A Quantum Diaries Survivor

Since I am currently preparing the slides of the talk I will give next week at PPC2008, a conference being held in Albuquerque on the interconnection between particle physics and cosmology, I have my hands full with material that would be perfect for this blog. The talk is a review of new results from the CDF experiment, and there is literally a ton of them! What makes it hard for me is to sort out the stuff that i  really the very best and most worthy of being shown at the particular event.

I am however not posting here direct CDF results, but rather a plot that my friend Sven Heinemeyer was kind to produce according to my directives, which I meant to allow me to summarize in my talk the status of electroweak fits by separating the main contributions of experimental measurements. In the graph below, showing the dependence of the Higgs boson mass on the value of W boson and top quark masses, you can see several different regions highlighted with black, blue, and magenta lines. The black lines bracket the LEP II determination of the W mass; the blue ellipse describes the Tevatron measurements of the two parameters, and the magenta hatched “wing profile” area shows the allowed values of the two quantities according to electroweak fits performed using LEP I and SLD determinations of electroweak parameters.

Also shown in the plot is the SM-allowed range (in red), where the Higgs boson has a mass varying between the lower LEP II limit of 114.4 GeV (upper border of the red hatched area) and 400 GeV (lower border), and the SUSY allowed region (hatched green), which shows the zone allowed by different choices of some of the many SUSY parameters, in particular the mass of supersymmetric particles.

Now, let me make a few points on the plot above.

1. Although precise, the indirect experimental input shown in the plot is still incapable of discriminating between SM and SUSY - and it probably never will by itself, since LHC will soon rule out or find SUSY before it shrinks the ellipse sizably (ok, ok, I am neglecting the possibility of split SUSY…)
2. the celebrated LEP I / SLD data looks obsolete from this particular vantage point, in light of the more recent direct measurements; this would however be an unfair interpretation, given that electroweak fits have many more parameters than just W and top quark masses.
3. The LEP I / SLD data is obsolete as far as the top quark is concerned: in the plot it does not even appear to constrain it if compared with the ultra-precise (+-0.8%) Tevatron determination!
4. The top quark mass has been bouncing up and down a bit, although always well within errors, in the last 5 years, from 178 to 170 to 172.4 GeV. This has slightly moved up and down the preferred value of fit Higgs mass in the SM. However, as the ellipse shrinks, this is becoming less of an issue. In fact, to justify the effort of producing the best possible top mass measurement, we used to say that a 1 GeV precision on the top mass was equivalent to a 7 MeV precision on the W mass as far as the knowledge we would obtain on MH was concerned, based on the slope of the Higgs contours in the plot above. Now that the error on top mass is well below 2 GeV, however, it becomes clear that we will not gain much knowledge by increasing the precision much further. The W mass has become one of the main players in the game of precision SM fits now!
5. The ellipse includes 68% of the area of the two-dimensional gaussian centered on the Mw-Mt determination, just as much as the black bars do, but being two-dimensional it is deceiving: the single most precise determination of the W boson mass is in fact from CDF, and Tevatron and LEP II are basically at the same level of precision on that quantity!

Why is the comparison deceiving ? Because if you have one single quantity, you determine the 68% interval by integrating a gaussian distribution from its center outwards, until you “cover” 68% of its total integral (from -inf to +inf). If you add a dimension to your single-variable gaussian, and make it a two-dimensional gaussian shape, the 68% bounds remain the same unless you integrate by expanding an ellipse, rather than a band, around the center. The ellipse encompasses values of the 2-dimensional distribution which have the same “probability”, but in so doing it “cuts the corners”, and to total a 68% of the 2-dim integral it now has to extend past the one-dimensional 68% boundaries in each of the two variables. A sketch will clarify matters:

Well, not exactly “clarified”… But I have no time to make the graph easier to understand. The point is that the ellipse “cuts” only a part of the band in each direction, and so the integral of the 2-dimensional curve it comprises is much smaller than the band. To make the ellipse include 68% of the 2-dimensional distribution constructed with the two gaussian curves, one has to widen it to a roughly double size.

So, paradoxically: if LEP II had a determination of the top quark mass too, the band bracketed by the two black lines in the plot by Heinemeyer would convert into an ellipse which would be about as wide in the vertical direction as the Tevatron blue ellipse.

Not convinced ? Oh well. Think at it this way: with a single measurement of the W mass, you say “the probability that the mass is between 80.35 and 80.45 GeV is 68%, because I determined it to be 80.4 and I have an error of 0.05 GeV”. Fine: the gaussian distribution, if integrated from -1-sigma to +1-sigma, provides 68% of its total normalization. The same goes if you claim that, having measured the top mass at $172.4 \pm 1.4 GeV$, there is a 68% chance that it lies in the interval 171-173.8 GeV. However, if you ask what is the probability that the W mass is between 80.35 and 80.45 GeV AND the top mass is between 171 and 173.8 GeV, this is much smaller than 68%, because independent probabilities multiply each other: it is, in fact, only 46.2%; but this corresponds to the square drawn around the circle in the graph! The probability that the two values lie in the ellipse with major axes equal to 1-sigma band widths is (if I recall correctly) about 37%.

The bottomline? Whenever you look at a plot with two measurements, one described by an ellipse and the other by a band, always regard the ellipse with more respect than it seems to deserve!

Jeff pointed out to me today the remarkable world wide telescope, a site where you can download a software created by Microsoft to browse the heavens as if you were commanding a powerful telescope. The constellations are not maps, but actual pictures, into which you can zoom as much as the images of the digital sky surveys (SDSS and others) allow.

My jaw dropped as I started using the software, which you can download and install on your computer, and which works pretty much like google Earth - downloading the region you are visualizing from the internet. A nice feature is the appearance of a frame of thumbnail pictures around the zoomed area, highlighting the most interesting celestial objects present there. If you click once on each pic the relevant object is highlighted on the map; clicking twice will allow you to download full-resolution image of the object directly from the online databases, including Hubble images.

What I find amazing, however, is the fact that browsing the night sky becomes a thrilling experience at your fingertips in front of the computer. The realism is perfect - these are pictures, in pure google earth style. However, while we never have the need to find a feature on the Earth surface by hovering over it in our real life, that is exactly what we do when we observe the night sky: so the learning experience provided by the program for a user who wants to get better at locating celestial objects is invaluable.

Above you can see a screenshot of part of the WWT window, which I centered on the Deer Lick group of galaxies - NGC7331, a milky way-like galaxy which is the largest member of the group, is on top. Below you can see Stephan’s quintet - a group of five small galaxies of 13th-14th magnitude which is among my favorite targets in deep-sky observing sessions. By zooming in (below), you get to see stars fainter than 18th magnitude, at a resolution comparable to that of  a meter-class instrument. Amazing!

I highly recommend downloading the software. Learning to locate objects will become a wonderful pastime!

Just a link to a post by Gianandrea Giacoma on the site of the sci.bzaar.net workshop, an event about which I wrote here, here and here.

In the post, Gian uses very kind words to introduce a video on my thoughts on the need of horizontality in scientific blogs. I already posted a link to my video yesterday (beware, it is in Italian - I will try to find the time for an English version though, or at least provide a transcript in English), but the one on the sci.bzaar.net site does not need to be downloaded before playing - a huge bonus since you might get bored halfway through (oh well, damned if you do. It’s just 7 minutes).

Today we had our meeting of the CMS analysis group in Padova, a monthly recurrence where we get adjourned of the various efforts going on. It was my turn to chair the meeting (I am co-convener of the meeting with Ezio Torassa and we alternate), and I had put together a tightly packed agenda, which included updates on the global cosmic runs (weeks of data taking when muons from cosmic rays are collected and used to understand the detector response), the tracker checkout (issues with the final commissioning of the silicon tracker), the trigger studies for SLHC (or how to measure muon momenta accurately enough to prevent being overwhelmed by the huge rate of fake muons of low transverse momentum, when we will take data with CMS at a luminosity of ), plus analyses of the decay, ttH production, and dimuon mass spectra.

Ignazio Lazzizzera, from the associated group of Trento, presented some kinematical distributions of muon tracks extracted from minimum bias Monte Carlo that will be used for SLHC studies. Minimum bias is a jargon that particle physicists use to describe events that withstood no selection whatsoever: events which suffered the minimum possible bias by the fact of having been collected by the detector. Such a collection of events is useful to understand what our “priors” are: at the full LHC luminosity (just a factor 10 below SLHC ones), every 25 nanoseconds we will have 20 proton-proton collisions to deal with, and only very rarely these interactions originate a high-momentum muon, which tags a potentially very interesting event. We have to rely on these minimum bias simulations to understand how easy it is for a light hadron -a pion or a kaon- to fool our detection system and be identified as a muon by our trigger, if we want to understand our chances of tuning trigger cuts and select good muons with high efficiency without being drowned in impossibly high rates from fake muons.

As Ignazio showed the plot below, which is the distribution of rapidity of simulated muon tracks in minimum bias data, I jumped on my chair. What was going on ? The two-humped distribution resembled a camel’s back!

To let you understand why such a distribution is unphysical, I need to take a step back. When you collide protons with other protons at high energy, what you are actually doing is creating hard interactions about proton constituents: quarks and gluons. Each of these constituents of a high-energy proton carries a fraction of the proton momentum: the two streams of “partons” (i.e. quarks or gluons) travel together in the positive and negative direction along the z axis - the beam direction- inside each proton; but some carry a larger, and many a smaller fraction of the total protons momentum.

Because of the variable amount of momentum carried by each parton, the collision center-of-momentum reference frame is not at rest in the detector reference frame: if a 90mph truck hits a 50mph compact car head on the debris will fly away following the truck direction!

What governs the probability that quarks and gluons carry a certain momentum fraction of the proton containing them are some functions called “Parton Distribution Functions“. They are shown below for the different constituents of protons.

As you see, it is increasingly probable (in a measured described by the PDF xf(x)) to find a parton carrying a smaller and smaller momentum fraction x (forget the u-distribution, which has a local maximum due to valence quarks: we are discussing the low-x tail of these shapes, since we are discussing not-so-high-energy interactions which constitute the bulk of collisions). Is this enough to figure out what will be the distribution of the debris, and in particular, the motion of the most energetic particles produced in the collision in the detector frame ?

Well, basically yes. If we label the momentum fractions of the colliding partons (which can be assumed massless for all practical purposes at LHC), the center-of-mass energy will be their geometric average times the 14 TeV globally possessed by the colliding protons. The motion of the center-of-momentum frame in the detector frame will instead be described by rapidity - the quantity , which reduces to .

Rapidity is, for the muons, the quantity plotted in the two-humped histogram above. Can there be a hole at zero in this distribution ? Not really! It does not take complicated math to realize that if you pick at random two values from a monotonous function, their values are most likely to be close to each other, and so their ratio will be close to one more often than not. The logarithm of one is zero, and at zero there cannot be a minimum! The distribution has to have a single maximum at zero rapidity instead!

You might find the above reasoning rather complicated. It is. However, had you worked at a hadron collider for 16 years, you would not need the math at all: the rapidity distribution of any physics process is (with very few exceptions) a broad distribution with a maximum at zero, unless the data have been biased by selection cuts.

I could thus explain what was going on in the distribution Ignazio was showing: the data he was plotting had been stripped of events which could fire the CMS trigger -that is, events with high-Pt, central muons in our case. Take a dromedar, substract stuff in the middle (the muons which are central), and you are left with a camel!

It remains to be seen why the minimum bias Monte Carlo had been selected this way. I suppose one such sample is rather useless for trigger studies!

On Saturday, May 15th, a conference called “sci.bzaar.net” will take place in Milano. It will bring together a restricted group of researchers, psychologists, bloggers, designers, physicists, writers, philosophers, computer scientists and web experts, who will discuss scientific divulgation, production of knowledge, and open culture in the academic world.

I will not be there in person, but a video I produced for the event will be shown - and I will connect with skype or some other means to take questions. You can see the agenda of the workshop here.

In addition, I produced for the web site of the event another short video where I discuss the importance of horizontality in a blog aimed at scientific divulgation. Unfortunately, I only have a version in Italian so far (the event is aimed at an italian public). I will paste below a writeup as I have the time, but if you are interested you can see me in the 7-minutes video here (beware though, it is kind of heavy - 500 Mbytes!).

Here is an excerpt of the latest LHC schedule for the following few months, as agreed in a meeting at CERN chaired by the Director-General, with the experiments and LHC machine heads.

Based on the good progress for the cool down of the LHC sectors, and on the powering tests from two sectors, the following planning was arrived at:

1. End of June: The LHC is expected to be cooled down. [...]
2. Mid of July: The experimental caverns will be closed [...]
3. End of July: First particles may be injected, and the commissioning with beams and collisions will start.
4. It is expected that it will take about 2 months to have first collisions at 10 TeV.
5. Energy of the 2008 run: Agreed to be 10 TeV. The machine considers this to be a safe setting to optimize up-time of the machine util the winter shut-down (starting likely around end of November).[...]
6. The winter shut-down will then be used to commissioning and train the magnets up to full current, such that the 2009 run will start at the full 14 TeV design energy.

The above means that the machine will deliver collisions from the end of September on, for at most nine weeks in 2008. More safely, one can assume 6 full weeks of data-taking. What luminosity do we expect to collect ?

A state-of-the-art estimate was made by a colleague, who used his past experience with LEP as well as the information on the current limitations of the RF system -which will make the proton bunches shorter than planned (RMS of 5.4 cm), and with a transverse size of 46 microns. At the lower energy the low-beta squeeze will also be loosened from 2 to 3 meters. These figures reduce the instantaneous luminosity, and the estimate for 6 weeks of collisions are of about 40 inverse picobarns of data in 2008.

If ATLAS and CMS will be fully on during the weeks of collisions, these 40 inverse picobarns will fruit, in my opinion:

• A top pair production cross section with 10-15% accuracy
• A sizable sample of vector boson decays to leptons, very useful for calibrations and checks of lepton efficiency studies
• The first estimates of b-tagging and tau-tagging capabilities of current algorithms
• no information on the Higgs
• no SUSY discovery (of course!)

All the above will have a chance of being ready for the 2009 winter conferences, if all goes well…

Here is a selected list of interesting links from blogs I read:

• Bee at Backreaction has the most complete list of reasons why you should not be bothered by the LHC destroying the Earth. Instructive, entertaining, to the point. With useful furthering of the matter in the comments thread.
• Peter at Not Even Wrong has two interesting posts out. In one he reports about Witten’s take on dark energy. In the other the question on what string theorists would do if their pet theory was proven wrong is discussed. Don’t miss the comments thread.
• Carl at Mass explains in detail why the current cosmology does not explain the angular correlations in the fluctuations of cosmic microwave background for large angles, while a changing speed of light would fit the data better. Controversial!
• Lubos at the Reference Frame discusses whether a theory that makes no predictions is to be preferred or disfavored, in relation to one that is more predictive. He also has a poll. Let’s all ask him to add a bullet, “A and B are equally unlikely because they are both favored by Lubos”,
• Jester at Resonaances has a short but poignant post on how to be a good crackpot. Recommended.
• Kea at Arcadian Functor has reached lesson 182 in category theory. Her explanations make you believe you know those things, and there are a bunch of graphs you cannot miss. Esthetically pleasing.
• Chad at Uncertain Principles has one of his imperdible dog dialogues out. Highly recommended.

Long overdue, here is the final part of a long post on the searches for new particles that may be the solution of a long-standing problem in astrophysics today: the missing mass in our Universe.

The large majority of cosmologists have become convinced, through the analysis of masses of data collected in the last two decades, that four-fifths of the matter in the Universe is non-baryonic. If we neglect particles which can only be created in high-energy collisions and decay in ridiculously small amounts of time, Baryons exists in just two forms: protons and neutrons. These make up the nuclei of atoms, and provide the fuel for stars to shine as they fuse into helium nuclei.

Non-baryonic matter does exist, and we know it well: we have electrons and neutrinos; but these are irrelevant. Electrons weigh less than a thousandth of a proton -and there are just as many electrons as protons around, to a very good approximation. As for neutrinos, despite our ignorance on their mass, they cannot make up the deficit of mass observed in the rotation speed of galaxies (exhibit one in support to Dark Matter: the speed of rotation does not decrease as much as it should if their mass was concentrated in stars) or in clusters of galaxies (exhibit two: gravitational effects we may detect visually do not match the observed distribution of galaxies in these agglomerates).

One intriguing solution to the problem lies in hypothesizing that a massive particle called neutralino wanders around in huge amounts, slow and unbothered by its close encounters with ordinary matter. Neutralinos would be electrically neutral, they would not interact strongly with matter, and they would be perfectly stable, lest they violate a very convenient quantum-mechanical conservation law. For more details on these hypotheses, see part II of this post.

So how can collider experiments detect this evanescent particle ? By producing pairs of higher-mass supersymmetric particles, which would chain-decay into non-supersymmetric ones plus a pair of those lightest supersymmetric particles, LSP. On the right you can see a decay chain whereby a gluino - a SUSY particle produced in large amounts in hadron collisions, due to its strongly interacting nature - emits a squark, the squark in turn emits another quark and decays into an excited neutralino, this emits a slepton, and the slepton ends up producing the lightest neutralino. All in all, from each of these chains (one per decay of each of the produced gluinos) one should observe two jets of hadrons from the quark hadronization, two leptons, and some missing energy. The missing transverse energy stolen by each neutralino would add as two vectors add in a plane: only rarely they would cancel each other out. In the graph below, for instance, two neutralinos leaving in different directions (the two dashed lines pointing towards the upper and lower left, in the transverse cut-away view of the ATLAS detector) would create a missing transverse energy vector pointing roughly mid-way between their exit directions.

The Tevatron experiments have searched for these events in their Run II data. The search in CDF considered the signature of two, three, or four hadronic jets plus a significant amount of missing energy from the neutralinos. This signature can be mimicked very effectively by the frequent, generic production of many jets by quantum chromodynamics interactions between quarks and gluons; the missing energy is thus required to be large and significant to suppress these processes.

The CDF experiment applied three different sets of selection cuts on their data to seek sensitivity to different regions of the parameter space of Supersymmetry. Indeed, as the mass of gluinos, squarks, and sleptons varies, so does the visible final state. For instance, if squarks and gluinos have a similar mass one is unlikely to detect a hadronic jet from the quark that is emitted in the transformation of the former into the latter. The signature pf pair-produced gluinos then more closely resembles one with only two jets and missing energy.

The figure on the right shows the final selection of the data in one of the three search regions. It is clear that known Standard Model processes provide a good modeling of the observed distribution of missing transverse energy in the data (black points with error bars), whereas a supersymmetric signal (the empty histogram in green, overlaid to SM contributions) would have instead stood out and created a disagreement.

From the distributions an upper limit can be extracted on the amount of signal contained in the data, and from the latter a limit is obtained in the cross section of gluino pair production: this translates into a mass exclusion range for squarks and gluinos. The final summarizing plot is shown below.

The plane is spanned by the mass of the two hypothetical particles. Colored areas have been excluded by different experiments; the CDF search extends the excluded region by the size of the red-painted area. We thus learn that gluinos cannot be lighter than 300 GeV, whatever the squark mass, otherwise CDF would have seen a bunch of anomalous events with large missing energy and jets.

The Tevatron protons and antiprotons do not have enough energy to investigate supersymmetric particles of mass much larger than the limit discussed above: so if Supersymmetry is the right theory of Nature, it may turn out to be the job of the Large Hadron Collider to discover it. With its 7-fold increase in energy and hundred-fold increase in interaction rates, the LHC is expected to provide a clear-cut answer: discover supersymmetry, or rule it out for good. As you can see in the plot below (where the plane is spanned by two convenient parameters among the multitude of choices: and ), the discovery reach of the CMS experiment extends to mass values in excess of a TeV - where supersymmetric particles would be close to useless, because they would not have a chance to solve the problems of electroweak symmetry breaking for which they were once invented.

The graph is complicated and it requires some more explanation: the blue areas are excluded by theoretical constraints and experimental searches, and the green area is also excluded. The colored wavy lines show instead the limits that CMS will be able to set in the plane -intending it will exclude anything to the left of the curves - with different searches, labeled by their respective “smoking guns”. The red curve is labeled for missing transverse energy, and it is one of the most performant in excluding the parameter space.

So, indeed, CMS and ATLAS will have an easy way to find signals of supersymmetry across the table -the wide space of parameters: they just need to study their distribution of missing transverse energy, just as we saw CDF do in the analysis mentioned above. The fanthom signal of a neutralino, which cannot interact with the detector and leaves unseen, turns out to be more striking at the end of the day than the multitude of jets and charged leptons the pyroclastic Supersymmetric production events would give rise to. Seeing events with a large amount of missing transverse energy would not allow us to determine which form of supersymmetry we are dealing with - whether a minimal supersymmetric extension of the Standard Model with two higgs boson doublets, or more complicated schemes. However, it would still allow us to claim that we have evidence for THE candidate particle which constitutes 80% of the stuff the Universe is made of.

I need to warn the reader here: of course, ATLAS and CMS have already studied dozens of methods, some of which are quite complicated, to extract very detailed information on Supersymmetry and very clean signatures of its presence from LHC data. These analyses focus on kinematical properties of the supersymmetric decays which are very model-dependent, and very complicated to explain. Although I reported about these methods in my seminar, I take the liberty here of jumping ahead a little…

So what instead if SUSY is not, after all, the right idea ?

Despite the general enthusiasm of theorists, phenomenologists, and other assorted believers, in fact, we have to keep a cool mind. Let’s review the cost of the purchase we have to make if we are to marry Supersymmetry:

• twenty brand-new particles, never before seen
• at least 104 new parameters, whose value is unknown and to be determined by improbable experiments
• a strict conservation of R-parity, the number you get by adding together spin, baryon, and lepton number in a suitable combination - the combination allows the proton and the lightest neutralino to remain stable
• We also have to agree that despite the fact that in principle the Tevatron and LEP colliders could have well stumbled into Supersymmetry, they haven’t - new physics chose to hide in the far away corner, just like the small coin that you dropped from your pocket.

Some of us think the above is too much to buy, for a theory which “solves” the mystery of a unnaturally small mass of the Higgs boson (provided the Higgs exists and is light as every evidence still suggests) and which collapses two crossings between running coupling constants into one single point. Ockham’s razor comes a-slashing: “entia non sunt multiplicanda praeter necessitatem“, one must not multiply entities. The most economical explanation is the best one… The razor cuts unnecessary entities.

One should mention, at the end of this long post which focused on the searches for just one candidate for dark matter - the one which hadron colliders may have a chance to find, the neutralino - that there is a long list of alternatives, of many flavors: kaluza-klein gravitons, sneutrinos, gravitinos, little higgses, axions, primordial black holes, charged massive particles, heavy neutrinos, sterile neutrinos, you name them.

It is for this very reason that in the end, LHC searches will require to follow the very important two-step procedure outlined by M.Mangano in a recent paper: first establish that an anomaly exists in the data, and only after it has been demonstrated to be utterly unexplainable by known phenomena, proceed with an exotic explanation.

To conclude, dark matter candidates have been searched at past and present collider experiments with no success. LHC appears to have the right energy and the potential to finally discover the source of this astounding enigma. In any case, we will know in a few years whether Supersymmetry is real or just a crazy concoction. If SUSY exists, new accelerators will be needed to investigate it in detail, but if it doesn’t, particle physics may be at a dead end. Despite this threatening possibility, we have extremely exciting years ahead of us!

Although ten short meaningless posts won’t outvalue a longer thoughtful one, for today I stick with the former. So let me just paste here a link to a post about me at sci.bzaar.net, the site of a workshop I will attend virtually next week.

In a few days I plan to provide the site owner, Gianandrea Giacoma, with a couple of short videos where I discuss some limits of blogs in the context of scientific outreach. If I am not too lazy I will produce an English version of those (the event is for an italian audience).

“The probability that there’s a bomb on your flight is really small, and yet still non negligible for anxious people like me. But the probability that there are two bombs is really ridiculously tiny! That’s why I always take one with me in my carry-on“.

Anonymous