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Single top seen with no leptons! January 14, 2009

Posted by dorigo in news, personal, physics, science.
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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 t \bar t \to W^+ b W^- \bar b \to l \nu b q \bar q' \bar b, 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 W \to l \nu decay has taken place! Energetic neutrinos are either due to a leptonic W decay or a Z boson decay to a pair of neutrinos, Z \to \nu \nu. 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, M_W=80.4 GeV– 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 M_W 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 W \to t \bar b, 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 (ME_T>50 GeV) 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 (NN>-0.1), 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 \sigma_t = 4.9^{+2.5 }_{-2.2} pb, in good agreement with standard model expectations. The measured significance of the signal is quoted at 2.1-\sigma, while the expected sensitivity of the search is given by the paper at 1.4-\sigma: 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!

Some posts you might have missed in 2008 – part II January 6, 2009

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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 \Omega_b 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 b \bar b 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 \Lambda_b 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.

Top quark mass measured with neutrino phi weighting December 8, 2008

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I still remember when I moved the first steps in the world of experimental particle physics, a fresh new collaborator of the CDF experiment, in 1992. Back then, what the mass of the top quark could be was anybody’s guess. There were indications that the top was heavy, mainly due to the speed of oscillation of neutral B mesons; experimental searches had only set a limit which dictated that it had to be heavier than 91 GeV – about 97 protons. The top quark had to be heavy, but whether it was 120 or 150 or 200 GeV was really a favourite subject of speculations. We already knew, however, that a measurement would come first from a kinematic fit of single lepton decays.

Top quarks are mostly produced in pairs at hadron colliders. When they decay, top pairs always produce two b-quarks and two W bosons. While the b-quarks always end up fragmenting into a collimated stream of hadrons -what we call a jet-, W bosons may yield jets or lepton-neutrino pairs. Already in 1992, it was well-known that the single-lepton topology -the one arising when only one of the two W’s decayed into a lepton-neutrino pair, while the other yielded two additional hadronic jets- was the one which would discover the top, and which would allow its mass determination.

The single lepton topology includes a total of four jets, a lepton, and a neutrino. It is the best compromise between the number of signal events and the rate of mimicking background processes; but what’s more important, the escaping neutrino’s momentum can be figured out by the several constraints of the decay kinematics. You have two top quarks -their masses are the same-, then you have two W bosons -whose mass is 80.4 GeV-, and then you have overall a system whose transverse momentum components have to balance out. All in all, these are five constraints -five requirements on the observed momenta of the detected final state bodies- and since you only miss three components of the neutrino momentum, you can “solve the system” of equations, and determine both the neutrino momentum AND the top mass.

This is indeed how things went in 1994, when CDF published its first evidence for top quark production. Back then, the measurement of top quark mass using dilepton decays -ones arising when both W bosons decay into lepton-neutrino pairs- was considered unfeasible, or at least very unpractical.

In dilepton decays along with two b-quark jets and two charged leptons you get two neutrinos, and not just one: you thus have six unknown components of their momenta, and you need to know both if you want to reconstruct the decay kinematics completely. Because of those six unknowns, in the face of the five constraints listed above, the system is under-constrained: you cannot solve it, no more than you can give a univocal value to x,y,z in the system x+y+z=0,  x-y-z=1.

Brute-force computing comes to the rescue, however. The large statistics of dileptonic top pair decays collected by the CDF experiment in Run II -330 event candidates to play with- allows sophisticated statistical methods to be used, together with a good dose of number crunching. The idea is simple: even though the decay kinematics is unconstrained, one can make hypotheses for the neutrino momenta in the plane transverse to the beam direction (in this plane, a vector of missing energy does size up the combination of neutrino momenta), and to each hypothesis will correspond a reconstructed top quark mass, and an associated likelihood.

In fact, each of the objects detected in a dilepton top pair decay  -hadronic jets, charged leptons, missing transverse energy- is known within a well-determined uncertainty. Using the probability distribution function of each observable quantity, a likelihood can be computed. The method put together by CDF consists in scanning the angles of the two neutrinos in the transverse plane -their azimuthal angle phi– and determining the most likely top mass in each configuration. A simple weighting of the masses with the probability that neutrinos did in fact have those values of phi, given the measured momenta of jets and charged leptons, and the associated uncertainties, produces a very good estimate of the true top quark mass.

In the plot below you can see that the method allows to measure a top quark mass from a sample of dilepton decays which is almost exactly the same as the true one. For different samples of simulated top quark decays -each of them produced with a different top quark mass- the reconstructed mass matches perfectly the input one, and the output versus input points line up in a straight line bisecting the x,y axes.

The second plot shows the difference between reconstructed and true mass as a function of the true (input) mass. The difference is consistent with zero, and there is no dependence of \Delta M on the input mass: two features which make the measurement technique very solid and trustworthy.

In the end, one finds a “most likely” top quark mass per event, and a histogram of the latter can be drawn, and interpreted as the sum of background processes and signal. Monte Carlo simulations allow to predict the shape of backgrounds in this distribution, as well as the signal shape, once a particular top quark mass value is hypothesized. Different top quark masses produce different reconstructed mass distributions, such that from the distribution found in the data, the top mass can be derived.

Below you can see the mass distirbution obtained from 330 top pair candidates using the neutrino phi weighting technique. The data is represented by the black empty histogram; the fitted function consists of the sum of a background template (in magenta) and a signal template (in cyan). The inset shows the likelihood resulting from a fit of the distribution, as a function of the top quark mass. The minimum of the likelihood corresponds to the most likely top quark mass: 165.1 GeV.

So, through a careful study of the mass distribution, CDF is able to measure a top mass of 165.1 \pm 3.3 \pm 3.1 GeV from 2.9 inverse femtobarns of data. This is a very precise result,  surpassing the combined precision that CDF and D0 had on the top mass at the end of Run I by using their single lepton decays. It shows that refined methods of analysis and measurement can overcome the difficulty of experimental situations. Neutrinos can be sized up despite the fact that we never measured one directly in our detector!

This new result by CDF does not alter much the world average value of the top quark mass; but it will almost certainly drive it down slightly, once it will be included in a global average. A lower top mass means a lower Higgs boson mass in global electroweak fits… And this makes things interesting for the searches of the Higgs boson, in two ways: first, because it increases the tension with current experimental upper limits (from LEP II: M_H>114.4 GeV), thus exposing the potential faults of the Standard Model; and second, because it makes it even more probable that the Higgs boson is in fact light -quite close to the 1.7-sigma excess found by LEP II in 2002. If the Higgs boson indeed weighs 115 GeV, it will take a while for LHC experiments to find it -this is the region of mass where less-than-straightforward decays have to be exploited to evidence a signal.

These are interesting times ahead of us! The options are still all on the table: no Higgs, a light Higgs, or a heavy one. Each of these has its own potential for a revolution of our understanding of the subnuclear world!

Back to the neutrino-phi weighting technique by CDF: I think it is worth mentioning, at the end of this post, that the improvements in the new analysis have produced a 20% better uncertainty -what’s equivalent to 44% more time spent running the experiment. As they say, a bit of analysis is worth a megabyte of code!

Another pro-LHC top mass measurement October 3, 2008

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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

\large N = \sigma L,

where N is the rate, in Hertz, of events produced, \sigma is the cross section responsible for the production, and L 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 t \to W b \to l \nu b (l 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 b \to W^* c \to l \nu c, 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 M_t = 181.3 \pm 12.4 \pm 3.5 GeV/c^2: 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.

New zoom in on the Higgs mass from Summer 2008 Tevatron results! July 31, 2008

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Many thanks to Sven Heinemeyer, who provided me this morning with a fresh update of the traditional plot summarizing the status of Standard Model measurements of top quark and W boson masses, their consistency with SM and SUSY, and their impact on the Higgs boson mass. Have a look at it below (a better version, in .eps format, is here):

As you can see, the consistency between direct determinations at the Tevatron (blue ellipse) and the LEP II(black lines) and LEP I/SLD results (hatched purple lines) is still quite good.

One detail worth mentioning: when plotting a 68% CL ellipse atop a 68% interval, the interval will look more restrictive in the variable which is measured (in the case of blue and black lines, the W boson mass, which is in the Y axis), because of the need of the ellipse to extend way past the 1-sigma limits to accommodate a total area of 68%.

The Tevatron results on the W mass are no worse than the LEP II ones by now – and they are based on only one experiment -CDF- analyzing a twentieth of the currently available data! The W mass reach of CDF is estimated at 15 MeV, a result three times better than the current one.

So, there is still a lot to squeeze from Tevatron data, despite the update you are looking at now “only” includes an improved measurement of the top quark mass, which now sits at 172.4 +-1.2 GeV – a 0.7% accuracy on this important parameter of the Standard Model.

It remains me to congratulate with my colleagues in CDF and D0 for their continuing effort. Well done, folks!

UPDATE: a commenter asks for the 95% CL ellipse in the plot above. I advise him and whomever else wants much more information to visit Sven’s site.

Also, two other blogs have posted today discussing this result: Lubos Motl and Marco Frasca. NB: Lubos advertises his blog in the comment section below, and he says he did a much better job than me in discussing the new results… I believe him: I wrote mine with my kids running around, asking me to finally leave for a hike on the mountains. I believe Lubos has no kids so… Enjoy!