## The hard task of finding hadronic vector boson decays October 13, 2008

Posted by dorigo in news, personal, physics, science.
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Today I wish to report about a new result by CDF, a measurement which interests me for several reasons, as I hope I will be able to explain in detail below. It is the search for the production of pairs of vector bosons -WW or WZ pairs, to be precise- in 2-TeV proton-antiproton collisions provided by Fermilab’s Tevatron collider, using a mixed signature of lepton plus jets.

Processes responsible for WW/WZ production

WW production is well known: it has been observed by CDF already in Run I before 1996, and is now studied in detail by CDF and D0 with the large data samples they acquired since 2002 in Run II. The interest stems from the fact that a heavy Higgs boson might decay precisely to that final state ($p \bar p \to H \to WW$), and indeed the close match between data and Standard Model predictions have recently allowed to exclude the existence of the Higgs boson at a mass of 170 GeV, as I reported elsewhere.

Instead, WZ production is not the signature of anything new -or so we think-, but it is still quite important to measure precisely to test our understanding of the Standard Model, and indeed both CDF and D0 have good determinations of the production rate of those odd pairs. Everything agrees with theory.

All the measurements mentioned above have been carried out by using the fully leptonic final state of vector boson decays: W bosons have been sought in the electron-electron neutrino decay, or in the muon-muon neutrino decay; Z bosons have been tagged by their decay to electron-positron or muon-antimuon decays. Despite their rarity, these multi-lepton events are so clean you’d spot them from a mile away: two or three leptons of high energy flying away at large angles from the beam and from each other, a large energy imbalance due to the neutrino(s), and little else to report in the detector.

Instead, the new result by CDF is the first which reports on the final state including a lepton and a neutrino from one W decay, plus a pair of hadronic jets from the other W or Z boson. The event thus contains a so-called “W+jets” signature, one which is dear to top quark hunters, but also ridden by a very large and unforgiving background from quantum chromodynamics (QCD) processes accompanying the W boson production. It is precisely the presence of this large background which has so far prevented to observe WW/WZ events using the $l \nu j j$ signature.

But not any more. With a data sample corresponding to 1.2 inverse femtobarns of proton-antiproton collisions, CDF has pulled off a small, but meaningful signal of that process. Since I feel in a didactic vein today, I will take a moment to explain a few things to the lesser equipped among those of you who are still reading this post, before describing in more detail the analysis and its results.

W and Z bosons and the imperfect democracy of their decay

W and Z bosons are undoubtedly fascinating particles. Discovered by Carlo Rubbia’s UA1 experiment in 1983, these particles are the carriers of the weak interaction. The W boson is electrically charged, and weighs 80.4 GeV – about as much as a Krypton atom, or five water molecules if you prefer; it is responsible for radioactive decays of many atomic species and for the reactions which make stars burn. The necessity of the existence of the W boson, at least as a virtual body which allowed the exchange of electric charge and other quantum numbers between quarks and leptons, was understood quite early on, by the detailed study of nuclear beta decay. Beta decay is the process whereby neutrons freed from the stabilizing field of the atomic nucleus turn into a proton, an electron, and a anti-neutrino (beta decay of course also describes the radioactive decay of unstable heavy nuclei).

At 91.19 GeV, the Z boson is even heavier than the W, but it is instead electrically neutral; the Z remained mysterious longer than the W, until it was predicted (in 1967), indirectly seen (in 1973, in neutrino-nucleon interactions in the Gargamelle bubble chamber at CERN), and then found by UA1, as I already mentioned above.

W and Z bosons may be produced in energetic particle collisions, but they decay in the matter of $10^{-25}$ seconds, a time short enough that your stocks cannot lose any of their value even in these uncertain days. When they decay, W bosons are quite democratic, while Z bosons are a bit biased. Let’s see what that means.

Elementary particles in the SM

The W boson disintegration rules are the simplest. A W decay will produce two fermions belonging to the same generation (I am avoiding the complications of the CKM matrix, so if you know about quark mixing bear with me). Fermions are quarks and leptons, and if you ever saw a picture of the building blocks of the Standard Model, well – anything that is not a force carrier is a fermion: the boxes on the left in the picture shown here. Fermions are the matter fields: they make up matter in its stable states (up and down quarks make up nucleons, and electrons complete the picture) and in all the unstable states (all other leptons and quarks); all neutrinos are stable in this simplified picture.

For a negatively charged W the above rule means it will decay to an electron and an electron anti-neutrino, for instance; or a muon and a muon anti-neutrino; or a tauon and a tauon anti-neutrino. Those above are the leptonic decays, but then there are also quark decays: a down and a anti-up quark, or a strange and a anti-charm quark. The $W^-$ wouldn’t mind decaying to a bottom and a anti-top quark pair too, but top quarks are too heavy, and energy conservation prevents that.

So let us take stock: the W has in total five ways to decay: $W^- \to e \bar \nu_e$, $W^- \to \mu \bar \nu_\mu$, $W^- \to \tau \bar \nu_\tau$, $W^- \to d \bar u$, $W^- \to s \bar c$. As we said they are democratic: so each of these five decays will be equally probable, and will happen 20% of the times, right ?

Wrong. Quarks exist in three different colour each, and they have equal rights. If you tell a W not to produce a red d quark, since another blue d quark was created by the previous W, it will piss him off, just as if the next guy in the queue told you and your wife you can buy only one ticket at the booth. So there’s actually nine (three leptonic, six hadronic) fermion-antifermion pairs to allow for: each will have a 11% probability of being the product of the next W boson decay: a perfect democracy! This, however, implies that two thirds of the times, a W decay will produce  a pair of quarks in the final state. This is important in the light of the analysis I am going to describe in a while.

For Z bosons things aren’t quite as simple as for W bosons. Electroweak symmetry breaking modifies the picture a bit, and Z bosons end up decaying to fermion-antifermion pairs of each kind with different probabilities. Z boson decays, in exchange, are easier because they involve pairs of each particle and its own antimatter partner. So, a Z can decay to each of the following: $e^+e^-, \mu^+ \mu^-, \tau^+ \tau^-, \nu_e \bar \nu_e, \nu_\mu \bar \nu_\mu, \nu_\tau \bar \nu_\tau$ (leptonic decays), and $u \bar u, d \bar d, s \bar s, c \bar c, b \bar b$ (hadronic decays). The rules of the standard model make each of these eleven possibilities (12 minus one: again, top quarks are forbidden by energy conservation since they weigh far more than half a Z boson) different: the Z is not democratic!

I will save you the details, and just mention that one has in the end about a one-in-thirty probability to see a charge lepton pair of each kind (for a total of three-in-thirty, or 10%), a one-in-fifteen probability to see a neutrino-antineutrino pair of each kind (for a total of three-in-fifteen, or 20%), and an overall 70% chance to see quarks. Again, quark pairs are the most probable decay of a vector boson!

Putting things together…

Once we know the numbers listed above, it is quite easy to determine what is the chance that a WW pair produces a fully leptonic final state, and when instead it goes in a $l \nu_l j j$ final state, the one we deal with today. (Please note: the $j$ symbolizes the final product of a quark or an antiquark: a hadronic jet). Let me compute that for you, but please first note that tau leptons are tough to detect in hadronic collisions, and they are left out of the search: so we are only interested in either a $e \nu_e j j$ or a $\mu \nu_\mu j j$ final state.

We said that each leptonic decay of a W boson happens one ninth of the time, and the hadronic one (two quarks, which make two jets in the end) happens two thirds of the time overall. So we get a $WW \to e \nu_e j j$ decay in $1/9 \times 2/3$ of the cases. But wait: if the first W goes hadronic and the second goes to $e \nu_e$, we are just as happy, so we need to multiply the result by two: in other words, we do not care if the final state is $e^+ \nu_e j j$ or if it is $e^- \bar \nu_e j j$. In the end we have $1/9 \times 2/3 \times 2 = 4/27$, or about 15%. So if we look for both electrons and muons, the total is 30%.

Let’s see instead what is the chance of a fully leptonic decay, one with two electrons, or two muons, or an electron and a muon; plus, of course, a pair of neutrinos, which we do not see in the detector, let alone determine which kind of flavor they have or if they are neutrinos or antineutrinos…

This time we take $WW \to e \nu e \nu$ for a starter: this is easy: simply one ninth times one ninth, or 1/81: a meager 1.2%. The same of course goes for a $WW \to \mu \mu \nu \nu$ final state. Instead, the mixed case $WW \to e \mu \nu \nu$ happens twice as frequently. In total, we get a 4/81 chance, which is 5%. Six times fewer WW pairs decay fully leptonically than single-leptonically!

Now, you have gotten the gist of it, so I will just mention what the result is for WZ pairs. In the fully leptonically final state, when again we are only interested in $W \to e \nu$, $W \to \mu \nu$, and $Z \to ee$, $Z \to \mu \mu$ decays, things go as follows:

• $WZ \to e \nu e e$: 1/9 times 1/30 = 1/270
• same for $WZ \to e \nu \mu \mu$
• same for $WZ \to \mu \nu ee$
• same for $WZ \to \mu \nu \mu \mu$

In total, 4 WZ pairs in 270 will yield the pretty, clean and unmistakable three-lepton signature. That is a pretty small 1.5% fraction of the cases!

Instead, a $WZ \to l \nu_l j j$ final state (where l stands for either electron or muon, of course, and again j indicates the jet resulting from a quark hadronization) happens more often:

• $WZ \to e \nu_e j j$: 1/9 times 7/10 = 7/90
• same thing for muon decays of the W

In total we have $WZ \to l \nu_l j j$ happening at a rate of 7/45=15.5%, which is ten times larger!

Hadronic signal: if it’s easy we don’t like it

The above section attempted to show why the single-lepton final state of WW/WZ decays is more frequent than the fully leptonic one. But is it worth looking for it ? Well, yes and no. As I said before, when hadrons are sought in the final state of a proton-antiproton collision, high rates are to be expected. QCD backgrounds are large, and any signal will be tough to extract. There are, in fact, only few examples of hadronic decays of W and Z bosons extracted from proton-antiproton collisions. Let me list them:

• UA2 in 1987 collected a special set of data for the specific purpose of finding a signal of $W/Z \to jj$ decays in events with two hadronic jets. They could afford to collect data with a very low-energy jet trigger, which enabled them to model with a smooth curve the invariant mass distribution of background events to masses much smaller than 80 GeV, thus evidencing a small bump at around that value, the combined result of W and Z boson decays to quark pairs. That analysis demonstrated that W and Z bosons decayed as predicted by the Standard Model, although there was really no question about it.
• CDF in 1997 found hadronic decays of top quark pairs, in the decay chain $t \bar t \to Wb W \bar b \to 6j$ yielding six hadronic jets in the final state. Again, not an improvement on the top quark measured characteristics (with leptons top quarks had been found two years earlier and a mass and cross section had been extracted with more precision), but still a very good display of the potentiality of that decay channel. While backgrounds from QCD are originally overwhelming the signal by more than three orders of magnitude (for each signal event there are thousands of background events looking similar), a careful selection based on the kinematical differences of the two processes allows to increase the signal fraction. I was author of that first observation paper, by the way.
• CDF in 1998 showed how to isolate $Z \to b \bar b$ decays from the huge QCD background, using b-jet identification as well as tight kinematical cuts. That was my Ph.D. thesis, and I have discussed it several times in this blog.
• I should also include in this list a search for top quark pairs in multijet events that I co-authored with my Ph.D. student, Giorgio Cortiana, in 2005. In that case we could show that without asking for a charged lepton, but only relying on jets and missing transverse energy -again technically a purely hadronic signature-, the signal of top pairs producing four jets, a neutrino, and a lepton which was lost or misidentified was extractable with relative ease. Back then, this fruited CDF’s third-best measurement of the top pair cross-section, a remarkable result given the fact that such a final state had been totally neglected for top searches thus far.

In Run II the all-hadronic top pair decay has shown it can fruit very precise measurements of the top quark mass. The decay of Z bosons to b-quark pairs has been used to determine the accuracy of jet energy measurements (which is also important for top mass measurements). And hadronic decays of the Higgs boson, $H \to b \bar b$ -which are quite similar to the $Z \to b \bar b$ process- are now sought with momentum by both CDF and D0.

The above notes explain why I am particularly interested in hadronic signals of vector bosons.  So I cannot but be happy to see a new analysis on this topic produced by my experiment.

The search for WW/WZ in lepton+jets

CDF searches for events containing an electron or a muon of high momentum, a significant amount of missing transverse energy, and two hadronic jets. The signal-to-noise fraction before any further selection is of the order of one or two percent, and must be increased by a suitable technique.

Kinematic variables used for the NN

The method used is to put together a neural network using as input several kinematical distributions (shown above) which are capable to somehow distinguish -although only on a statistical basis- the diboson signal from QCD backgrounds. The latter, by the way, are due to the production of a W boson yielding the regular lepton-neutrino signature, plus two hadronic jets which do not come from another boson, but are instead due to gluon radiation off the quarks which produced the collision materializing the W.

The neural network produces an output per each event: just a number between zero and one, as in the plot on the left. The larger this number is, the more likely the event is a signal of WW/WZ production (shown in red in the plot).  One can thus select data with a high value of this output, increasing the signal fraction: after a selection on the NN output, the dataset contains a total of 15,016 events, about 500 of which are due to WW/WZ decay. To put that signal in evidence, the invariant mass of the two jets is computed and its distribution is fit with two different shapes: a falling, exponential-like function describing the QCD background, and a resonance peak for the signal, which is actually the sum of W and Z hadronic decays.

In the plot above, which shows a dijet mass distribution, the background shape resulting by the fit has been subtracted, putting in evidence the excess around 80 GeV (black points with error bars). The red curve shows its interpretation in terms of a combined WW/WZ signal.

The fit produces an estimate of 410+-212 signal events in the histogram: this is not enough to claim to have observed the searched process, because such a signal could be the result of a statistical fluctuation; however, it has the expected characteristics of WW/WZ production, as well as the expected size. The cross section is not simple to quote because what is measured is a combination of two processes: technically one writes $\sigma_{WW} \times B(l \nu) \times B(W \to jj) + \sigma_{WZ} \times B(l \nu) \times B(Z \to jj) =$ $1.47 \pm 0.77 \pm 0.38 pb$, where the first uncertainty is statistical and the second accounts for known systematics.

The above measurement is not too meaningful, given the small significance (less than 2-sigma: pseudoexperiments indicate that a fluctuation would produce a similar effect about 4% of the time). More scientifically correct is to quote an upper limit on the production cross section: that comes up at $\sigma < 2.88 pb$, which is above the theoretical calculation for the WW/WZ process (2.09 pb), as it should.

I am confident that the same analysis, once it will be performed on four times larger dataset CDF has already collected, will result in a more meaningful measurement. In any case, I am glad to see W and Z boson decays again emerge from a dijet mass distribution!

Those of you in need of more information are encouraged to visit the public web page of this analysis.

1. Nicola - October 14, 2008

sounds familiar…..😀

2. Kuroki Kaze - October 20, 2008

Booom!!! (Brain explodes)

3. Igor Ivanov - October 22, 2008

Dear Tommaso,

D0 has just published 0810.3873, which seems to be the same analysis you describe. They find WW/WZ signal at 4.4 sigma. Were they more lucky than CDF or what?

Igor

4. D0 bags evidence for semileptonic dibosons « A Quantum Diaries Survivor - October 24, 2008

[…] news, physics, science. Tags: D0, hadronic signals, Higgs boson, Tevatron, weak decays trackback A week ago I discussed here the recently approved analysis by which CDF shows a small hint of WW/WZ signal in their Run II […]

5. Some posts you might have missed in 2008 - part II « A Quantum Diaries Survivor - January 6, 2009

[…] October 24: the analysis by which D0 extracts evidence for diboson production using the dilepton plus dijet final state, a difficult, background-ridden signature. The same search, performed by CDF, is reported in detail in a post published on October 13. […]

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