A Fascinating New Higgs Boson Search By The DZERO
Experiment
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
