, might eventually spot an otherwise unnoticed breach in the theory, opening the way to the unknown. Two: by studying peculiar and rare final states of particle collisions one might stumble in some unexpected, unpredicted new process, again resulting in a disclosure of new physics. 

Also, please consider: measuring something which is predicted to be very small or even better, exactly zero (or undiscernible from zero) is a very effective way to probe your theory, much better than checking whether physical quantity A is equal to seven hundred gudungoons or seven hundred and twelve gudungoons. The reason for this is that zero is a quite peculiar number: any departure from zero sticks out as a lamppost, while a departure from a non-zero quantity can at most be as significant as the prediction is precise. Or if you prefer, a rare unknown effect may only be seen by checking if zero is exactly zero, rather than if some non-zero quantity is in the high-gudungoons range or not.

In any case, there one last input I have so far denied you: the number of collisions that have been produced since 2002 in the core of CDF and DZERO amounts to about 400 trillions each! If the Higgs boson exists, a handful of those events have most certainly been popping up: maybe once a year, but they must have! Now, go tell the needle hiding in the haystack that DZERO searches for a few events in 400 trillions, and you'll see it rolling away in laughter. But physicists are clever! So let me tell you how clever they have been now.

The DZERO search

DZERO searched for the process in 2.1 inverse femtobarns of collisions, which is little less than a third of what they have accumulated this far. This delay is due to the gigantic amount of computing required to reconstruct and analyze the information, as much as to the complexity of the analyses, which must at some point "freeze" the datasets they use before performing further steps which may take months to complete. Inverse femtobarns sound like complicated things the first time you hear about them, but they actually simply count the number of projectiles that have crossed a unit area in the center of the detector. Multiply that by the "effective area" of their targets, and you get the number of hits.

The first step of the analysis consisted in figuring out the best way to get rid of most the large number of collision events stored by the data aquisition system, those which were the least likely to have originated by the production of the ephemeral trio of heavy particles and their subsequent disintegration into stable particles -those actually producing the observable detector signals which constitute the "event" data. 

Here I have to unveil a detail I so far hid: the data stored by DZERO amount to much fewer than hundreds of trillion events, because the rate at which collisions occur in the core of the detector during data taking is about three megahertz -three millions per second-, which is way too high to allow detector readout and storage. A online trigger system in fact takes care to neglect those collisions which resulted in elastic scattering or low-energy release, and only read out and store the most interesting, energetic events. The trigger system is one of the most complicated parts of the detector hardware, but I will not discuss it further here: suffices to say that the offline analysis starts with a dataset of only billions of events, ones containing an already pre-selected signal of high-energy electrons or muons.

Electrons and muons. These are the diamonds collider experiments mine for. Their presence immediately signals that the original hadrons gave rise to an electroweak interaction, as opposed to the much more frequent strong interactions that quarks (and gluons) are most likely entertain themselves with. A high-energy electron or muon can only be produced by the decay of a W or Z boson or by a photon, the carriers of the electroweak interaction. In our case, these particles signal the decay of top quarks, and DZERO uses their presence to select a sample of top quark pair decays.

The decay chain of a top quark pair yielding one electron and jets can be written as follows:. Here you see that one of the W bosons produced an electron-neutrino pair, while the other yielded one further quark-antiquark pair. Each of the quarks (both the bottom quarks duo and the generic ones labeled by the letter q) produces a energetic jet of hadrons, and the top-antitop signature one ends up observing in the detector is called "single lepton", to distinguish it from "all hadronic" and "dilepton" ones containing respectively only jets or two leptons and two jets. As for the neutrino accompanying each lepton in the W boson decay, they leave the detector unseen, but their presence is inferred by the imbalance in the energy flowing out of the collision point.

My DZERO colleagues know extremely well how to best select top-antitop events in the single lepton final state: they have been doing this since CDF showed the way, in the days prior to the top quark discovery in 1995. But in the case at hand, a Higgs boson must be present in the event: this particle, if it is not too heavy, decays most of the time into an additional pair of b-quark jets. The total signature DZERO is after is thus one of lepton plus many jets, nominally six of them. Since, however, jets may be lost in uninstrumented regions of the solid angle around the collision point, or overlap to other jets, or fail to have enough energy to provide a clear identification, DZERO chooses to concentrate on two different signatures: lepton plus four jets, and lepton plus five or more jets.

After selecting the above topologies, the data is still polluted with processes that have little to do with top quark pair production (not to mention the exceedingly rare tth events). A further cleanup is provided by requiring that at least one of the jets contains an indication of having been originated by a bottom quark. Bottom quarks are not as heavy as top quarks, and thus are not as rare; but they are still rare enough that their presence is a strong indication of a top decay. 

In the end, DZERO applies a technique we might call "Divide et Impera" (divide and rule): by slicing and dicing the selected event set into different classes (each consisting in a well-defined event signature) a small signal is easier to find, even if some classes will contain a much smaller fraction of it than others. Below is a table from the preliminary paper produced by DZERO: as you can see, electron plus jets and muon plus jets are separated, and then events with only 4, or 5+ jets, are kept distinct. Further, the number of b-quark jets identified in the event (dubbed "b-tags") allows to define a total of 12 exclusive subsets. To decode them, take "5j2t" as an example: that class contains events with at least 5 jets (5j), and exactly two b-tags found in them (2t).
 

In the table, top-antitop events are estimated separately from "non-tt backgrounds", to highlight the power of the DZERO selection: especially in the 2- and 3-b-tags classes, the top contribution far exceeds the other annoying processes that pollute the selected dataset. Also, the observed event counts (shown in the last line for both electron+jet and muon+jet topologies) match pleasingly the expected sum of backgrounds, indicating that there are no surprises and possibly no mistakes. Finally, please notice how the number of events has been reduced by orders of magnitude by the combination of requirements on the presence of a lepton and many jets. Still, the expected signal across the table sums up to less than one event. One event in 626 ? That is not a needle in the haystack anymore! Kudos to DZERO for their clever selection then!

The final step of the analysis is different from what has become common practice in the searches of small signals buried in large backgrounds nowadays. Rather than relying on the modeling of many observed characteristics of the quite complicated kinematics these multi-object final states possess, DZERO uses a single, dumb but foulproof variable: the HT, which is computed as the sum of transverse energies of all the jets, the lepton, and the inferred neutrino. This quantity provides a quite model-independent tool to discriminate tth from tt events, and its use sidesteps a theoretically nagging problem: our insufficient understanding of the main background to the search, the production of top-antitop quark pairs accompanied by bottom-antibottom pairs.

In the figure below, a HT distribution is shown for the sum of the two classes most "signal-rich": the ones corresponding to five or more jets and three or more b-tags. The black points show the observed data events (a total of five entries), and the red distribution shows the expectation from known processes (basically dominated by top-antitop production). The black histogram instead shows the expected HT distribution that the signal would display, if it had a production rate exceeding by 100 times the predictions from theory. The different shape of red and black histogram is the whole point of using HT as a discriminating variable.
 

The 12 HT distributions are finally tested by comparing data to the expectation from the sum of backgrounds (which includes both top production and non-top processes). A complex, very accurate method is used to combine the variegated information coming from the twelve distributions into a single response -the ratio between the probability that the data contain both signal and background together, divided by the probability that they contain only backgrounds. The study of that quantity allows to set a upper limit on the number of signal events contained in the data, which can then be converted in a limit on the signal cross-section by suitably multiplying for the signal detection and reconstruction efficiency, numbers that can be estimated by Monte Carlo simulation programs. 

The whole procedure is repeated for different hypotheses of the unknown value of the Higgs boson mass, and the limit thus becomes a function of it. The end result is displayed, as has become customary, as a curve showing, as a function of the Higgs mass, the ratio between the resulting upper limit on signal cross section and the cross section that is predicted by the Standard Model theory. That is to say, if for a given hypothetical Higgs mass a limit is set at a value equal 100, that means that DZERO's data exclude the presence of tth production at a rate exceeding 100 times the predicted production rate, in case the Higgs has that mass. 
 

As you can check in the graph on the right, the limit is not very stringent! In fact, an exclusion of a mass range for the Higgs boson would result if the limit curve assumed values below 1.0 in that range (the hatched black line). Instead, the red curve (labeled Observed limit) is floating at values well above 30 times the Standard Model prediction. This should not be read to imply that the DZERO search has not been fruitful or successful! The result is, in fact, quite interesting, for several reasons. 

First of all, an anomalous coupling of the Higgs boson to the top quark might boost the production rate above Standard Model predictions, and the DZERO limit sets a bound on that occurrence. Second, the final states investigated by the search had never before studied in detail at the Tevatron, and it feels good to see we do understand the production of top quarks in association with b-quarks. Third, the search provides guidance for future investigations in the same direction. Fourth, the limit, although very loose, can be combined with advanced statistical procedures with the much more stringent ones coming from higher-rate production processes of the Higgs boson, eventually contributing to advancing our knowledge of that elusive particle. Elusive is certainly an appropriate word: Higgs bosons have been hypothesized more than forty years ago, and we still have to see one of them...

The only remaining taks, at the end of this long article, is for me to ask you, dear readers, whether the alarm bell I mentioned at the beginning needs to be serviced!

Further reading:

A call for ideas on how to improve a prospective search for tth events with the CMS detector
Home page of the DZERO experiment
Home page of the Fermi National Accelerator Laboratory
Real-time display of Tevatron performances