As the less distracted among you have already figured out, I have permanently moved my blogging activities to www.scientificblogging.com. The reasons for the move are explained here.

Since I know that this site continues to be visited -because the 1450 posts it contains draw traffic regardless of the inactivity- I am providing here monthly updates of the pieces I write in my new blog here. Below is a list of posts published last month at the new site.

The Large Hadron Collider is Back Together – announcing the replacement of the last LHC magnets

Hera’s Intriguing Top Candidates – a discussion of a recent search for FCNC single top production in ep collisions

Source Code for the Greedy Bump Bias – a do-it-yourself guide to study the bias of bump fitting

Bump Hunting II: the Greedy Bump Bias – the second part of the post about bump hunting, and a discussion of a nagging bias in bump fitting

Rita Levi Montalcini: 100 Years and Still Going Strong – a tribute to Rita Levi Montalcini, Nobel prize for medicine

The Subtle Art of Bump Hunting – Part I – a discussion of some subtleties in the search for new particle signals

Save Children Burnt by Caustic Soda! – an invitation to donate to Emergency!

Gates Foundation to Chat with Bloggers About World Malaria Day – announcing a teleconference with bloggers

Dark Matter: a Critical Assessment of Recent Cosmic Ray Signals – a summary of Marco Cirelli’s illuminating talk at NeuTel 2009

A Fascinating New Higgs Boson Search by the DZERO Experiment – a discussion on a search for tth events recently published by the Tevatron experiment

A Banner Worth a Thousand Words - a comment on my new banner

Confirmed for WCSJ 2009 – my first post on the new site

A recent discussion in this blog between well-known theorists and phenomenologists, centered on the real meaning of the experimental measurements of top quark and W boson masses, Higgs boson cross-section limits, and other SM observables, convinces me that some clarification is needed.

The work has been done for us: there are groups that do exactly that, i.e. updating their global fits to express the internal consistency of all those measurements, and the implications for the search of the Higgs boson. So let me go through the most important graphs below, after mentioning that most of the material comes from the LEP electroweak working group web site.

First of all, what goes in the soup ? Many things, but most notably, the LEP I/SLD measurements at the Z pole, the top quark mass measurements by CDF and DZERO, and the W mass measurements by CDF, DZERO, and LEP II. Let us give a look at the mass measurements, which have recently been updated.

For the top mass, the situation is the one pictured in the graph shown below. As you can clearly see, the CDF and DZERO measurements have reached a combined precision of 0.75% on this quantity.

The world average is now at . I am amazed to see that the first estimate of the top mass, made by a handful of events published by CDF in 1994 (a set which did not even provide a conclusive “observation-level” significance at the time) was so dead-on: the measurement back then was ! (for comparison, the DZERO measurement of 1995, in their “observation” paper, was ).

As far as global fits are concerned, there is one additional point to make for the top quark: knowing the top mass any better than this has become, by now, useless. You can see it by comparing the constraints on coming from the indirect measurements and W mass measurements (shown by the blue bars at the bottom of the graph above) with the direct measurements at the Tevatron (shown with the green band). The green band is already too narrow: the width of the blue error bars compared to the narrow green band tells us that the SM does not care much where exactly the top mass is, by now.

Then, let us look at the W mass determinations. Note, the graph below shows the situation BEFORE the latest DZERO result;, obtained with 1/fb of data, and which finds ; its inclusion would not change much of the discussion below, but it is important to stress it.

Here the situation is different: a better measurement would still increase the precision of our comparisons with indirect information from electroweak measurements at the Z. This is apparent by observing that the blue bars have width still smaller than the world average of direct measurements (again in green). Narrow the green band, and you can still collect interesting information on its consistency with the blue points.

Finally, let us look at the global fit: the electroweak working group at LEP displays in the by now famous “blue band plot”, shown below for March 2009 conferences. It shows the constraints on the Higgs boson mass coming from all experimental inputs combined, assuming that the Standard Model holds.

I will not discuss this graph in details, since I have done it repeatedly in the past. I will just mention that the yellow regions have been excluded by direct searches of the Higgs boson at LEP II (on the left, the wide yellow area) and the Tevatron ( the narrow strip on the right). From the plot you should just gather that a light Higgs mass is preferred (the central value being 90 GeV, with +36 and -27 GeV one-sigma error bars). Also, a 95% confidence-level exclusion of masses above 163 GeV is implied by the variation of the global fit with Higgs mass.

I have started to be a bit bored by this plot, because it does not do the best job for me. For one thing, the LEP II limit and the Tevatron limit on the Higgs mass are treated as if they were equivalent in their strength, something which could not be possibly farther from the truth. The truth is, the LEP II limit is a very strong one -the probability that the Higgs has a mass below 112 GeV, say, is one in a billion or so-, while the limit obtained recently by the Tevatron is just an “indication”, because the excluded region (160 to 170 GeV) is not excluded strongly: there still is a one-in-twenty chance or so that the real Higgs boson mass indeed lies there.

Another thing I do not particularly like in the graph is that it attempts to pack too much information: variations of , inclusion of low-Q^2 data, etcetera. A much better graph to look at is the one produced by the GFitter group instead. It is shown below.

In this plot, the direct search results are introduced with their actual measured probability of exclusion as a function of Higgs mass, and not just in a digital manner, yes/no, as the yellow regions in the blue band plot. And in fact, you can see that the LEP II limit is a brick wall, while the Tevatron exclusion acts like a smooth increase in the global of the fit.

From the black curve in the graph you can get a lot of information. For instance, the most likely values, those that globally have a 1-sigma probability of being one day proven correct, are masses contained in the interval 114-132 GeV. At two-sigma, the Higgs mass is instead within the interval 114-152 GeV, and at three sigma, it extends into the Tevatron-excluded band a little, 114-163 GeV, with a second region allowed between 181 and 224 GeV.

In conclusion, I would like you to take away the following few points:

• Future indirect constraints on the Higgs boson mass will only come from increased precision measurements of the W boson mass, while the top quark has exhausted its discrimination power;
• Global SM fits show an overall very good consistency: there does not seem to be much tension between fits and experimental constraints;
• The Higgs boson is most likely in the 114-132 GeV range (1-sigma bounds from global fits).

Yesterday Sven Heinemeyer kindly provided me with an updated version of a plot which best describes the experimental constraints on the Higgs boson mass, coming from electroweak observables measured at LEP and SLD, and from the most recent measurements of W boson and top quark masses. It is shown on the right (click to get the full-sized version).

The graph is a quite busy one, but I will try below to explain everything one bit at a time, hoping I keep things simple enough that a non-physicist can understand it.

The axes show suitable ranges of values of the top quark mass (varying on the horizontal axis) and of the W boson masses (on the vertical axis). The value of these quantities is functionally dependent (because of quantum effects connected to the propagation of the particles and their interaction with the Higgs field) on the Higgs boson mass.

The dependence, however, is really “soft”: if you were to double the Higgs mass by a factor of two from its true value, the effect on top and W masses would be only of the order of 1% or less. Because of that, only recently have the determinations of top quark and W boson masses started to provide meaningful inputs for a guess of the mass of the Higgs.

Top mass and W mass measurements are plotted in the graphs in the form of ellipses encompassing the most likely values: their size is such that the true masses should lie within their boundaries, 68% of the time. The red ellipse shows CDF results, and the blue one shows DZERO results.

There is a third measurement of the W mass shown in the plot: it is displayed as a horizontal band limited by two black lines, and it comes from the LEP II measurements. The band also encompasses the 68% most likely W masses, as ellipses do.

In addition to W and top masses, other experimental results constrain the mass of top, W, and Higgs boson. The most stringent of these results are those coming from the LEP experiment at CERN, from detailed analysis of electroweak interactions studied in the production of Z bosons. A wide band crossing the graph from left to right, with a small tilt, encompasses the most likely region for top and W masses.

So far we have described measurements. Then, there are two different physical models one should consider in order to link those measurements to the Higgs mass. The first one is the Standard Model: it dictates precisely the inter-dependence of all the parameters mentioned above. Because of the precise SM predictions, for any choice of the Higgs boson mass one can draw a curve in the top mass versus W mass plane. However, in the graph a full band is hatched instead. This correspond to allowing the Higgs boson mass to vary from a minimum of 114 GeV to 400 GeV. 114 GeV is the lower limit on the Higgs boson mass found by the LEP II experiments in their direct searches, using electron-positron collisions; while 400 GeV is just a reference value.

The boundaries of the red region show the functional dependence of Higgs mass on top and W masses: an increase of top mass, for fixed W mass, results in an increase of the Higgs mass, as is clear by starting from the 114 GeV upper boundary of the red region, since one then would move into the region, to higher Higgs masses. On the contrary, for a fixed top mass, an increase in W boson mass results in a decrease of the Higgs mass predicted by the Standard Model. Also note that the red region includes a narrow band which has been left white: it is the region corresponding to Higgs masses varying between 160 and 170 GeV, the masses that direct searches at the Tevatron have excluded at 95% confidence level.

The second area, hatched in green, is not showing a single model predictions, but rather a range of values allowed by varying arbitrarily many of the parameters describing the supersymmetric extension of the SM called “MSSM”, its “minimal” extension. Even in the minimal extension there are about a hundred additional parameters introduced in the theory, and the values of a few of those modify the interconnection between top mass and W mass in a way that makes direct functional dependencies in the graph impossible to draw. Still, the hatched green region shows a “possible range of values” of the top quark and W boson masses. The arrow pointing down only describes what is expected for W and top masses if the mass of supersymmetric particles is increased from values barely above present exclusion limits to very high values.

So, to summarize, what to get from the plot ? I think the graph describes many things in one single package, and it is not easy to get the right message from it alone. Here is a short commentary, in bits.

• All experimental results are consistent with each other (but here, I should add, a result from NuTeV which finds indirectly the W mass from the measured ratio of neutral current and charged current neutrino interactions is not shown);
• Results point to a small patch of the plane, consistent with a light Higgs boson if the Standard Model holds
• The lower part of the MSSM allowed region is favored, pointing to heavy supersymmetric particles if that theory holds
• Among experimental determinations, the most constraining are those of the top mass; but once the top mass is known to within a few GeV, it is the W mass the one which tells us more about the unknown mass of the Higgs boson
• One point to note when comparing measurements from LEP II and the Tevatron experiments: when one draws a 2-D ellipse of 68% contour, this compares unfavourably to a band, which encompasses the same probability in a 1-D distribution. This is clear if one compares the actual measurements: CDF (with 200/pb of data), DZERO (with five times more statistics), LEP II (average of four experiments). The ellipses look like they are half as precise as the black band, while they are actually only 30-40% worse. If the above is obscure to you, a simple graphical explanation is provided here.
• When averaged, CDF and DZERO will actually beat the LEP II precision measurement -and they are sitting on 25 times more data (CDF) or 5 times more (DZERO).

You can follow it at this link.

Both CDF and DZERO have announced yesterday the first observation of electroweak production of single top quarks in proton-antiproton collisions. Both papers (this one from CDF, and this one from DZERO) claim theirs is the first observation of the long sought-after subatomic reaction. Who is right ? Who has more merit in this advancement in human knowledge of fundamental interactions ? Whose analysis is more credible ? Which of the two results has fewer blemishes ?

To me, it is always a matter of which one is the most relevant question. And to me, the most relevant question is, Who cares who did it ? ... with the easy-to-guess answer: not me. As I have had other occasions to say, I am for the advancement of Science, much less for the advancement of scientific careers, leave alone to which experiments those careers belong.

The top quark is interesting, but so far the Tevatron experiments had only studied it when produced in pairs with its antiparticle, through strong interactions. Electroweak production of the top quark is also possible in proton-antiproton collisions, at half the rate. It is one of those rare instances when the electroweak force competes with the strong one, and it is due to the large mass of the top quark: producing two is much more demanding than producing only one, due to the limited energy budget of the collisions. The reactions capable of producing a single top quark are described by the diagrams shown above. In a), a b-quark from one of the projectiles becomes a top by intervention of a weak vector boson; in b), a gluon “fuses” with a W boson and a top quark is created; in c), a W boson is produced off-mass-shell, and it possesses enough energy to decay into a top-bottom pair.

Since 1995, when CDF and DZERO published jointly the observation of the top quark, nobody has ever doubted that electroweak processes would produce single tops as well. Not even one article, to my knowledge, tried to speculate that the top might be so special to have no weak couplings. The very few early attempts at casting doubt on the real nature of what the Tevatron experiments were producing died quickly as statistics improved and the characterization of the newfound quark was furthered. So what is the fuss about finding out that the reaction resulting from the Feynman diagrams shown above can indeed be directly observed ?

There are different facets in a thorough answer to  the above question. First of all, competition between CDF and DZERO: each collaboration badly wanted to get there first, especially since this was correctly predicted from the outset to be a tough nut to crack. Second, because seeing single top production implies having direct access to one element of the Cabibbo-Kobayashi-Maskawa mixing matrix, the element , which is after all a fundamental parameter in the standard model (well, to be precise it is a function of some of the latter, namely of the CKM matrix parameters, but let’s not split hairs here). Third, you cannot really see a low-mass Higgs at the Tevatron if you did not measure single top production first, because single top is a background in Higgs boson searches, and one cannot really discover something by assuming something else is there, if one has not proven that beforehand.

So, single top observation is important after all. I am a member of the CDF collaboration, and I am really proud I belong to it, so my judgement on the whole issue might be biased. But if I have to answer the question that gave the title to this post, I will first give you a very short summary of  the results of the two analyses,  deferring to a better day a more detailed discussion. This will allow me to drive home a few points.

The two analyses: a face-to-face summary

• Significance: both experiments claim that the signal they observe has a statistical significance of 5.0 standard deviations.

1. CDF uses 3.2 inverse femtobarns, and finds a 5.0-sigma-significance signal of single top production. The sensitivity of the analysis is better measured by the expected significance, which is quoted at 5.9-sigma.
2. DZERO uses 2.4 inverse femtobarns, and finds a 5.0-sigma-significance of single top production. The sensitivity of the DZERO analysis is quoted at 4.5-sigma.

• Cross-section: both experiments measure a cross section in agreement with standard model expectations.

1. CDF measures , a relative uncertainty of about 24%.
2. DZERO measures , a relative uncertainty of about 23%.

• Measurements of the CKM matrix element: both experiments quote a direct determination of that quantity, which is very close to 1.0 in the SM, but cannot exceed unity.

1. CDF finds , a 12% accuracy.
2. DZERO finds , a 11% accuracy.

• Data distributions: both experiments have a super-discriminant which combines the information from different searches. This is a graphical display of the power of the analysis, and should be examined with care.

1. CDF in its paper shows the distribution below, as well as the five inputs that were used to obtain it. The distribution shows the single-top contribution in red, stacked over the concurring backgrounds. At high values of the discriminant, the single top signal does stick out, and the black points -the data- follow the sum of all processes nicely.

2.DZERO in its paper has only the distribution shown below. I was underwhelmed when I saw it. Again, backgrounds are stacked one on top of the other, the top distribution is the one from single top (this time shown in blue), and the data is shown by black dots. It does not look like the data prefer the hypothesis of backgrounds+single top over the background-only one all that much!

Maybe I am too partisan to really make a credible point here, and since I did not follow in detail the development of these analyses -from their first publications as evidence for single top, to updates, until yesterday’s papers- I may very well be proven wrong; however, by looking at the two plots above, and by knowing that they both appear to provide a 5.0-sigma significance, I am drawn to the conclusion that DZERO believes their background shapes and normalization much better than CDF does!

Now, believing something is a good thing in almost all human activities except Science. And if two scientific collaborations have a very different way of looking at how well their backgrounds are modeled by Monte Carlo simulations (which, at least as far as the generation of subatomic processes is concerned, are -or can be- the same), which one is to praise more: the one which believes the simulations more to extract their signal, or the one which relies less on them?

The above question is rethorical, and you should have already agreed that you value more a result which is less based on simulations. So let us look into this issue a bit further. CDF bases its result on a total sample of 4780 events, where the total uncertainty is estimated at +-533 events. DZERO bases its own on a sample of 4651 events, with a total uncertainty estimated at +-234 events! What drives such a large difference in the precision of these predictions ?

The culprit is one of the backgrounds, the production of W bosons in association with heavy flavor quarks – an annoying process, which enters all selection of top quarks and Higgs bosons at the Tevatron. CDF has it at 1855 events, with an uncertainty of 486 -or 26.2%; it is shown in green in the CDF plot above. DZERO has it at 2646 events, with an uncertainty of 173, or 6.5%; it is also shown in green in the DZERO plot.  Do not be distracted by the different size of the contribution of W+heavy flavor in the two datasets: different selection strategies drive the numbers to differ, and besides, it is rather the total number of events of the two analyses which is similar by pure chance. The point here is the uncertainty.

Luckily, the DZERO analysis does not appear to rely too much on the background normalization -this is not a simple counting experiment, where the better you know the size of expected backgrounds, the smaller your uncertainty on the signal; rather, the shapes of backgrounds are important, and the graphs above show that the data appears indeed well-described by the discriminant shape. And of course, background shapes are checked in control samples, so both experiments have many tools to ensure that the different contributions are well understood. However, the issue remains: how much do the different estimates of the W plus heavy flavor uncertainty impacts the significance of the measurements ? The DZERO paper mentions that one of their largest uncertainties arises from the modeling of the heavy flavor composition of W+jet events, but it does not provide further details.

I would be happy to receive an informed answer in the comments thread about the points I mention above…

The paper, submitted to PRL yesterday evening, is here.
I will discuss the details later today…

UPDATE: a reader points out that the above link was broken. Now fixed.

This post has a rather long introduction which does not discuss single top production, but rather explains how the techniques for detecting top quark pairs at the Tevatron have evolved since the first searches. Informed readers who are interested mainly in the new CDF result for the single top cross section may skip the first two sections below…

Introduction: missing energy as the main tag top quarks

In the years before the top quark discovery, and for a few years thereafter, top quark pairs produced by the Tevatron proton-antiproton collider were searched by the CDF and D0 experiments with a quite clear, if a bit unimaginative, three-pronged strategy.

A top quark pair candidate event could be extracted from backgrounds if it contained two charged leptons -basically electrons or muons-, missing transverse energy, and two hadronic jets (the dilepton signature, pictured above); or if there were one charged lepton, missing transverse energy, and three or four hadronic jets (the single-lepton signature, shown on the right); or finally, if it just showed six hadronic jets (the all-hadronic signature).

(A note to avoid letting down from square one those of you who feel inadequate for not knowing what a jet, or missing energy, are: Jets are the result of the materialization of high-energy quarks, which are kicked out of the colliding protons or materialized by the released energy, into streams of hadronic particles; they appear in collider detectors as localized deposits of energy. Missing energy results from the escape of undetected particles, typically neutrinos. More on this below…)

The three final states mentioned above were the result of the different decay modes of the two W bosons always present in a top pair decay: if both W bosons decayed to lepton-neutrino pairs one would get a dilepton event; if one decayed to a lepton-neutrino and the other to a pair of hadronic jets the single-lepton final state would arise; and if both decayed to jets one would get the six-jet topology. Life in the top physics group was just that easy.

The dilepton final state is the cleanest of the three channels, and the all-hadronic final state the dirtiest: in proton-antiproton collisions a simple rule of thumb states that the more leptons you are after, the cleaner your signal is, and conversely the more jets you look for, the deeper you have to dig in the mud of strong interactions. That is because strong interactions (or QCD, for Quantum ChromoDynamics) produce lots and lots of jets, and very rarely do they yield leptons; and QCD is the name of the game in proton-antiproton collisions.

It took quite a while to realize that one could imagine other successful ways to extract top-quark pairs from Tevatron data. A sizable step forward on this issue was made by yours truly with the help of a graduate student, I am proud to note. Let me explain this in a few lines.

While the search for leptons (electrons, muons, tauons) is a way to clean the dataset from QCD backgrounds, the explicit identification of these particles results by force in a reduction of the available top signal. The CDF and D0 experiments are well-suited to detect electrons and muons, but only when these particles are produced at a large angle from the proton beam axis -i.e., “centrally”; moreover, the lepton identification efficiency is never 100% even in those cases. As for tauons, they are much harder to detect, because the tauon is a heavy particle, so that despite being a lepton it has the chance to decay into light hadrons, mimicking a hadronic jet.

All in all, if one considers the single-lepton final state of the process , which arises in a total of 44% of the cases, the typical fraction of top pair decays one may hope to collect in a clean dataset is not larger than 10%. The rest is lost when one explicitly requires to have reconstructed a central, clean lepton signal.

Put this way, it does beg the question. What are we going to do with the large fraction of lost top pair decays ? The answer, for eight years after the top discovery, was simple: nothing. There had been, in truth, attempts at loosening the identification requirements on leptons; but the fact that leptons are the means by which those events are collected -they are requested by the online triggering system- called for a more radical solution. So Giorgio Cortiana and I, while looking for a suitable thesis topic for him, decided to drop the lepton request altogether, and to simply look for top pairs in data just containing missing transverse energy and jets.

Missing transverse energy is a powerful signature at hadron colliders by itself, because it may signal the presence of an energetic neutrino escaping the detector. The signature arises from a simple calculation of the energy flowing out of the interaction point in the plane transverse to the beam direction: in that plane, momentum conservation implies that the vector sum of all particles is zero, compatibly with measurement uncertainties: if it very different from zero, either one or more particles have escaped unnoticed, or some of them have been measured imprecisely.

If a significant amount of missing transverse energy effectively tags an energetic neutrino, there is no need to search for an additional charged lepton to confirm that a leptonic decay has taken place! Energetic neutrinos are either due to a leptonic W decay or a Z boson decay to a pair of neutrinos, . Now, Z bosons are even more rare than W bosons, so they do not constitute a too worrisome background. By ignoring the charged lepton that might accompany the missing transverse energy, one gains access to all the bounty of single lepton decays of top quark pairs which the tight search discards -because the charged lepton went unseen in a hole of the detector, or failed the identification criteria.

Giorgio and I published two papers using the missing-energy-plus-jets signature: a cross-section measurement for top-pair production (paper here) which, at the time of publication, was the third-best result on that quantity, and a top quark mass measurement (paper here) which, despite carrying a large uncertainty, showed that the sample could be a promising ground for top physics measurements despite the lack of kinematic closure (the fact that one lepton is present but is unidentified means that one cannot completely define the decay kinematics: one then speaks of unconstrained kinematics). Now, I am glad to see that the same signature we used for top quark pairs is being exploited in CDF for a single top quark search.

A few words on single top production

Single tops are produced in proton-antiproton collisions by weak interaction processes, but they are not much less frequent than strongly-produced top pairs,
because a pair of top quarks weighs twice as much as a single top quark does, and this has a huge impact in the cross section. Usually, the single-top production signature amounts to the leptonic top decay products -a charged lepton, missing energy, and a jet- accompanied by another jet or two, produced by the quark(s) originally recoiling against the top quark. If one considers the simplest diagrams giving rise to a single top quark, there are two very different processes: s-channel
W* decay and t-channle W-gluon fusion. Let me explain what these are.

A regular, “on-shell” W boson -one which has a mass very close to the peak of the W
resonance, - does not decay into a top and a bottom quark: that is because the W is lighter than the required final state particles! But a W boson produced “off-mass-shell”, i.e. with a mass much larger than its normal value, can indeed decay that way. One just has to remember that W bosons may have any mass from 0 to whatever value, but the probability that the mass is far from quickly becomes small, following a curve called a Breit-Wigner; one I have recently posted in a discussion about Z bosons, incidentally. You can check the shape there, bearing in mind that the peak for W bosons is 10 GeV smaller, and the width about 20% smaller. Anyway, when a off-mass-shell W boson decays as , as shown in the diagram on the right in the figure below, the final state ends up containing two b-quarks, plus the decay products of the second W boson appearing in the process -the one emitted by the top decay. So one has a lepton, missing transverse energy, and two b-jets.

The second way by means of which a single top quark may be produced in proton-antiproton collisions is shown on the left above, and it occurs via the splitting of a gluon from the proton into a bottom-antibottom quark pair: while one of them does not concern us, the other interacts with a W boson emitted from the other projectile, and a top quark is the result. One thus obtains the signature of three jets plus lepton plus missing transverse energy, and two of the jets still have b-quarks in them.

The new CDF result

Single top production has been sought at the Tevatron with enthusiasm in Run II, and CDF and D0 have already shown sizable signals of that process in datasets containing leptons, missing energy, and jets. But finally, a new analysis by the Purdue University group in CDF (Artur Apresyan, Fabrizio Margaroli, and Karolos Potamianos, led by Daniela Bortoletto) is now finding a signal without the help of the charged lepton. I of course cannot but be happy about it, since it is just another demonstration of the potentiality of the “lepton-ignoring” technique!

The new analysis selects events with a significant amount of missing transverse energy () accompanied by two or three hadronic jets. Events are not collected as signal candidates if the missing Et has a small azimuthal angle with a jet, because that is a hint that the former may be due to a fluctuation of the energy measurement of the latter. After that selection, a combination of b-quark tagging algorithms is used to select a sample rich with two b-quark jets -the other important background-reducing characteristic of top decays.

Three different classes of b-enriched events are selected. Two classes depend solely on the presence in the jets of one or two “Secvtx” b-tags: these are explicitly reconstructed secondary vertices, signalling the decay in flight of a B-hadron. A third class collects events with one Secvtx b-tag plus a jet tagged by a different algorithm, “JetProb“. JetProb computes the probability that charged tracks contained in a jet originate from the primary vertex, and tags jets which are likely to contain a long-lived particle.

The three classes have a different signal purity, and their separate analysis allows to extract more information from the data sample than a combination of all b-tagged events.

A neural-network classifier is used to discriminate single-top events from the surviving backgrounds, which are predominantly due to a combination of three processes: “W+jets” production, which arises when a W boson is created along with QCD radiation; top pair production, which does produce missing energy and b-tagged jets, but has typically a larger number of jets; and the more generic QCD-multijet background, which may contaminate the sample when missing transverse energy is faked by a weird fluctuation in the energy measurement of one of the hadronic jets, not removed by the azimuthal angle cuts mentioned above. Since the latter is the largest offender, this neural network -through the choice of kinematical variables- is aimed in particular at downsizing QCD events.

Above you can see the NN output for the class of events containing two Secvtx b-tags; points with error bars are the data, and the expected backgrounds are shown by color-coded histograms. The QCD background (in green) populates the negative region, as expected.

After the selection of high-NN-output events (), about a thousand events survive in the “one Secvtx” class, and about a hundred in the “two Secvtx” and “one Secvtx-one JetProb” class. The first class is dominated by QCD backgrounds, while the second and the third have top pairs as the main contribution. These backgrounds are precisely estimated using a tagging-matrix approach: a parametrization of the probability of finding b-tags in jets as a function of the jet characteristics. Control samples of data are used to verify that the background expectations are accurate.

The analysis does not end there, though: the single top signal is small, and the samples have to be purified further. The authors use another neural network, trained with variables sensitive to the signal kinematics, and extract the signal size from the NN output distributions in the three different classes.

Below you can see the second-NN output for the first class of events. As you can see, the s-channel and t-channel single-top production processes are small, but the fit prefers to include them in the mixture.

The graph below displays the results class by class, and the combination.

The analysis finds a very nice result: the single top cross section is measured at , in good agreement with standard model expectations. The measured significance of the signal is quoted at , while the expected sensitivity of the search is given by the paper at : this is a very important number to quote, as it allows one to size up with precision the relative importance of this determination, decoupling from statistical fluctuation effects that may influence the particular value found by the analysis.

Given the fact that it is based on a data sample orthogonal to others, once combined with the other determinations the new measurement described above will give a sizable contribution to the significance of the CDF signals of single top production: the authors must be heartily congratulated for their  result!

And the goodies are not over: the measurement of the cross section for single top production can be directly translated in a determination of the $V_{tb}$ matrix element of the Cabibbo-Kobayashi-Maskawa matrix. The plot below shows the result obtained by this search. Of course we are still far from a meaningful determination, and this also reflects in the unphysical value obtained, which is however in good agreement with the expectation, close to 1.0 in the standard model.

I have not seen it there yet, but a public web page describing these results and linking to a public note on the analysis will soon appear in the public web page of single top searches in CDF.

UPDATE: The public web page of the analysis is here, and a .pdf file with the public note describing the result is at this link. Enjoy!

Here are the questions asked at an exam in Subnuclear Physics this morning:

• Draw the strong and electromagnetic coupling constants as a function of , explain their functional dependence using feynman graphs of the corrections to the photon and gluon propagators, write their formula, and compute the value of the constants at , given the values at (QED) and (QCD).
• The GIM mechanism: explain the need for a fourth quark using box diagrams of kaon decays to muon pairs. How does the charm contribution depend on its mass ? What conclusion could be drawn by that dependence in the case of B mixing measurements in the eighties ?
• Discuss a measurement of the top quark mass. For a dileptonic decay of top quark pairs, discuss the final state and its production rate.
• Discuss decay modes of W bosons and their branching fraction values. Discuss decay modes of Z bosons and their branching fraction values.

The student answered well all questions and he got 30/30 points.

Here is the second part of the list of useful physics posts I published on this site in 2008. As noted yesterday when I published the list for the first six months of 2008, this list does not include guest posts nor conference reports, which may be valuable but belong to a different place (and are linked from permanent pages above). In reverse chronological order:

December 29: a report on the first measurement of exclusive production of charmonium states in hadron-hadron collisions, by CDF.

December 19: a detailed description of the effects of parton distribution functions on the production of Z bosons at the LHC, and how these effects determine the observed mass of the produced Z bosons. On the same topic, there is a maybe simpler post from November 25th.

December 8: description of a new technique to measure the top quark mass in dileptonic decays by CDF.

November 28: a report on the measurement of extremely rare decays of B hadrons, and their implications.

November 19, November 20, November 20 again , November 21, and November 21 again: a five-post saga on the disagreement between Lubos Motl and yours truly on a detail on the multi-muon analysis by CDF, which becomes a endless diatriba since Lubos won’t listen to my attempts at making his brain work, and insists on his mistake. This leads to a back-and-forth between our blogs and a surprising happy ending when Motl finally apologizes for his mistake. Stuff for expert lubologists, but I could not help adding the above links to this summary. Beware, most of the fun is in the comments threads!

November 8, November 8 again, and November 12: a three-part discussion of the details in the surprising new measurement of anomalous multi-muon production published by CDF (whose summary is here). Warning: I intend to continue this series as I find the time, to complete the detailed description of this potentially groundbreaking study.

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.

September 23: a description of an automated global search for new physics in CDF data, and its intriguing results.

September 19: the discovery of the baryon, an important find by the D0 experiment.

August 27: a report on the D0 measurement of the polarization of Upsilon mesons -states made up by a pair- and its relevance for our understanding of QCD.

August 21: a detailed discussion of the ingredients necessary to measure with the utmost precision the mass of the W boson at the Tevatron.

August 8: the new CDF measurement of the lifetime of the baryon, which had previously been in disagreement with theory.

August 7: a discussion of the new cross-section limits on Higgs boson production, and the first exclusion of the 170 GeV mass, by the two Tevatron experiments.

July 18: a search for narrow resonances decaying to muon pairs in CDF data excludes the tentative signal seen by CDF in Run I.

July 10: An important measurement by CDF on the correlated production of pairs of b-quark jets. This measurement is a cornerstone of the observation of anomalous multi-muon events that CDF published at the end of October 2008 (see above).

July 8: a report of a new technique to measure the top quark mass which is very important for the LHC, and the results obtained on CDF data. For a similar technique of relevance to LHC, also check this other CDF measurement.

To start 2009 with a tidy desk, I wish to put some order in the posts about particle physics I wrote in 2008. By collecting a few links here, I save from oblivion the most meaningful of them -or at least I make them just a bit more accessible. In due time, I will update the “physics made easy” page, but that is work for another free day.

The list below collects in reverse chronological order the posts from the first six months of 2008; tomorrow I will complete the list with the second half of the year. The list does not include guest posts nor conference reports, which may be valuable but belong to a different list (and are linked from permanent pages above).

June 17: A description of a general search performed by CDF for events featuring photons and missing transverse energy along with b-quark jets – a signature which may arise from new physics processes.

June 6: This post reports on the observation of the decay of J/Psi mesons to three photons, a rare and beautiful signature found by CLEO-c.

June 4 and June 5 offer a riddle from a simple measurement of the muon lifetime. Readers are given a description of the experimental apparatus, and they have to figure out what they should expect as the result of the experiment.

May 29: A detailed discussion of the search performed by CDF for a MSSM Higgs boson in the two-tau-lepton decay. Since this final state provided a 2.1-sigma excess in 2007, the topic deserved a careful look, which is provided in the post.

May 20: Commented slides of my talk at PPC 2008, on new results from the CDF experiment.

May 17: A description of the search for dimuon decays of the B mesons in CDF, which provides exclusion limits for a chunk of SUSY parameter space.

May 02 : A description of the search for Higgs bosons in the 4-jet final state, which is dear to me because I worked at that signature in the past.

Apr 29: This post describes the method I am working on to correct the measurement of charged track momenta by the CMS detector.

Apr 23, Apr 28, and May 6: This is a lengthy but simple, general discussion of dark matter searches with hadron colliders, based on a seminar I gave to undergraduate students in Padova. In three parts.

Apr 6 and Apr 11: a detailed two-part description of the detectors of electromagnetic and hadronic showers, and the related physics.

Apr 05: a general discussion of the detectors for LHC and the reasons they are built the way they are.

Mar 29: A discussion of the recent Tevatron results on Higgs boson searches, with some considerations on the chances for the consistence of a light Higgs boson with the available data.

Mar 25: A detailed discussion on the possibility that more than three families of elementary fermions exist, and a description of the latest search by CDF for a fourth-generation quark.

Mar 17: A discussion of the excess of events featuring leptons of the same electric charge, seen by CDF and evidenced by a global search for new physics. Can be read alone or in combination with the former post on the same subject.

Mar 10: This is a discussion of the many measurements obtained by CDF and D0 on the top-quark mass, and their combination, which involves a few subtleties.

Mar 5: This is a discussion of the CDMS dark matter search results, and the implications for Supersymmetry and its parameter space.

Feb 19: This is a divulgative description of the ways by which the proton structure can be studied in hadron collisions, studying the parton distribution functions and how these affect the scattering measurements in proton-antiproton collisions.

Feb 13: A discussion of luminosity, cross sections, and rate of collisions at the LHC, with some easy calculations of the rate of multiple hard interactions.

Jan 31: A summary of the enlightening review talk on the standard model that Guido Altarelli gave in Perugia at a meeting of the italian LHC community.

Jan 13: commented slides of the paper seminar gave by Julien Donini on the measurement of the b-jet energy scale and the cross section, the latter measured for the first time ever at a hadron machine. This is the culmination of a twelve-year effort by me and my group.

Jan 4: An account of the CDF search for Randall-Sundrum gravitons in the final state.

A few months ago I reported here on a CDF technique to measure the mass of the top quark without relying on hadronic jets, whose energy measurement is plagued by many systematic uncertainties. Techniques not relying on the calorimetric measurement of jet energy deposits are quite important for the CMS and ATLAS experiments at the LHC, since the jet energy scale will be very difficult to determine with sufficient accuracy there.

A large statistics of top pair production events is warranted by the 14 TeV proton-proton collisions of the LHC: with respect to the Tevatron, a factor of 100 increase in cross section will be due to the x7 increase in energy, and will be compounded by a factor of 10 increase in instantaneous luminosity.  The rate of production of events of any kind is given by the master formula

,

where is the rate, in Hertz, of events produced, is the cross section responsible for the production, and is the instantaneous luminosity.

The above means that LHC, after the initial warm-up phase (when energy will be 10 TeV and luminosity will be low), will be producing top quarks at a rate a thousand times higher than what the Tevatron is doing now. This huge statistics will thus allow CMS and ATLAS to extract precise determinations of the top mass from otherwise statistics-limited methods, provided these come with light-weight systematic uncertainties.

And the Tevatron is providing another one proof-of-principle. A new result by CDF uses events selected with a single-lepton topology: one of the top quarks decays to three hadronic jets, the other decays to a jet plus a lepton – neutrino pair. The lepton (an electron or a muon, with a transverse energy larger than 20 GeV) triggers the event collection with high efficiency, and its presence reduces backgrounds quite effectively. After some additional, now standard, selection cuts the data sample contains a large fraction of real top-pair decays. At this point, we note that two of the hadronic jets produced by the fragmentation of quarks emitted in the top decay process are in truth due to b-quarks: each top quark almost always produces a b-quark in its decay, in fact.

Just as the top quark may yield a lepton in its decay (see graph on the right, which describes also decays only yielding quarks), through the chain ( stands for the lepton), the b-quark may also decay “semi-leptonically”, as this particular chain is called; in the case of the b-quark, the chain is , where the superscript asterisk on the W stresses the fact that this particle is virtual, having much less energy than its rest mass.

Because the mass of the b-quark is light with respect to that of the heavy top, all bodies produced in its decay remain within the jet: the b-quark is emitted from the top decay with a large momentum, and the same momentum is imparted to the b daughters, which conserve the original quark direction. The jet will therefore often contain an identified electron or muon. The new technique focuses on these additional, “soft” leptons produced within the hadronic jet, by noting that the invariant mass of the combination between the soft lepton and the primary lepton which triggered the event -the one directly coming from the top quark decay chain- is a kinematical quantity strongly correlated with the mass of the decayed top quark. By measuring the former, one gets information on the latter!

Above, the average soft lepton-trigger lepton mass is shown as a function of the top mass, as predicted by a Monte Carlo simulation of top decays with different input mass values. The correlation is linear and well-behaved.

Alice Bridgeman, Lucio Cerrito, Ulysses Grundler, and Xiaojian Zhang, a group of physicists from University of Illinois led by Tony Liss (left in the picture; also shown Cerrito, second from left, and Grundler, last on the right), a veteran in CDF with two decades of experience in top quark physics, exploited the above feature with a sample of 2 inverse femtobarns of proton-antiproton collisions. 240 candidate top-pair events, containing about 130 real top-pair decays, were selected to contain a single-lepton topology and a soft-lepton in one of the jets. The invariant mass distribution of the trigger lepton-soft lepton pair resulting from the above selection is shown in the picture below.

The black points describe the dilepton mass in the data, the cyan histogram is the background contribution, and the blue line shows the likelihood fit. The inset shows the likelihood values as a function of the unknown top mass value. The minimum is found at : the first uncertainty is statistical, and it shows that the method is not useful at the Tevatron -where CDF and D0 have already measured the top mass with an uncertainty of less than two GeV. However, the systematic uncertainty is much smaller, and it can still be reduced by more accurate studies. Most importantly, systematic effects due to the measurement of the jets in the calorimeter are totally avoided by this technique.

More information on this particular analysis is available in the public page of the measurement.

Among the huge amount of beautiful new measurements produced at the Tevatron by the CDF and D0 experiments last month, just in time for showing at ICHEP 2008, the international conference in High-Energy Physics, there is one which does not make headlines, but it deserves one. It is the measurement of the top pair production cross section, a number which is by itself not terribly informative – it is basically only a check that perturbative calculations with Quantum Chromodynamics work well when they deal with an energy scale where the strong coupling constant is small enough. That is: the above is the only thing one gets from a precise measurement of the top cross section provided one is convinced that there is no other process, so far undiscovered, hiding in top production or top decay.

It is absolutely fair to ask oneself whether top pairs are produced at the Tevatron energy solely by quark-antiquark annihilation and gluon-gluon fusion, the two leading order QCD processes, or whether there is a heavy object X which decays to top quarks, thus enhancing the observed rate of top quarks over what QCD predicts. It is also perfectly legitimate to investigate whether the cross section is in line with predictions regardless of the final state in which one searches for top quarks: some non-standard decays of top could modify the mix. Further, one could hypothesize that the top quark dataset -the data enriched with top events which are used by the experiments to measure cross sections- contains some other process which messes up some of the measurements.

The above ideas are to me the most important reason for being interested, 14 years after I first got to know that the top quark existed, in the very precise new determinations of top quark pair cross section obtained by CDF. So let us look at the graph on the right, which details some of the recent determinations, which have been averaged into a result which carries a 8% total uncertainty, beating by 1% the most precise theoretical estimates (9% relative error).

One interesting thing to note is that the cross sections measured with SLT are higher than the average. SLT is the soft-lepton tagging algorithm, which tags b-quark jets coming from top decay through the identification of a muon or an electron embedded in the jet. In Run I, CDF measured a top cross section which was 9 picobarns when using SLT, while about 6 picobarns when using SVX tags -secondary vertices in the jets. Back then, the disagreement was the source of a huge controversy on the hypothesized presence of new physics in the sample of events containing SLT tags. The data did lend itself to some exotic interpretations, but things petered out after years of review and internal diatribas. Now, it does not look like there will be a reprise of that controversy, but the fact remains that SLT cross sections are still there: higher than they should be!

In any case, I salute this new, important result by the CDF top group, and by dozens of dedicated physicists who put their time and efforts into obtaining a very precise measurement. Now the ball is in the theorists’ court, to improve the precision on the theoretical estimate.

UPDATE – ok, a moment after posting the above piece, I looked back at the picture, and I realized that it is not true that the CDF determination is more accurate than theory. It is the theory band which has an 8% uncertainty if I am not mistaken, while CDF has the 9% measurement. That does not change much of the discussion, however, since once the result found by D0 is added to the above one, experiment does get the better hand.

UPDATE II: I also forgot to point interested readers to the public note describing the result!

This morning I gave my seminar at PPC08, and I was able to record it on my camera. So, rather than giving a transcript, I could in principle get away easily by pasting here a simple link to my presentation in .mpg format. However, I will be able to do that only as I go back home next week, since transferring 500mbytes via wireless is not something I want to entertain myself with. I am thus going to put here a few of the slides, commenting them as I did during my talk, and I will update the post next week to include the link to the video file. For now, you can get a pdf file with all the slides here.

Note: This post is dedicated to Louise Riofrio, who kindly mentions my talk in her wonderful blog today…

I started with the usual mention of the experimental apparata: the first is the Tevatron collider (see slide below), which has delivered 4 inverse femtobarns of 2-TeV proton-antiproton interactions to the CDF and D0 detectors so far. The inverse femtobarn is a unit of measure of integrated luminosity , which tells you how many events are produced for a process with a given cross section : since the total proton-antiproton cross section is about 60 millibarns, 4 inverse femtobarns correspond to , or a total of 240 trillion proton-antiproton collisions. I mentioned that the Tevatron expects to double the delivered luminosity if it will be allowed to run through year 2010, and I promised to show what that means for the precision of some critical measurements and searches.

Next I discussed the CDF detector (see slide below). I pointed out that its original design dates back to the year 1980, and that it was constructed to discover the top quark – something it achieved in 1995, but it has produced an enormous amount of excellent measurements in addition. CDF is a magnetic spectrometer where a inner tracking system made of 7 layers of silicon microstrip sensors is embedded in a large drift chamber, and the two are contained within a 1.4 Tesla solenoid. Outside the magnet are electromagnetic and hadronic calorimeters, surrounded by muon chambers.

I discussed only a few results on top physics. The top quark is a remarkable particle: the heaviest of all known elementary bodies, it decays before having time to hadronize since its natural width is an order of magnitude larger than the scale of quantum chromodynamical interactions. So we can study its properties free from the hassle of non-calculable soft QCD effects. The large mass of the top begs the question: why is it so large ? Why is its yukawa coupling very close to unity ? Is some form of new physics hiding in the phenomenology of top production and decay ?

Production of top quark pairs at the Tevatron occurs mainly by quark-antiquark annihilation, the diagram shown on the left in the slide below. Since each top almost always decays to a W boson and a b-quark, one can classify the final states according to the decay products of the two W bosons. In the upper right graph one can see how the possible final states break down in terms of relative rates: the most probable -and most background-ridden- is the all-hadronic final state, where both W bosons decay to quark pairs, and you get six hadronic jets from the top pairs. I also discussed single top production mechanisms, shown in the diagrams at the bottom: these have a comparable production rate, but they are much harder to extract from the data due to larger backgrounds.

I then showed a summary of top pair cross section measurements, mentioning that there are by now dozens of different determinations. The average has a uncertainty of 12%, and its agreement with NNLO predictions shows that the technology of perturbative QCD calculations is in good shape.

After discussing one measurement of top cross section in detail, I went on with mass determinations. The technology of these measurements has improved greatly in the past few years, and by now the top mass is measured by CDF with a 1.1% uncertainty. The average with D0 has been carried out on results obtained with 2/fb of data, and it produces , which is a 0.8% uncertainty. The top quark mass is important for the building of models of new physics beyond the standard model, and of course it provides a stringent constraint to electroweak fits of standard model observables. It is foreseen that the full Run II dataset in 2010 will allow the Tevatron to reach a 1 GeV precision on the top mass, or even slightly better than that.

I next showed the combined measurement of single top production cross section. A very complicated and advanced technique using evolved neural networks and genetic algorithms allows to optimize the measurement, and a 3.7-sigma evidence for the signal is obtained by CDF. This is a unlucky chance, since the expected sensitivity exceeded 5-sigma. But we have already collected enough data to grant the canonical “observation-level” significance in the near future, as the data is analyzed. I also mentioned that the future measurements will allow to determine the matrix element with a precision of 7%.

As far as new results on B physics are concerned, I only showed a couple. One is about the discovery of the exhilarating baryons, which are seen through the exclusive decay chain to J/psi mesons and baryons, with the latter in turn producing two pions and a proton with two separate vertices. The other is the new CDF limit on the branching fraction of mesons to muon pairs, a process heavily suppressed in the standard model, which is enhanced in SUSY models. I discussed the latter result elsewhere recently.

I then presented two searches for supersymmetry recently performed in CDF: one for chargino-neutralino production in events with three leptons and missing transverse energy, and another for squarks and gluino signatures in jets and missing transverse energy. I also discussed these results recently in this blog, in a recent series of posts about dark matter searches at colliders.

I showed results on W mass and width measurements, on which CDF has the best measurements in the world. In particular, the W mass measurement has been produced with only 200 inverse picobarns of data, which is a twentieth of the data we have collected this far: CDF may reach below 20 MeV on the accuracy of W mass determination.

Diboson production has been observed in all its manifestations by CDF: the latest ones were WZ and ZZ production, which may give rise to spectacularly clean events (see the event display shown in the slides below: a perfect WZ candidate). The measurements of cross section are in excellent agreement with SM predictions.

Finally, I discussed the current limits on Higgs boson production. I think I have discussed this particular topic frequently enough in this blog to allow myself to skip a description of my slides here. I concluded my talk mentioning the string of successes of CDF in the recent past, and the prospects for precision SM measurements and reach of Higgs searches. I pointed out that CDF is the longest lasting physics experiment ever (yeah yeah, if we exclude the pitch drop experiment)…

There were several questions by the audience, most of them centered on Higgs boson limits and searches. I was of course happy to answer them, in particular to show that the results have kept improving more than the increase of luminosity they relied upon. In conclusion, it is always a great pleasure to present CDF results… A remarkable experiment indeed!