Here is a list of noteworthy pieces I published on my new blog site in May. Those of you who have not yet updated their links to point there might benefit from it…

Four things about four generations -the three families of fermions in the Standard Model could be complemented by a fourth: a recent preprint discusses the possibility.

Fermi and Hess do not confirm a dark matter signal: a discussion of recent measurements of the electron and positron cosmic ray fluxes.

Nit-picking on the Omega_b Discovery: A discussion of the significance of the signal found by DZERO, attributed to a Omega_b particle.

Nit-picking on the Omega_b Baryon -part II: A pseudoexperiments approach to the assessment of the significance of the signal found by DZERO.

The real discovery of the Omega_b released by CDF today: Announcing the observation of the Omega_b by CDF.

CDF versus DZERO: and the winner is…: A comparison of the two “discoveries” of the Omega_b particle.

The Tevatron Higgs limits strenghtened by a new theoretical study: a discussion of a new calculation of Higgs cross sections, showing an increase in the predictions with respect to numbers used by Tevatron experiments.

Citizen Randall: a report of the giving of honorary citizenship in Padova to Lisa Randall.

Hadronic Dibosons seen -next stop: the Higgs: A report of the new observation of WW/WZ/ZZ decays where one of the bosons decays to jet pairs.

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

This post and the few ones that will follow are for experts only, and I apologize in advance to those of you who do not have a background in particle physics: I will resume more down-to-earth discussions of physics very soon. Below, a short writeup is offered of Steve King’s talk, which I listened to during day three of the “Neutrino Telescopes” conference in Venice, three weeks ago. Any mistake in these writeups is totally my own fault. The slides of all talks, including the one reported here, have been made available at the conference site.

Most of the talk focused on a decision tree for neutrino mass models. This is some kind of flow diagram to decide -better, decode- the nature of neutrinos and their role in particle physics.

In the Standard Model there are no right-handed neutrinos, only Higgs doublets of the symmetry group , and the theory contains only renormalizable terms. If the above hypotheses all apply, then neutrinos are massless, and three separate lepton numbers are conserved. To generate neutrino masses, one must relax one of the three conditions.

The decision tree starts with the question: is the LSND result true or false ? if it is true, then are neutrinos sterile or CPT-Violating ? Otherwise, if the LSND result is false, one must decide whether neutrinos are Dirac or Majorana particles. If they are Dirac particles, they point to extra dimensions, while if they are Majorana ones, this brings to several consequences, tri-bimaximal mixing among them.

So, to start with the beginning: Is LSND true or false ? MiniBoone does not support the LSND result but it does support three neutrinos mixing. LSND is assumed false in this talk. So one then has to answer the question, are then neutrinos Dirac or Majorana ? Depending on that you can write down masses of different kinds in the Lagrangian. Majorana ones violate lepton number and separately the three of them. Dirac masses couple L-handed antineutrinos to R-handed neutrinos. In this case the neutrino is not equal to the antineutrino.

The first possibility is that the neutrinos are Dirac particles. This raises interesting questions: they must have very small Yukawa coupling. The Higgs Vacuum Expectation Value is about 175 GeV, and the Yukawa coupling is 3E-6 for electrons: this is already quite small. If we do the same with neutrinos, the Yukawa coupling must be of the order of 10^-12 for an electron neutrino mass of 0.2 eV. This raises the question of why this is so small.

One possibility then is provided by theories with extra dimensions: first one may consider flat extra dimensions, with right-handed neutrinos in the bulk (see graph on the right). These particles live in the bulk, whereas we are trapped in a brane. When we write a Yukawa term for neutrinos we get a volume suppression, corresponding to the spread of the wavefunction outside of our world. It goes as one over the square root of the volume, so if the string scale is smaller than the Planck scale ( we get the right scale.

The other sort of extra dimensions (see below) are the warped ones, with the standard model sitting in the bulk. The wavefunction of the Higgs overlaps with fermions, and this gives exponentially suppressed Dirac masses, depending on the fermion profiles. Because electrons and muons peak in the Planck brane while we live in the TeV brane, where the top quark peaks, this provides a natural way of giving a hierarchy to particle masses.

Some of these models address the problem of dark energy in the Universe. Neutrino telescopes studying neutrinos from Gamma-ray bursts may shed light on this issue along with Quantum Gravity and neutrino mass. The time delay relative to low-energy photons as a function of redshift can be studied against the energy of neutrinos. The function lines are different, and they depend on the models of dark energy. The point is that by studying neutrinos from gamma-ray bursts, one
has a handle to measure dark energy.

Now let us go back to the second possibility: namely, that neutrinos are Majorana particles. In this case you have two choices: a renormalizable operator with a Higgs triplet, and a non-renormalizable operator with a lepton violation term, . Because it is non-renormalizable you get a mass suppression, a mass at the denominator, which corresponds to some high energy scale. The way to implement this is to imagine that the mass scale is due to the exchange of a massive particle in the s-channel between Higgs and leptons, or in the t-channel.

We can concentrate on see-saw mechanisms in the rest of the talk. There are several types of such models, type I is essentially exchanging a heavy right-handed neutrino in the s-channel with the Higgs. Type II is instead when you exchange something in the t-channel, this could be a heavy Higgs triplet, and this would also give a suppressed mass.

The two types of see-saw types can work together. One may think of a unit matrix coming from a type-II see-saw, with the mass splittings and mixings coming from the type-I contribution. In this case the type II would render the neutrinoless double beta decay observable.

Moving down the decision tree, we come to the question of whether we have precise tri-bimaximal mixing (TBM). The matrix (see figure on the right) corresponds to angles of the standard parametrization, , , . These values are consistent with observations so far.

Let us consider the form of the neutrino mass matrix assuming the correctness of the TBM matrix. We can derive what the mass matrix is by multiplying it by the mixing matrix. It has three terms, one proportional to mass , one to , and one multiplied to . These matrices can be decomposed into column vectors. These are the columns of the TBM matrix. When you add the matrices together, you get the total matrix, symmetric, with the six terms populating the three rows (, , )  satisfying some relations: , , .

Such a mass matrix is called “form-diagonalizable” since it is diagonalized by the TBM matrix for all values of a,b,d. A,b,d translate into the masses. There is no cancelation of parameters involved, and the whole thing is extremely elegant. This suggests something called “form dominance”, a mechanism to achieve a form-diagonalizable effective neutrino mass matrix from the type-I see-saw. Working in the diagonal MRR basis, if is the Dirac mass, this can be written as three column vectors, and the effective light neutrino mass matrix is the sum of three terms. Form dominance is the assumption that the columns of the Dirac matrix are proportional to the columns of the TBM matrix (see slide 16 of the talk). Then one can generate the TBM mass matrix. In this case the physical neutrino masses are given by a combination of parameters. This constitutes a very nice way to get a diagonalizable mass matrix from the see-saw mechanism.

Moving on to symmetries, clearly, the TBM matrix suggests some family symmetry. This is badly broken in the charged lepton sector, so one can write explicitly what the Lagrangian is, and the neutrino Majorana matrix respects the muon-tauon interchange, whereas the charged matrix does not. So this is an example of a symmetry working in one way but not in the other. To achieve different symmetries in the neutrino and charged lepton sectors we need to align the Higgs fields which break the family symmetry (called flavons) along different symmetry-preserving directions (called vacuum alignment). We need to have a triplet of flavons which breaks the A4 symmetry.

A4 see-saw models satisfy form dominance. There are two models. Both have R=1. These models are economical, they involve only two flavons. A4 is economical: yet, one must assume that there are some cancelations of the vacuum expectation values in order to achieve consistency with experimental measurements of atmospheric and solar mixing. This suggests a “natural form dominance”, less economical but involving no cancelations. A different flavon is associated to each neutrino mass. An extension is “constrained sequential dominance”, which is a special case, which supplies strongly hierarchical neutrino masses.

As far as family symmetry is concerned, the idea is that there are two symmetries, two family groups from the group . You get certain relations which are quite interesting. The CKM mixing is in relation with the Yukawa matrix. You can make a connection between the down-Yukawa matrix and the electron Yukawa. This leads to some mixing sum rule relations, because the PMNS matrix is the product of a Cabibbo-like matrix and a TBM matrix. The mixing angles carry information on corrections to TBM. The mixing sum rule one gets is a deviation from 35 degrees of , which is due to a Cabibbo angle coming from the charged sector. Putting two things together, one can get a physical relation between these angles. A mixing sum rule, .

The conclusions are that neutrino masses and mixing require new physics beyond the Standard Model. There are many roads for model building, but their answers to key experimental questions will provide the signposts. If TMB is accurately realized, this may imply a new symmetry of nature: a family symmetry, broken by flavons. The whole package is a very attractive scheme, sum rules underline the importance of showing that the deviations from TBM are non-zero. Neutrino telescopes may provide a window into neutrino mass, quantum gravity and dark energy.

After the talk, there were a few questions from the audience.

Q: although true that MiniBoone is not consistent with LSND in a simple 2-neutrino mixing model, in more complex models the two experiments may be consistent. King agrees.

Q: The form dominance scenario in some sense would not apply to the quark sector. It seems it is independent of A4. King’s answer: form dominance is a general framework for achieving form-diagonalizable elements starting from the see-saw mechanism. This includes the A4 model as an example, but does not restricts to it. There are a large class of models in this framework.

Q: So it is not specific enough to extend to the quark sector ? King: form dominance is all about the see-saw mechanism.

Q: So, cannot we extend this to symmetries like T’ which involve the quarks ? King: the answer is yes. Because of time this was only flashed in the talk. It is a very good talk to do by itself.

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).

The CDF collaboration will present at a public venue (Fermilab’s Wilson Hall) its discovery of the new Y(4140) hadron, a mysterious particle created in B meson decays, and observed to decay strongly into a state, a pair of vector mesons. I have described that exciting discovery in a recent post.

From this site you can connect to streaming video (starting at 4.00PM CDT, or 9.00PM GMT – should last about 1.30 hours).

Hot off the press: Mark Williams, a DZERO member speaking at Moriond QCD 2009 -a yearly international conference in particle physics, where HEP experimentalists regularly present their hottest results- has shown today the preliminary results of their analysis of dimuon events, based on 900 inverse picobarns of proton-antiproton collision data. And the conclusion is…

DZERO searched for an excess of muons with large impact parameter by applying a data selection very similar, and when possible totally equivalent, to the one used by CDF in its recent study. Of course, the two detectors have entirely different hardware, software algorithms, and triggers, so there are certain limits to how closely one analysis can be replicated by the other experiment. However, the main machinery is quite similar: they count how many events have two muons produced within the first layer of silicon detector, and extrapolate to determine how many they expect to see which fail to yield a hit in that first layer, comparing to the actual number. They find no excess of large impact parameter muons.

Impact parameter, for those of you who have not followed this closely in the last few months, is the smallest distance between a track and the proton-antiproton collision vertex, in the plane transverse to the beam direction. A large impact parameter indicates that a particle has been produced in the decay of a parent body which was able to travel away from the interaction point before disintegrating. More information about the whole issue can be found in this series of posts, or by just clicking the “anomalous muons” tab in the column on the right of this text.

There are many things to say, but I will not say them all here now, because I am still digesting the presentation, the accompanying document produced by DZERO (not ready for public consumption yet), and the implications and subtleties involved. However, let me flash a few of the questions I am going to try and give an answer to with my readings:

• The paper does not address the most important question – what is DZERO’s track reconstruction efficiency as a function of track impact parameter ? They do discuss with some detail the complicated mixture of their data, which results from triggers which enforce that tracks have very small impact parameter -effectively cutting away all tracks with an impact parameter larger than 0.5cm- and a dedicated trigger which does not enforce an IP requirement; they also discuss their offline track reconstruction algorithms. But at a first sight it did not seem clear to me that they can actually reconstruct effectively tracks with impact parameters up to 2.5 cm as they claim. I would have inserted in the documents an efficiency graph for the reconstruction efficiency as a function of impact parameter, had I authored it.
• The paper shows a distribution of the decay radius of neutral K mesons, reconstructed from their decay into pair of charged pions. From the plot, the efficiency of reconstructing those pions is excessively small -some three times smaller than what it is in CMS, for instance. I need to read another paper by DZERO to figure out what drives their K-zero reconstruction efficiency to be so small, and whether this is in fact due to the decrease of effectiveness with track displacement.
• What really puzzles me, however, is the fact that they do not see *any* excess, while we know there must be in any case a significant one: decays in flight of charged kaons and pions. Why is it that CDF is riddled with those, while DZERO appears free of them ? To explain this point: charged kaons and pions yield muons, which get reconstructed as real muons with large impact parameter. If the decay occurs within the tracking volume, the track is partly reconstructed with the muon hits and partly with the kaon or pion hits. Now, while pions have a mass similar to that of muons, and thus the muon practically follows the pion trajectory faithfully, for kaons there must be a significant kink in the track trajectory. One expects that the track reconstruction algorithm will fail to associate inner hits to a good fraction of those tracks, and the resulting muons will belong to the “loose” category, without a correspondence in the “tight” muon category which has muons containing a silicon hit in the innermost layer of the silicon detector. This creates an excess of muons with large impact parameter. CDF does estimate that contribution, and it is quite large, of the order of tens of thousands of events in 743 inverse picobarns of data! Now where are those events in the DZERO dataset, then ?

Of course, you should not expect that my limited intellectual capabilities and my slow reading of a paper I have had in my hands for no longer than two hours can produce foulproof arguments. So the above is just a first pass, sort of a quick and dirty evaluation. I imagine I will be able to give an answer to those puzzles myself, at least in part, with a deeper look at the documentation. But, for the time being, this is what I have to say about the DZERO analysis.

Or rather, I should add something. By reading the above, you might get the impression that I am only criticizing DZERO out of bitterness for the failed discovery of the century by CDF… No, it is not the case: I have always thought, and I continue to think, that the multi-muon signal by CDF is some unaccounted-for background. And I do salute with relief and interest the new effort by DZERO on this issue. I actually thank them for providing their input on this mystery. However, I still retain some scepticism with respect to the findings of their study. I hope that scepticism can be wiped off by some input – maybe some reader belonging to DZERO wants to shed some light on the issues I mentioned above ? You are most welcome to do so!

UPDATE: Lubos pitches in, and guess what, he blames CDF… But Lubos the experimentalist is not better than Lubos the diplomat, if you know what I mean…

Other reactions will be collected below – if you have any to point to, please do so.

• Matti Pitkanen
• Marco Dal Mastro”

This morning CDF released the results of a search for narrow resonances produced in B meson decays, and in turn decaying into a pair of vector mesons: namely, . This Y state is a new particle whose exact composition is as of yet unknown, except that CDF has measured its mass (4144 MeV) and established that its decay appears to be mediated by strong interactions, given that the natural width of the state is in the range of a few MeV. I describe succintly the analysis below, but first let me make a few points on the relevance of area of investigation.

Heavy meson spectroscopy appears to be a really entertaining research field these days. While all eyes are pointed at the searches for the Higgs boson and supersymmetric particles, if not at even more exotic high-mass objects, and while careers are made and unmade on those uneventful searches, it is elsewhere that action develops. Just think about it: the baryon, the , those mysterious X and Y states which are still unknown in their quark composition. Such discoveries tell the tale of a very prolific research field: one where there is really a lot to understand.

Low-energy QCD  is still poorly known and not easily calculable. In frontier High-Energy Physics we bypassed the problem for the sake of studying high-energy phenomena by tuning our simulations such that their output well resembles the result of low-energy QCD processes in all cases where we need them -such as the details of parton fragmentation, or jet production, or transverse momentum effects in the production of massive bodies. However, we have not learnt much with our parametrizations:  those describe well what we already know, but they do not even come close to guessing whatever we do not know. Our understanding of low-energy QCD is starting to be a limiting factor in cosmological studies, such as in baryogenesis predictions. So by all means, let us pursue low-energy QCD in all the dirty corners of our produced datasets at hadron colliders!

CDF is actively pursuing this task. The outstanding spectroscopic capabilities of the detector, combined with the huge size of the dataset collected since 2002, allow searches for decays in the one-in-a-million range of branching ratios. The new discovery I am discussing today has indeed been made possible by pushing to the limit our search range.

The full decay chain which has been observed is the following: . That mesons decay to muon pairs is not a surprise, as is the decay to two charged kaons of the vector meson. Also the original decay of the B hadron into the final state is not new: it had been in fact observed previously. What had not been realized yet, because of the insufficient statistics and mass resolution, is that the and mesons produced in that reaction often “resonate” at a very definite mass value, indicating that in those instances the decay actually takes place in two steps as the chain of two two-body decays: and .

The new analysis by CDF is a pleasure to examine, because the already excellent momentum resolution of the charged particle tracking system gets boosted when constraints are placed on the combined mass of multi-body systems. Take the B meson, reconstructed with two muons and three charged tracks, each assumed to be a kaon: if you did not know that the muon pair comes from a nor that two of the kaons come from a , the mass resolution of the system would be in the few tens of MeV range. Instead, by forcing the momenta of the two muons to be consistent with the World average mass of the , , and by imposing that the two kaons make exactly the extremely well-known mass (), much of the uncertainty on the daughter particle momenta disappears, and the B meson becomes an extremely narrow signal: its mass resolution is just 5.9 MeV, a per-mille measurement event-by-event!

The selection of signal events requires several cleanup cuts, including mass window cuts around the J/Psi and phi masses, a decay length of the reconstructed B+ meson longer than 500 microns, and a cut on the log-likelihood ratio fed with dE/dx and time-of-flight information capable of discriminating kaon tracks from other hadrons. After those cuts, the B+ signal really stands above the flat background. There is a total of 78+-10 events in the sample after these cuts, and this is the largest sample of such decays ever isolated. It is shown above (left), together with the corresponding distribution in the candidate mass (right).

A Dalitz plot of the reconstructed decay candidates is shown in the figure on the right. A Dalitz plot is a scatterplot of the squared invariant mass of a subset of the particles emitted in the decay, versus the squared invariant mass of another subset. If the decay proceeds via the creation of an intermediate state, one may observe a horizontal or vertical cluster of events. Judge by yourself: do the points appear to spread evenly in the allowed phase space of the B+ decays ?

The answer is no: a significant structure is seen corresponding to a definite mass of the system. A histogram of the difference between the reconstructed mass of the system and the mass is shown in the plot below: a near-threshold structure appears at just above 1 GeV energy. An unbinned fit to a relativistic Breit-Wigner signal shape on top of the expected background shape shows a signal at a mass difference of , with a width of 11.7+-5.7 MeV.

The significance of the signal is, after taking account of trial factors, equal to 3.8 standard deviations. For the non-zero width hypothesis, the significance is of 3.4 standard deviations, implying that the newfound structure has strong decay. The mass of the new state is thus of 4143+-2.9 MeV.

The new state is above the threshold for decay to pair of charmed hadrons. The decay of the state appears to occur to a pair of vector mesons, , in close similarity to a previous state found at 3930 MeV, the Y(3930), which also decays to two vector mesons in . Therefore, the new state can be also called a Y(4140).

Although the significance of this new signal has not reached the coveted threshold of 5 standard deviations, there are few doubts about its nature. Being a die-hard sceptic, I did doubt about the reality of the signal shown above for a while when I first saw it, but I must admit that the analysis was really done with a lot of care. Besides, CDF now has tens of thousands of fully reconstructed B meson decays available, with which it is possible to study and understand even the most insignificant nuances to every effect, including reconstruction problems, fit method, track characteristics, kinematical biases, you name it. So I am bound to congratulate with the authors of this nice new analysis, which shows once more how the CDF experiment is producing star new results not just in the high-energy frontier, but as well as in low-energy spectroscopy. Well done, CDF!

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.

It was with great pleasure that I found yesterday, in the public page of the DZERO analyses, a report on their new search for Higgs boson decays to photon pairs. On that quite rare decay process -along with another not trivial decay, the reaction- the LHC experiments base their hopes to see the Higgs boson if that particle has a mass close to the LEP II upper bound, i.e. not far from 115 GeV. And this is the first high-statistics search for the SM Higgs in that final state to obtain results that are competitive with the more standard searches!

My delight was increased when I saw that results of the DZERO search are based on a data sample corresponding to a whooping 4.2 inverse-femtobarns of integrated luminosity. This is the largest set of hadron-collider data ever used for an analysis. 4.2 inverse femtobarns correspond to about three-hundred trillion collisions, sorted out by DZERO. Of course, both DZERO and CDF have so far collected more than that statistics: almost five inverse femtobarns. However, it always takes some time before calibration, reconstruction, and production of the newest datasets is performed… DZERO is catching up nicely with the accumulated statistics, it appears.

The most interesting few tens of billions or so of those events have been fully reconstructed by the software algorithms, identifying charged tracks, jets, electrons, muons, and photons. Yes, photons: quanta of light, only very energetic ones: gamma rays.

When photons have an energy exceeding a GeV or so (i.e. one corresponding to a proton mass or above), they can be counted and measured individually by the electromagnetic calorimeter. One must look for very localized energy deposits which cannot be spatially correlated with a charged track: something hits the calorimeter after crossing the inner tracker, but no signal is found there, implying that the object was electrically neutral. The shape of the energy deposition then confirms that one is dealing with a single photon, and not -for instance- a neutron, or a pair of photons traveling close to each other. Let me expand on this for a moment.

Background sources of photon signals

In general, every proton-antiproton collision yield dozens, or even hundreds of energetic photons. This is not surprising, as there are multiple significant sources of GeV-energy gamma rays to consider.

1. Electrons, as well as in principle any other electrically charged particle emitted in the collision, have the right to produce photons by the process called bremsstrahlung: by passing close to the electric field generated by a heavy nucleus, the particle emits electromagnetic radiation, thus losing a part of its energy. Note that this is a process which cannot happen in vacuum, since there are no target nuclei there to supply the electric field with which the charged particle interacts (one can have bremsstrahlung also in the presence of neutral particles, in principle, since what matters is the capability of the target to absorb a part of the colliding body’s momentum; but in that case, one needs a more complicated scattering process, so let us forget about it). For particles heavier than the electron, the process is suppressed up to the very highest energy (where particle masses are irrelevant with respect to their momenta), and is only worth mentioning for muons and pions in heavy materials.
2. By far the most important process for photon creation at a collider is the decay of neutral hadrons. A high-energy collision at the Tevatron easily yields a dozen of neutral pions, and these particles decay more than 99% of the time into pairs of photons, . Of course, these photons would only have an energy equal to half the neutral pion mass -0.07 GeV- if the neutral pions were at rest; it is only through the large momentum of the parent that the photons may be energetic enough to be detected in the calorimeter.
3. A similar fate to that of neutral pions awaits other neutral hadrons heavier than the : most notably the particle called eta, in the decay . The eta has a mass four times larger than that of the neutral pion, and is less frequently produced.
4. And other hadrons may produce photons in de-excitation processes, albeit not in pairs: excited hadrons often decay radiatively into their lower-mass brothers, and the radiated photon may display a significant energy, again critically depending on the parent’s speed in the laboratory.

All in all, that’s quite a handful of photons our detectors are showered with on an event-by-event basis! How the hell can DZERO sort out then, amidst over three hundred trillion collisions, the maybe five or ten which saw the decay of a Higgs to two photons ?

And the Higgs signal amounts to…

Five to ten events. Yes, we are talking of a tiny signal here. To eyeball how many standard model Higgs boson decays to photon pairs we may expect in a sample of 4.2 inverse femtobarns, we make some approximations. First of all, we take a 115 GeV Higgs for a reference: that is the Higgs mass where the analysis should be most sensitive, if we accept that the Higgs cannot be much lighter than that: for heavier higgses, their number will decrease, because the heavier a particle is, the less frequently it is produced.

The cross-section for the direct-production process (where with X we denote our unwillingness to specify whatever else may be produced together with the Higgs) is, at the Tevatron collision energy of 1.96 TeV, of the order of one picobarn. I am here purposedly avoiding to fetch a plot of the xs vs mass to give you the exact number: it is in that ballpark, and that is enough.

The other input we need is the branching ratio of H decay to two photons. This is the fraction of disintegrations yielding the final state that DZERO has been looking for. It depends on the detailed properties of the Higgs particle, which likes to couple to particles depending on the mass of the latter. The larger a particle’s mass, the stronger its coupling to the Higgs, and the more frequent the H decay into a pair of those: the branching fraction depends on the squared mass of the particle, but since the sum of all branching ratios is one -if we say the Higgs decays, then there is a 100% chance of its decaying into something, no less and no more!- any branching fraction depends on ALL other particle masses!!!

“Wait a minute,” I would like to hear you say now, “the photon is massless! How can the Higgs couple to it?!”. Right. H does not couple directly to photons, but it can nevertheless decay into them via a virtual loop of electrically charged particles. Just as happens when your US plug won’t fit into an european AC outlet! You do not despair, and insert an adaptor: something endowed with the right holes on one side and pins on the other. Much in the same way, a virtual loop of top quarks, for instance, will do a good job: the top has a large mass -so it couples aplenty to the Higgs- and it has an electric charge, so it is capable of emitting photons. The three dominant Feynman diagrams for the decay are shown above: the first two of them involve a loop of W bosons, the third a loop of top quarks.

So, how much is the branching ratio to two photons in the end ? It is a complicated calculus, but the result is roughly one thousandth. One in a thousand low-mass Higgses will disintegrate into energetic light: two angry gamma rays, each roughly carrying the energy of a 2 milligram mosquito launched at the whooping speed of four inches per second toward your buttocks.

Now we have all the ingredients for our computation of the number of signal events we may be looking at, amidst the trillions produced. The master formula is just

where is the number of decays of the kind we want, is the production cross section for Higgs at the Tevatron, is the integrated luminosity on which we base our search, and B is the branching ratio of the decay we study.

With , , and , the result is, guess what, 4.2 events. 4.2 in three hundred trillions. A needle in the haystack is a kids’ game in comparison!

The DZERO analysis

I will not spend much of my and your time discussing the details of the DZERO analysis here, primarily because this post is already rather long, but also because the analysis is pretty straightforward to describe at an elementary level: one selects events with two photons of suitable energy, computes their combined invariant mass, and compares the expectation for Higgs decays -a roughly bell-shaped curve centered at the Higgs mass and with a width of ten GeV or so- with the expected backgrounds from all the processes capable of yielding pairs of energetic photons, plus all those yielding fake photons. [Yes, fake photons: of course the identification of gamma rays is not perfect -one may have not detected a charged track pointing at the calorimeter energy deposit, for instance.] Then, a fit of the mass distribution extracts an upper limit on the number of signal events that may be hiding there. From the upper limit on the signal size, an upper limit is obtained on the signal cross-section.

Ok, the above was a bit too quick. Let me be slightly more analytic. The data sample is collected by an online trigger requiring two isolated electromagnetic deposits in the calorimeter. Offline, the selection requires that both photon candidates have a transverse energy exceeding 25 GeV, and that they be isolated from other calorimetric activity -a requirement which removes fake photons due to hadronic jets.

Further, there must be no charged tracks pointing close to the deposit, and a neural-network classifier is used to discriminate real photons from backgrounds using the shape of the energy deposition and other photon quality variables. The NN output is shown in the figure below: real photons (described by the red histogram) cluster on the right. A cut on the data (black points) of a NN output larger than 0.1 accepts almost all signal and removes 50% of the backgrounds (the hatched blue histogram). One important detail: the shape of the NN output for real high-energy photons is modeled by Monte Carlo simulations, but is found in good agreement with that of real photons in radiative Z boson decay processes, . In those processes, the detected photon is 100% pure!

After the selection, surviving backgrounds are due to three main processes: real photon pairs produced by quark-antiquark interactions, compton-like gamma-jet events where the jet is mistaken for a photon, and Drell-Yan processes yielding two electrons, both of which are mistaken for photons. You can see the relative importance of the three sources in the graph below, which shows the diphoton invariant mass distribution for the data (black dots) compared to the sum of backgrounds. Real photons are in green, compton-like gamma-jet events are in blue, and the Drell-Yan contribution is in yellow.

The mass distribution has a very smooth exponential shape, and to search for Higgs events DZERO fits the spectrum with an exponential, obliterating a signal window where Higgs decays may contribute. The fit is then extrapolated into the signal window, and a comparison with the data found there provides the means for a measurement; different signal windows are assumed to search for different Higgs masses. Below are shown four different hypotheses for the Higgs mass, ranging from 120 to 150 GeV in 10-GeV intervals. The expected signal distribution, shown in purple, is multiplied by a factor x50 in the plots, for display purposes.

From the fits, a 95% upper limit on the Higgs boson production cross section is extracted by standard procedures. As by now commonplace, the cross-section limit is displayed by dividing it by the expected standard model Higgs cross section, to show how far one is from excluding the SM-produced Higgs at any mass value. The graph is shown below: readers of this blog may by now recognize at first sight the green 1-sigma and yellow 2-sigma bands showing the expected range of limits that the search was predicted to set. The actual limit is shown in black.

One notices that while this search is not sensitive to the Higgs boson yet, it is not so far from it any more! The LHC experiments will have a large advantage with respect to DZERO (and CDF) in this particular business, since there the Higgs production cross-section is significantly larger. Backgrounds are also larger, however, so a detailed understanding of the detectors will be required before such a search is carried out with success at the LHC. For the time being, I congratulate with my DZERO colleagues for pulling off this nice new result!

Three weeks ago the DZERO collaboration published new results of their low-mass Higgs boson search. This is about the production of Higgs bosons in association with a W boson, with the subsequent decay of the Higgs particle to a pair of b-quark jets, and the decay of the W to an electron-electron neutrino or muon- muon neutrino pair: in symbols, what I mean is , or . I wish to describe this important new analysis today, but first let me make a point about the reaction above.

In order to make this blog more accessible than it would otherwise be, I frequently write things inaccurately: precision is usually pedantic and distracting. But here I beg you to please note a detail I will not gloss over for once: to be accurate, one should write …, because what we care for is inclusive production of the boson pair. If we omit the X, strictly speaking we are implying that the two protons annihilated into the two bosons, with exactly nothing else coming out of the collision. While that reaction is possible, it is ridiculously rare -actually, the annihilation into ZH is possible, while the one into WH does not conserve electric charge and is strictly forbidden. Anyway, bringing along a symbol to remind ourselves of the fact that our projectiles are like garbage bags, which fill our detectors with debris when we throw them at one another, is cumbersome and annoying, while accurate. I hope, however, you realize that this is an important detail: Higgs bosons at a hadron collider are always accompanied by debris from the dissociating projectiles.

Two words on associated WH production and its merits

The associated production of the Higgs together with a W boson is the “golden” signature for low-mass Higgs hunters at the Tevatron collider. While producing the Higgs together with another heavy object is not effortless (you are required to produce the collision with more energetic quarks in the two colliding protons, and this makes the production less frequent), the W boson pays back with extra dividends by producing a very clean signature in its leptonic decay, and by allowing the event to be spotted easily by the online triggering system, and collected with high efficiency by the data acquisition.

If you compare the collection of WH events to the collection of directly produced Higgs bosons (, where again I prefer accuracy by specifying the X), you immediately see the advantage of the former: while their production rate is four times smaller and the leptonic W decay only occurs 20% of the times, this 0.25 x 0.2=0.05=1/20 reduction factor is a small price to pay, given the trouble one would have triggering on direct events: the decay to a pair of b quarks is the dominant one for low Higgs boson masses, but the common nature of b-jets makes it unobservable.

Higgs decays to b-quark pairs produced alone simply cannot be triggered in hadronic collisions, because they are immersed in a background which is six orders of magnitude higher in rate, namely the production of bottom-antibottom quark pairs by strong interactions. Even assuming that the online triggering system of DZERO were capable of spotting b-quark jet pairs with 100% purity (which is already a steep hypothesis), the trigger would have to accept a million background events in order to collect just one fine signal event !

Yes, life is tough for hadronic signatures at a hadron collider. Even finding the signal, which is a thousand times more frequent, is a tough business -it took CDF years to find a reasonable sample of those decays, while DZERO has not yet published anything on the matter. But the Tevatron experiments cannot ignore the fact that, if a low Higgs mass is hypothesized, the decay is the most frequent: the Higgs boson likes to decay into the heaviest pair of particles it can produce. If the total mass of a pair of W bosons or Z bosons is too heavy, the next-heaviest pair of decay products is b-quarks. This dictates the need to search for , and the trouble of triggering on such a process in turn makes the associated WH (or ZH) production the most viable signal.

The DZERO analysis

The new analysis by DZERO studies a total integrated luminosity of 2.7 inverse femtobarns. This corresponds to 150 trillion proton-antiproton collisions, but DZERO has netted almost twice as much data already by now, and it is only a matter of time before those too get included in this search: so one has to bear in mind that the statistical power of the data is soon going to increase by about 40%: the data increase corresponds to an increase in precision by the square root of two, or a factor of 1.41.

DZERO selects events which have an electron or a muon with high energy -the tag of a leptonic decay of the W boson-, missing transverse energy, and two or three hadronic jets. The presence of a energy imbalance in the plane transverse to the beam direction is a comparatively clean signature of the escape of the energetic neutrino produced together with the charged lepton by the W decay, and two jets are expected from the decay of the Higgs boson to a pair of b quarks. However, you might well ask, quid opus fuit tertium ?

No, I bet you would not ask it that way -for some reason, a reminescence of Latin sprung up in my mind. Quid opus fuit tertium – What is the matter with the third one ? The third jet is not specifically a signature of any one of the decay products of the WH pair we are after. However, if you remember what I mentioned above, we are searching for inclusive production of a WH pair: that means we accept the fact that the two projectiles also produced an additional energetic stream of hadrons in the final state. That possibility is by no means rare, and in fact it amounts to about 20% of the Higgs production events. By selecting events with two or three jets, DZERO increases its acceptance of signal events sizably.

A technique which has become commonplace in the hunt of elusive subnuclear particles is to slice and dice the data: categorizing events in disjunct classes is a powerful analysis strategy. By taking two-jet events on one side, and three-jet events on the other, DZERO can study them separately, and appreciate the different nuisances of each class. In fact, they further divide the data into subsets where one jet was tagged as a b-quark-originated one, or two of them were.

And they also keep separated the electron+jets and the muon+jets events: this also does make sense, since the experimental signatures of electrons and muons are slightly different, as are the resulting energy resolutions. In total, one has eight disjunct classes, depending on the number of jets, the number of b-tags, and the lepton species.

In order to decide whether there is a hint of Higgs bosons in any of the classes, backgrounds are studied using Monte Carlo simulations of all the Standard Model processes which could contribute to the eight selected signatures. These include the production of a W boson plus hadronic jets (“W+jets“) as well as the production of top quark pairs: both these processes produce energetic leptons in the final state; but another background is due to events which do not actually contain a lepton, and where a hadronic jet was mistook for one. The latter is called “QCD background” highlighting its origin in strong interaction processes yielding just hadronic jets: despite the rarity of a jet faking a energetic lepton, the huge rate of QCD events makes this background sizable.

Among the characteristics that can separate the WH signal from the above backgrounds, the identity of the parton originating the hadronic jets is a powerful one: b-jets are more rare than light-quark ones, but there must be two of them in a decay. DZERO uses a neural network which employs seven discriminating variables to select jets with a likely b-quark content.

The good thing with a neural-network b-tagger is that the output of the network can be dialed to decide its purity. And in fact, DZERO does exactly that. They start with a loose selection which has a rate of “false positives” of 1.5% (light-quark jets that are classified as b-tagged). If two jets have such a loose b-tag, the event is classified as a “double b-tag”; otherwise, the NN output requirement is made tighter, and “single-b-tag” events are collected by requiring that the b-tag has a better purity, with a “false positive” rate of 0.5%. These cuts have been optimized for their combined sensitivity to the Higgs signal.

Apart from b-tags, the signal displays a different kinematics than all backgrounds. Again, seven variables are used, which now describe the event kinematics: the transverse energy of the second-leading jet, the angle between jets, the dijet invariant mass, and a matrix-element discriminant, which is computed by comparing the probability density of the quadrimomenta of the objects produced in the decay in a WH event to that of backgrounds. In the figure above, the matrix element discriminant is shown for all the processes contributing to the class of W+2jet events with two b-tags. The output of the neural network shows that Higgs events fall in the right-side of the distribution, while backgrounds pile up mostly on the left, as can be seen in the figure below.

Results of the search

Since no signal is observed in the NN output distribution seen in the data, DZERO proceeds to set upper limits on the signal cross-section. For 2-jet events they use the NN output is used, while they use the dijet mass distribution for the 3-jet event classes. No justification is provided in their paper for this choice, which looks slightly odd to me, but I imagine they have done some optimization studies before taking this decision. However, I would imagine that the NN output is in principle always more discriminant than just one of the variables on which the network is constructed… Maybe somebody from DZERO could clarify this point in the comments thread, to the benefit of the other readers ?

At the end of the day, DZERO obtains limits on the cross section of the searched signal, which are still above the standard model predictions whatever the Higgs mass: therefore, they do not provide an exclusion of mass values, yet. These results, however, once combined with other results from CDF and DZERO, will one day directly imply that a SM Higgs cannot exist, if its mass is in a specified range. In the graph below you can see the limit set by this analysis on the WH production cross-section as a function of Higgs mass.

The black curve shows the 95% exclusion, while the hatched red curve shows the result that DZERO was expecting to find, based on pseudoexperiments. The comparison of the two curves is not terribly informative, but it does show that there were not surprises from the data.

The result can also be shown in the standard “LLR plot” above, which is showing, again as a function of the Higgs boson mass, the log-likelihood ratio of two hypotheses: the “background only” and the “signal+background” one. Let me explain what that is. For each mass value on the x-axis, imagine the Higgs is there. Then, with large statistics, the data would show a propension for the “signal plus background” hypothesis, and the LLR would be large and negative. If, instead, the Higgs did not exist at any mass value, the LLR would be large and positive. The two hypotheses can be run on pseudo-data of the same statistical power as the data really collected, thus producing the red and black hatched lines in the plot below. The two curves are different, but the red one does not manage to depart from the green band constructed around the black hatched one: that means that the data size and the algorithms used in the analysis do not have enough power to discriminate the two hypotheses, not even at 1-sigma level (which is the meaning of the width of the green band, while the yellow one shows two-sigma contours). The full black line shows the behavior of real data: they have a propension of confirming the background-only hypothesis at low mass, and a slight penchant for the signal+background one at about 130 GeV. But this is a really, really small fluctuation, well within the one-sigma band!

I think the LLR plot is a great way to describe the results of the search visually. It at once tells you the power of the analysis and the available data, and the outcome on the real events collected. Now, it takes twenty thick lines of text to explain it, but once you’ve grabbed its meaning…

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.

I wish 2009 will bring an answer to a few important questions:

• Can LHC run ?
• Can LHC run at 14 TeV ?
• Will I get tenure ?
• Are multi-muons a background ?
• Are the Pamela/ATIC signals a prologue of a new scientific revolution ?
• Will England allow a NZ scientist to work on Category Theory on its soil ?
• Is the Standard Model still alive and kicking in the face of several recent attempts at its demise ?

I believe the answer to all the above questions is yes. However, I am by no means sure all of them will be answered next year.

NB: This post is aimed at physicists.. However if you are not one, but you are really curious, you might find out that for once the annoying feeling of reading cryptic jargon is paid back by some real news!

I guess the most important message of the post you are about to read is: Do not check the arxiv today if you really cannot spend a couple of hours reading. Make it three. The  paper just released by CDF, titled “Study of multi-muon events produced in ppbar collisions at sqrt(s)=1.96 TeV” is guaranteed to have you fastened to the chair until you are done with its 70 pages.

The article reports on a very careful investigation produced by CDF, using Run II data collected by a trigger selecting events with two (or more) muons of low transverse energy. The study addresses two or three long-standing inconsistencies in measurements of bottom quark production and phenomenology at the Tevatron:

• the cross section for production appears in good agreement with next-to-leading order QCD predictions when b-quarks are tagged by a reconstruction of their decay vertex, while it is found to be significantly larger when the cross section is measured by identifying b-quarks through their semileptonic decay;

• the invariant mass spectrum of pairs of leptons produced in sequential semileptonic decays () is not well modeled by the simulation of b-flavored hadrons in CDF;

• the value of the time-integrated mixing probability of b flavoured hadrons is measured at the Tevatron to be significantly larger than that measured by LEP experiments.

The source of these apparently unrelated inconsistencies is traced back by the study to a sample of events where muons are originated several centimeters away from the primary interaction point (the proton-antiproton collision vertex), which makes b-quark decay as implausible a source as any other Standard Model process, no better than the other backgrounds which the study shows to be insufficient explanation for the observed events: punch-through from pions and kaons, or secondary hadronic interactions in the detector material.

Once a large sample of such weird events are statistically isolated -better say evidenced- in the sample, a further anomaly is found in the number of additional muons contained in narrow cones around the original ones, something which cannot be easily explained with conventional physics. The paper discusses the characteristics of these events, without falling in the trap of putting together an exotic explanation. Instead, what is made clear in the paper is that those measurements quoted above -lepton-based cross sections and phenomenology of b-quarks studied in high-energy hadron collisions- are affected by the findings described in this paper.

Below I offer two plots extracted from the preprint. The first one shows the impact parameter distribution of muons in the events constituting the anomalous signal (black points), compared to the impact parameter of muons attributable to QCD sources (in red). The impact parameter resolution for these tracks is 2.5 times smaller than the bin size. One observes a abnormal tail of muons with very large impact parameter. I recall that the impact parameter, which is measured in the plane transverse to the beam direction, is the distance of closest approach of the backward extrapolation of the track to the primary interaction vertex. A impact parameter of one centimeter is huge, given that the typical decay length of a B meson is of the order of a pair of millimeters.

On the right you see an exponential fit to the impact parameter distribution of the trigger muons for the anomalous events, for events with just two (top) or more than two (bottom) muons inside two narrow cones around the trigger muons. The distribution agrees with the decay of a particle with a lifetime in the 20 picosecond range.

To quote the paper, the first lines of the Introduction offer a quite clear picture of the situation:

“This article presents the study of events, acquired with a dedicated dimuon trigger, that we are currently unable to fully explain with our understanding of the CDF II detector, trigger, and event reconstruction. We are continuing detailed studies with a longer timescale for completion, but we present here our current findings.“

The conclusions are also clear, but I will leave them to those of you who want to read a paper which might, just might, constitute the first evidence of physics beyond the Standard Model, ever.

That said, if you have read this blog long enough, you know me for a tough sceptic. I of course would be simply delighted if the CDF signal of multi-muons really were a first evidence for new physics; but I have to play the devil’s advocate, and so one word of caution, make it five paragraphs, is mandatory. Of course, despite the evidence is pretty solid from a statistical standpoint, one must lean back and take a breath. We are discussing the possibility that something really spectacular has just lurked out of CDF data. Extraordinary claims require extraordinary evidence, and once statistical evidence is plain, one must delve with systematics. CDF did, and they have not found any significant source which might account for the effect. But investigations should and will continue.

Is CDF sure about the impossibility of explaining this effect away ? No, CDF does not exclude that possibility, although it is my opinion that the collaboration has reviewed the paper with more care and detail than most of the other papers it has published in its illustrious, 25-year-long life. That means nothing in terms of the likelihood that this result is indeed new physics. It just says we are as sure as we can be that we cannot presently explain it with known sources. Also worth mentioning is that CDF is a really disciplined collaboration, which has really been careful with their claims so far. And the present paper is no exception.

Is there a simple New Physics explanation of the observed effect ? No, as far as I understand no existing model of new physics predicted such a signature in advance, although one must acknowledge that a few ideas exist in the literature which might have a connection with the effect, if proven real. However, there is a paper discussing a similar signature, which probably benefitted from knowing the CDF result in advance from an internal source. I will leave this issue to another time and another place.

Can CDF find more evidence in the near future ? Yes, the analysis of electron events may shed more light on the matter, and although electrons are harder to isolate than muons when they have a low energy, the analysis will be carried out.

Can D0 find a similar signal ? Surely. D0 is a similar detector to CDF, and although their charged particle tracking is slightly inferior to CDF’s, their muon system is more extended, and their silicon detector is also at least as good as that of CDF (ok, even slightly better). The problem with D0, I think, is the time it will take to perform such a complicated analysis. One must not forget that before focusing on these anomalous events, CDF produced a lengthy investigation of the correlated cross section, which is the back-bone of the multi-muon analysis, since it demonstrates the understanding of heavy flavors in low-transverse-momentum lepton samples in CDF when particles with large impact parameter are excluded. So, it may take a while to D0 to confirm or disprove the effect CDF is now publishing.

Does the signal hint at other anomalies in different analyses ? That, I am sorry to say, is anybody’s guess. If the multi-muon events are a signal of new physics, then I am sure there is something else to be found, somewhere. The problem is: what is that ? One might be tempted to speculate that data samples collected in past experiments could in principle contain a similar signature: charged tracks with very large impact parameter have been seldom studied at colliders, and tracking algorithms might have purposely discarded those tracks, or could be proven inefficient in their collection. For instance, CDF does collect, with its fantastic SVT trigger, events containing tracks showing a significant impact parameter. However, the efficiency with which the SVT collects those events, if studied as a function of impact parameter, dies out much too soon. Hell, nobody designs a detector aimed at collecting a new physics signature no theorists have thought about!

I imagine hordes of theoretical physicists canceling flights, conferences, and courses today, making room for some serious thinking in their agendas. Good luck!

UPDATE: see the interesting discussion developing at Peter Woit’s site, where he points out a paper by Arkani-Hamed and collaborators which appears quite extraordinarily to have foreseen the above signature of new physics, in a very timely fashion!

UPDATE: there are other bloggers who’ve discussed this. Lubos, Carl, Matti (happy birthday Matti). Others to be added soon…

UPDATE: other excellent, entertaining bloggers have added their own comments to the story: Jester, Chad, theorema egregium. In italian: Marco. In dutch: astroblogs.

UPDATE: John, a fellow collaborator in CDF and one very skilled physicist, explains the result at cosmic variance.

New heavy bosons are predicted by several models of physics beyond the standard model. In particular, heavy versions of the Z° boson, called generically Z’ but sometimes distinguished by greek subscripts (, , etc.), might constitute the quickest route to a discovery of superstring-inspired E6 models; and also Kaluza-Klein spin-2 gravitons may appear as a Z’. I won’t describe what those models are about (and besides, I am not the best person to do that), but just mention that many of my colleagues pin their hopes of finding new physics on just such a signature: the production of a new Z’ boson, with its decay to a pair of charged leptons. A pair of muons of several hundred GeV, for instance, is a great discovery channel, because muons cannot easily be mistaken with other final state particles -all collider detectors have an outer shell of drift chambers specifically designed to detect muons, in fact, exploiting the high penetrating power of these particles.

With only a few days separating us from the official start of LHC operations, it is now as good a time as any to take stock with respect to the experimental situation with the search for Z’ bosons. A recent result by CDF, based on 2.3 inverse femtobarns of proton-antiproton collisions produced by the Tevatron accelerator, has pushed the lower limit for the mass of these particles above the TeV. Interestingly, one TeV was a reference point good enough for CMS and ATLAS to produce expectation plots in their technical design reports. Take CMS, for instance: the expected dimuon mass spectrum after just 100 inverse picobarns (about ten times the data that LHC will collect this fall) would present a very narrow, distinctive peak of about 18 events, as shown by the empty histogram over the sharply falling background (shown by the green histogram).

The graph above would be a unmistakable evidence for the production of a new massive neutral particle. Unfortunately, we now know it’s just not going to happen. The CDF result excludes a Z’ boson with mass below 1030 GeV. The analysis is straightforward: having noticed that the mass is measured with the momenta of the two muons, which are obtained from their curvature in the 1.4 Tesla magnetic field, one finds that the mass resolution degrades significantly with dimuon mass, but if one plots the inverse of the mass, this has a fixed relative resolution, making it much easier to search for a signal of unknown mass in a wide range. The data (blue points) is shown in the plot below.

From the very good agreement of all data points with the expectation -which is due to the sum of electroweak production of muon pairs through the so-called Drell-Yan mechanism (yes, that includes the regular Z° boson decay) and background processes due to QCD- it is not too hard to extract direct lower limits on the cross-section times branching-ratio of . These are shown below (the red curve) as a function of the hypothetical Z’ mass.

The plot is busy as much as it is colorful. First off, ignore the stretched Brazil flag, and only look at the red curve. That is the upper limit on the cross section, at 95% Confidence Level. That is the result of trying to fit a signal in the histogram of inverse masses, which does not seem to contain any. At 1 TeV, the limit is set at 3.5 femtobarns. Since a SM-like Z’ would have a 4.5 femtobarn cross section, such a particle is excluded. All mass values above 1030 GeV are instead still possible.

The “brazil flag” is then just a prediction of the cross-section limit that CDF could set, a priori computed using the analysis methodology, before looking at the data. The red line wiggles around but stays within the 1-sigma band (yellow).

The phase space of new physics continues to shrink, without any real hint from collider data of the SM becoming inadequate…