A Quantum Diaries Survivor

Jeff is a physics professor at the University of Cassino, and a long-time colleague and friend of mine. He worked in the SLD and CDF collaborations as a particle physicist, but later moved on to study radiation damage on silicon detectors for particle and astroparticle applications.

Besides admiring him for his wicked sense of humor, which he uses to make the workplace around him always a pleasant place, I have the highest esteem of Jeff as a professor, because he is quite skilled in explaining physics concepts in simple terms. He always looks for the most intuitive way to understand things, as you might appreciate in the contribution he offers below.

The following describes a very elegant and simple derivation of the relativistic formula for the addition of velocities, .

It is due to David Mermin. I fell in love with it and have been telling it for the past four years now to the students of my general physics course. The students are first year telecommunications and electrical engineering students. Before sitting in on my course all of them have heard about Einstein and most of them heard the expression “the velocity of light is constant”. I do not have the time to discuss special relativity in detail. My course is quite traditional. I discuss reference frames, inertial frames, Galilean transformations and covariance of Newton’s laws. I then point out that when describing mechanical waves the frame that is stationary respect to the medium is a special reference! In particular the wave motion can be made to disappear by moving respect to the medium with a velocity equal to that of the wave. It is clear at this point that the constancy of the velocity of light cannot be understood by assuming Newton’s laws and then modeling light as a mechanical wave in a medium (the ether). I then restate the constancy of the velocity of light and begin Mermin’s derivation.

The derivation uses:

• only one reference frame (no use of Lorentz transformations),
• simple kinematics (always good to brush up on),
• the constancy of the velocity of light (something that every telecommunications and electrical engineering student should know),
• the idea that some things are invariant; i.e. while many quantities are relative, observers will agree on some absolutes.

Consider a train of length L moving along the x-axis at a constant velocity v respect to an inertial frame of reference (the observer watching the events unfold). At the trailing end of the train a loaded gun is aimed in the forward direction and fired at time : the bullet and flash of light emerge and travel in the forward direction with different speeds: w the velocity of the bullet, c the velocity of light. A mirror at the front end of the train reflects the light back towards the advancing bullet. Let f be the fraction of the length of train that the reflected light travels before meeting up with the bullet. The constancy of light (Einstein’s dictum) tells us that the velocity of light in the forward direction is equal to the velocity of light in the backward direction; i.e. .

The space-time plot looks like this:

Let be the time for the light flash to reach the forward-going mirror and be the time the reflected light needs to return from the mirror and meet up with the forward-moving bullet. Simple kinematics allows us to label the space-time plot:

Simple algebra:

It is important to note that the expression for f we just obtained is valid if the velocity of light in the forward and backward direction are equal. Note:

• A classical pre-Einstein physicist would say this expression is valid only if the observer is stationary respect to the ether frame.
• On the other hand Einstein says that any inertial observer would use the same velocity of light; i.e. Einstein tells us that this expression is valid for any observer (generic inertial frame).

Following Einstein we consider a particular observer (frame), one that is moving along with the train. For this observer the velocity of the train is . For clarity let us use the symbol u to indicate the velocity of the bullet with respect to this observer; i.e. with respect to the train.

Suppose the train has 10 windows and the reflected light and the bullet meet up at the third window from the front (). It is important to realize that all observers will agree on the value of f. The fraction f is an invariant!

The constancy of the velocity of light allows us to impose the invariance of f the following way:

Q.E.D. !

I have wanted to write some version of the present post for a while, and so it is a relief to publish it at last. In fact, it is rather strange to have completely avoided discussing in my blog the problem I have invested the best part of my research time in the last three months -plus a fair share of last year’s thinking-, and it was due time that I filled that void somehow.

Unfortunately, strange as it may seem, there are topics in my research activities that are hard to explain in simple terms. The problem I have been working on is not difficult to state, nor too difficult to solve, but it is extremely complicated and varied, so that a comprehensive description is challenging. However, I want to make an attempt…

The problem I have been dealing with, together with a small and focused group of bright colleagues (Sara Bolognesi, Marco De Mattia, and Chiara Mariotti: lads from Padova and ladies from Torino University) is the one of calibrating the momentum of charged tracks detected by the CMS experiment at CERN.

After being produced in a proton-proton collision in the core of CMS, charged particles have their position measured in a dozen layers of silicon detector before they hit the calorimeter system; the few penetrating ones surviving the encounter with trillions of heavy nuclei are also detected by the large set of muon chambers situated outside them. With the information provided by the silicon detectors -and, for muon candidates, by the muon system- a very performant and refined software algorithm reconstructs and fits the trajectory of the track, providing a measurement of the five parameters describing the helical trajectory; most notably, the curvature inside the solenoid, which yields a precise determination of transverse momentum through the formula (where B is the magnetic field intensity -about 4 Tesla- and is transverse momentum).

There are a number of reasons why a precise determination of the momentum of charged tracks is crucial. Let me just flash a few:

1. Charged particles are measured with a better precision than neutral ones, and a careful determination of their momentum allows to calibrate in turn other parts of the detector.
2. Some physics measurements such as the mass of the W boson rely heavily on track momentum.
3. The identification of a high-mass resonance -say a new Z’ boson- may require the reconstruction of its decay, and a scale error on the momentum of those high-energy tracks translates in a worse resolution in the Z’ mass, and a diminished discovery reach.
4. B-physics crucially needs charged tracks to be precisely reconstructed in order for exclusive B decays to be extracted from backgrounds.

So how do we do it ?

We use resonances. A few neutral particles -vector mesons and the Z boson- decay to pairs of muons, and they can thus be extracted with small backgrounds from the data (events with two muons are easy to collect with CMS, and muons have the benefit that they are “perfect” tracks in several ways). We know the mass of these particles with great accuracy, thanks to previous experiments:

• The Z boson mass is known to be , a 0.023% precision.
• The Y(1S), the ground state of the vector meson family, has its mass known as , a 0.0028% measurement.
• The Y(2S) mass is , a 0.0031% measurement.
• The Y(3S) mass is , a 0.005% measurement.
• The J/Psi, the ground state of the vector meson family, has its mass known as , a 0.0004% measurement.
• The Psi(2S) has mass , a 0.001% measurement.

All the above particles are easy to trigger on, collect, reconstruct, and measure. With CMS we expect to collect thousands of these decays every day of running. Their mass can be measured on a event-by-event basis by reconstructing the momentum of the two muons they decayed into, using the relativistic equation

where M is the resonance mass, E is the muon energy, and P is the muon momentum vector.

By comparing the average mass of each reconstructed resonance to the reference values above, we get to know the scale of our momentum measurement, ; every time we measure a momentum we then do , forget P, use P’, and we are done. Easy enough, wouldnt’ you agree ?

Sure. Easy enough. But actually kind of lame. With the millions of dimuon resonances we collect, can’t we do something better ? Our detector is, in fact, a quite complicated set of devices. The momentum scale -or, to be precise, the bias on the momentum measurement- depends on very subtle effects, such as tiny distorsions in the magnetic field generated by the 4-Tesla solenoid, occasional mis-alignment (by a few microns, that is) of one of the thousands silicon sensors, erratic behavior of the reconstruction algorithm in very particular regions of the detector. We can, and we must, check the bias on our measured momentum more closely, because it in turn gives us a chance to verify the B field map, check the alignments, validate the reconstruction code.

In the simplified formulas described above to determine a corrected momentum P’, you might have noticed that we used the invariant mass of the two muons making the resonance, rather than each muon separately. Indeed, the decayed particle is not produced at rest in the laboratory frame of reference, so we cannot expect that the two muons share evenly their parent’s energy, M/2 each. Only by combining their momenta can we get a number to compare to the reference value. Or is there a smarter way ?

There is a smarter way. Strangely enough, to my knowledge it has not been used in the past for this application. Let me explain in short what it is. I will try to make this as simple as possible, but not simpler - in Einstein’s style.

In the formula for the relativistic mass above enters the energy and momentum -or better, if you allow a slip into special relativity jargon, quadrimomentum. We can, in purely symbolic terms, write:

where we have made explicit the fact that the computed invariant mass is a function f of the quadrimomenta of the two muons, and that each of the two quadrimomenta is in turn a function of many (i, in the formula) other variables, collected in two i-dimensional vectors x . These variables are the measured characteristics of the track: its angles, the region of the detector it crosses, its electric charge, you name them.

Still here ? Ok. The next step is to realize that what we really would love to have is a measurement of the momentum as a function of the particular characteristics x of the track, and not just , which only depends on the curvature . Through a knowledge of we could get sensitive to the effects mentioned above -B field distorsions, alignment errors, reconstruction biases.

There is a simple way: we can compute the probability that we observe a mass M, if the reference value is , as a function of the measured quantities of each muon, by assuming a functional form for the way the momentum P depends on the parameters. So let us write:

where the new function g( ) describes how the momenta vary with the vector of measured track parameters , and is a vector of unknown variables describing the function g( ).

(To let you understand what the heck I am talking about, assume that your detector measures a track momentum with a bias depending on momentum itself:

,

with , and , . This function describes momenta which are underestimated by 0.2% for small P, correctly estimated for P=10 GeV, and overestimated by 1% for every additional increase of P by 50 GeV. )

Using the parametrization, we compute for each event the measured mass as a function of the variables . WIth these numbers we finally form a likelihood function:

which of course implicitly depends on the functional form we have chosen for g. By maximizing L as a function of the parameters, we obtain their most likely values, and we are done: we get to know how our track momentum depends on its characteristics .

In the discussioon above I have not given much emphasis on the fact that the true form of the “bias function” g( ) is not known. One can in fact test different hypotheses with the data, and the value of the likelihood will be a measure of how well they describe the experimental situation. There’s more: the likelihood can be studied as a function of each of the components of the vector x, allowing to spot biases which require a more subtle parametrization.

The above discussion is a simplified view of the problem: In reality, things are much more complicated. Here is a short list of details I hid under the carpet above:

• We model the probability to observe a given mass in the likelihood function by convoluting a Lorentzian function (the Breit-Wigner, which is the true form of the mass distribution of the resonance) with a gaussian resolution function; the gaussian has parameters which also get fit simultaneously with the bias parameters . The figure below shows the probability distribution function of a measurement of mass M and resolution for a Z boson: for each point in the plane, defined by the two values , the probability is the height of the surface. Notice how the probability grows as the resolution increases, for values of mass very far from the true resonance mass (for instance, for a mass of 71 GeV-the left boundary of the surface), while the opposite happens for values of mass close to it.

• the fitter also assumes a functional form for the background (which is unavoidably included in the dataset containing the resonances), and fits it together with the bias and resolution parameters;
• Each of the six considered resonances can be fit individually, or all together. The window around the peaks defining events used or not used in the computation requires an optimization;
• The fitter iterates several times the whole procedure: after bias parameters are extracted, momenta get corrected, and a new parameter extraction must return values which are compatible with no bias.
• And so on…

The algorithm is indeed quite complicated. I spent the last three months implementing the fitting of resolution and background, and the algorithm is not yet complete but it now works well. It is particularly satisfactory to be able to launch the program on a set of resonances, and extract all at once not just the parameters that allow momenta to be corrected, but also a precise estimate of momentum resolution as a function of track kinematics - something that would once require detailed studies with simulations. All is now squeezed out of the data!

The work is far from over. With the help of my colleagues, we will test the code on a very large sample of simulated events in the next few months, to be ready for the data which will hopefully start pouring in this fall… But the work will only be started then: we plan to fit chunks of data on a monthly basis, checking the stability of the detector and the track reconstruction, and producing a correction function to be used by all analyses in need of a precise momentum measurement… It really is a long-term plan!

“The secret to creativity is knowing how to hide your sources.“

(Undisclosed source)

Update: Ok, if you happen to not know the author of the above, a hint: he also said…

“If we knew what we were doing, it would not be called research, would it ?“

(courtesy Jeff)

In part I of this long post I gave a writeup of part of the seminar I gave last Tuesday. There, I discussed some of the tools necessary for the searches that have been carried out at the Tevatron collider experiments, and will be performed at the LHC experiments, for dark matter candidates. In particular, I focused the attention on missing transverse energy (MEt), which is a measure of the amount of imbalance in the momentum flow out of the proton-proton collision, in the plane transverse to the beam. A dark matter (DM) candidate produced in a high-energy collision would create that imbalance by carrying away unseen a sizable amount of momentum: we assume such a DM candidate is weakly interacting, and so it leaves undetected just like a neutrino. In this post, I will continue the discussion, and I will give one first example of a direct search for DM performed at the Tevatron.

Cosmologists assure us that we need new particles beyond the Standard Model to accommodate a dark matter candidate. One possibility which is dear to many is the lightest neutralino, a particle belonging to the rich spectrum of new states predicted by supersymmetric (SUSY) theories. The neutralino is the lightest supersymmetric particle (LSP) and it is a quantum superposition of as many as four electrically neutral superpartners of the neutral bosons predicted by the model. The exact recipe depends on a few of the many parameters defining the particular kind of supersymmetry that Nature (the bitch, not the magazine) might have chosen for the Universe we live in. Those parameters are, of course, still unknown to us, and so are the phenomenological details of SUSY.

Indeed, supersymmetry is not even a model, but just a framework which dictates a new symmetry between ordinary and supersymmetric matter and fields. SUSY predicts the existence of one superpartner for each ordinary particle, as shown in the table on the left (SUSY particles have wiggles on their names). The introduction of these new entities solves one grievious problem in the Standard Model: the fact that a light Higgs boson -necessary for the experimental consistency of electroweak observations- is at odds with the expected huge corrections on its mass necessary to renormalize some divergent loops involving the boson coupled to ordinary matter. It is as if the mass of the Higgs boson ended up being of order one after having withstood subtraction and addition of a dozen different contributions of the order of a billions of billions each. The introduction of supersymmetric particles cancels the divergent loops, solving the problem at its root.

Supersymmetry has a second charming feature: it allows the running coupling constants which determine the strength of the three basic interactions -strong, electromagnetic, and weak- to become one and the same at a very high energy scale. These couplings do depend on the value of the energy at which they are measured: and it is indeed expected that they “become one single interaction” above a energy scale where they unify. In the standard model, one sees the three couplings meet at different values of energy, whilst supersymmetry allows them to have the same value at a common energy scale.

And supersymmetry allows a neutral weakly interacting particle, massive just enough to make a perfect candidate for the dark matter we infer exists in the Universe. Since dark matter has survived to our time from the big bang, this neutralino has to be perfectly stable: it simply cannot, CANNOT decay to anything else. Supersymmetric theories which include R-parity - a conserved integer quantum number which is a sum of particles spin, baryon and lepton numbers- have this feature built in.

R-parity was not invented to make the neutralino stable: rather, it was introduced to solve a couple of other outstanding problems of the theory, namely to maintain the stability of the proton and the universality of weak couplings despite the addition of new states. However, it is just what we need if we are to assume that neutralinos make up 20% of our universe today, rather than have decayed to ordinary matter and radiation. R-parity also has an important phenomenological consequence at colliders: it dictates that supersymmetric particles can only be produced in pairs in the collision of ordinary matter.

The CDF experiment carried out a search for neutralinos in its Run II dataset by considering the pair-production of chargino and neutralino as in the diagrams shown on the right. The neutralino emits a charged lepton, converting into the lightest state which leaves the detector without a trace; the chargino (a supersymmetric analog of the W boson) is expected to decay with the emission of one or two charged leptons and another light supersymmetric particle, LSP in short, as we already mentioned. The final state may thus include two or three charged leptons and a large amount of missing transverse energy from the combination of the two LSP.

The CDF detector, which collects proton-antiproton collisions at Fermilab 2-TeV Tevatron collider, is good at finding such a signature. Charged leptons are only produced in rare weak interaction processes at a proton-antiproton collider: the production of a W or Z boson, or the decay of a heavy quark. Electrons and muons of large transverse momentum are identified very effectively by a online trigger system, so the collection efficiency of events with two or three leptons is very high. In order to search for chargino-neutralino production, two different “signal regions” are defined by a set of selection cuts on the observed characteristics of the events before looking at the data. Similar “control regions“, which are expected to contain a negligible fraction of the searched process, are also defined.

Monte Carlo simulations of all known weak processes capable of yielding leptons in the final state are then compared to the data contained in the control region in a number of kinematical distributions. The comparison allows to gain confidence that the simulation is capable of predicting both the number and the kinematics of the experimental data. Only after these checks are successful, the signal region is opened, and data contained within are compared numerically to the expected sum of standard model processes contributing to the mixture.

CDF thus finds 6 events in a signal region defined to contain events with large missing Et, two well-identified leptons, and a third lepton candidate. Here, simulations predict events, mainly from diboson production and top pair production. In the other signal region, defined to have a third good lepton candidate, only one event is found, with an expectation of from standard model processes. The distribution of missing transverse energy observed in this latter case and the expected contributions from standard model processes and from supersymmetric contributions is shown in the plot above. There, you see the one candidate (the point with error bars with missing Et above 20 GeV, the cut defining the signal region in events with three charged leptons) compared to SM backgrounds: mostly diboson production. The white histogram is the SUSY contribution.

Simulations in fact can predict the amount of chargino-neutralino events the two signal regions would contain, as a function of the value of supersymmetric parameter space. One thus gets to know that, for instance, 6.9 events would be expected in the first signal region, and 4.5 in the second. The data clearly do not allow that interpretation.

Since no signal is found, the experiment can set a limit on the production rate of the sought process. The reasoning is quite down-to-earth:

“I observed one event; on average, standard model reactions should produce 0.88 events in that dataset, give or take a small error. Now, that one event could well be the result of SUSY, and the standard model fluctuated to yield zero events; similarly, SUSY could have contributed with an average of two, or even three events, to the selected dataset, and a unlucky fluctuation could have brought our observation to one single event.“

There is a limit to our credibility, of course. In particle physics, we use to set credible chances for these searches at one-in-twenty odds: a complicated but conceptually simple computation allows one to compute the “95% confidence level” (C.L.) upper limit on the average number of events that the cuts defining our signal region should include. It is the number N such that 95% of the times would yield, together with the 0.88 expected standard model yield, more (at least two, that is) than the one event we observed.

Once N is computed, converting it into a 95% C.L. on the chargino-neutralino cross section only requires accounting for the total luminosity of the collected data and the expected efficiency with which our signal region would capture those events: .

In the plot below, you can see the result of the exercise. The cross section limit is shown by the black line with blue and yellow bands signalling the one- and two-standard deviations boundaries expected for the particular search. The limit is plotted as a function of the chargino mass -one of the many free parameters of the considered model; the limit varies as a function of it because so does signal efficiency. Since the theoretical model would foresee a cross section (the red line) larger than the limit for all chargino masses lower than 140 GeV, there follows an exclusion of chargino masses below that value. You can see that CDF sizably extends the LEP limit on this particle, set at 103 GeV (the hatched band on the left).

(To be continued…)

This just to post a couple of links concerning yesterday’s talk by Ray Orbach at the Fermilab Ramsey auditorium: an article on the event and a video of his presentation.

Yesterday I gave a seminar on searches for dark matter at the Tevatron and LHC in Padova, to a wide audience. This was a one-afternoon-workshop intended to educate students and publicize the LHC experiments, but it gathered more audience than undergraduates: quite a few of the Department staff came to listen.

My talk was the last one in a tightly packed agenda, and it indeed started with some 40 minutes of delay, as I had predicted. However, despite the late time -5.40 in the afternoon is about time to catch a train on normal workdays, even for me- the audience stayed to listen.

I already posted my slides here, but since they are in italian, I feel the need to give a summary of my seminar in English here, now that I have some more time to do so. I will do this in at least two parts, because I am swamped with other obligations these days!

I started my seminar by comparing the Tevatron and the LHC (in the aerial view of Fermilab above, the Tevatron ring is compared to the size of LHC, overimposed as a red circle courtesy M.Schmitt): the former collides protons against antiprotons, the latter collides protons with other protons. The crucial differences are however not the projectiles, but two parameters: energy and luminosity at the Tevatron, and and at LHC. While E sets the limit of investigation in new physics phenomena - particles more massive than a few hundred GeV cannot be produced at the Tevatron - L is a parameter which dictates the rate of rare processes. The dumb product of the increases in E and L offered by LHC is a factor 1000, which can be thought as a rule of thumb for the increase in discovery reach of the ATLAS and CMS detectors with respect to their smaller, older brothers CDF and D0. Sure, discovery reach scales only with the square root of the collected data (proportional to L), but cross sections of rare phenomena scale with more than the square of the energy increase: for instance, top production at LHC is 100 times more frequent, at equal L.

I had to mention the huge legacy that the Tevatron offers to LHC: twenty years of investigations, discoveries, and measurements. The top quark mass is known with a 0.8% accuracy thanks to CDF and D0’s recent measurements. This grants CMS and ATLAS a standard candle with which to calibrate their calorimeter response to hadronic jets: it will be extremely important in the initial phase of running, when top quark pairs will be available for a check of the jet energy scale. But the Tevatron’s high precision studies of electroweak physics will do much more for the LHC: the tuning of parton distribution functions performed by CDF and D0 with detailed QCD studies will be crucial to tune the simulation and understand the cross section of rare phenomena.

I then spent five minutes discussing why the important quantity at a hadron collider is the momentum flow in a plane orthogonal to the direction of the beams. While in electron-positron colliders the center-of-mass of the collision is at rest (unless beams are asymmetric in energy on purpose, such as at BaBar or Belle), and particle momenta are equally important regardless of their outgoing direction, a hadron collision of high energy is in fact a collision between quarks and gluons. These constituents of hadrons (drawn as colored lines in the cartoon above, where protons are the black circles) carry a variable fraction of their container’s momentum, and as a result the collision center-of-mass may move in either direction along the beam. What characterizes a hard interaction is instead the momentum flowing orthogonally from this direction (the two red and blue lines exiting at large angle from the protons direction in the cartoon): transverse momentum is therefore a measure of the acceleration that the proton constituents participating in the collision underwent during the mindboggingly brief moment of their interaction.

As a quark or gluon escapes the collision point, it extends a gluon string. The QCD potential grows linearly with distance decelerating the outgoing parton, until it finds it energetically favorable to break in two, materializing a quark-antiquark pair at its midpoint. The process continues until a stream of colorless hadrons are created. These then decay with strong and weak interactions, producing a final stream of particles which collectively carries memory of the originating parton’s momentum. It is what we call a hadronic jet.

Jets are measured in the detector elements called calorimeters (see a description in two parts here and here) by destroying the particles they contain, both charged and neutral ones, in electromagnetic and nuclear interactions with heavy elements - typically tiles of lead or iron. What is measured in these devices is the total track length - the sum of paths of all secondary particles produced in the shower originated by the chain of interactions in the absorber. That quantity is proportional to the energy of the incident bodies. Ultimately, the originating quark or gluon energy and its direction are reconstructed with an accuracy sufficient to understand the characteristics of the process which caused its emission.

In general, a hadronic collision produces jets of particles. Sometimes, though, rarer and fancier objects -ones that are not present in the projectiles- are produced: leptons and photons of high energy. These do not feel the strong interactions, and are due to electroweak interactions, which involves the exchange of W and Z bosons, or heavy quarks which decay weakly. In general, electrons and muons are objects that the detectors are trained to detect with high efficiency. But for dark matter, the signal which is by far the most important of all is an indirect one: missing transverse energy.

Missing transverse energy -the energy carried away by a body which leaves the detector unseen- is reconstructed thanks to the law of conservation of momentum: the incoming projectiles carry no momentum in the direction orthogonal to the beam, and so the final products of a collision must balance their momenta in the transverse plane. When this does not happen, it may be due to an imperfect reconstruction of momenta -a likely cause only if missing Et is not large and not significantly different from zero-, or to the escape of a high-energy neutrino. A dark matter candidate would similarly cause the same imbalance.

The graph above shows an event with two electrons (giving pink energetic deposits) and large energy imbalance -indicated by the downward arrow. Most probably, this rare event collected by CDF is the decay of a pair of Z bosons: , where the two neutrinos escape giving collectively a trace of their creation by the energy imbalance they leave behind.

Missing transverse energy is defined as the opposite of the vector sum of all detected energetic deposits in the calorimeters, in the transverse plane. It is measured with a resolution with depends on the total transverse energy detected: in fact, its resolution scales with the square root of total transverse energy. The reason is the way energy is extracted from the number of track segments caused by hadronic showers: integer numbers follow Poisson statistics, and their uncertainty scales with the square root of the number -and so does energy, and so does missing transverse energy.

Why is a dark matter candidate going to cause missing energy in the detector ? Because dark matter particles cannot be electrically charged -or they would have been found quite easily in the Universe-, they cannot feel strong or electromagnetic interactions -or they would create exotic atoms we do not see-, and they are massive -they need to, if they are to solve the matter-energy balance equation of the Universe, which foresees that dark matter makes up for 20% of the total budget as compared to baryonic matter’s 4%.

One of the most appealing candidates for dark matter is the Supersymmetric particle called Neutralino. Supersymmetry is a model extending the Standard Model of particle physics. It predicts the existence of a new partner for each known quark, lepton, or boson we know - only, with different values of spin. This multiplication of known bodies is the price to pay for a theory that solves one big issue in the standard model: the inconsistency of the mass of the Higgs boson, which must be light if the Standard Model is to be consistent with the many measurements colliders performed at the electroweak scale, but should be far heavier to avoid having to invoke a delicate and unnatural cancelation of huge contributions from virtual divergent diagrams that are present in the theory. WIth Supersymmetry, the Higgs mass is “stabilized at the electroweak scale“: supersymmetric particles cancel automatically the unwanted loop effects of SM particles. SUSY also predicts a unification of forces at a common, very high-energy scale, in a way that is pleasing to the eye but admittedly not called for by any intrinsic requirement.

(To be continued in Part II)

In twenty minutes the mini-workshop on Dark Matter at LHC that we organized for Physics students will start in Aula B at our Physics Department “Galileo Galilei”, here in Padova. I will be closing the workshop with a talk named as this post: which is both a good and a bad thing. It is good to have the last word, but it is not good to see other unmoderated talks straggling past their allotted time and the audience leaving to catch the last train before you had a chance of hypnotizing them.

In any case, I have prepared a reasonably light-weight presentation. The slides are unfortunately in Italian, but I will give a transcript here as an update, later this evening or tomorrow. They are tightly packed - a feature which I call a annoying defect in other people’s presentations, but I find always excusable in my own. No, really - the reason for filling the slides up with text is to make the slides usable without the speaker: a commendable, unselfish reason, you will agree.

So, please find the slides here. I will remove the link once I manage to put together a transcript, since I am running short of space in the public area where I store my stuff. Incidentally, I will have to find a solution for that. Does anybody have an advice on free sites offering permanent access to a Gig of disk space ?

Due and happy thanks to a friend for pointing me to the following sentence, appeared minutes ago at the Cosmic Variance site in a guest post by Juan Collar:

“Thanks DAMA, for cheapening the level of our discourse to truly imbecilic levels. (Sean, if you edit this I will scratch the paint off your car. I may not write blogs, but I do read them: I know how to hurt you).”

No, I think Sean will not edit it - by now it is on record. In any case, I have two comments. The first is that I am happy that a comment I recently made in this blog about the presentation of the new DAMA result sounds polite and positive if compared with the above. The second is that I think we should all back off and realize that no matter whether an experiment will one day win the Nobel prize or be proven laughably wrong, every scientist who works in our field deserves our respect until proven an imbecile. Doing otherwise harms the whole field, and ourselves.

Oh, and - I still thank Sean for linking to my own commentary of the DAMA-LIBRA signal.

Carlo Rubbia gave the last talk at the Neutrino Oscillation conference in Venice last Friday. Below are some notes I collected during the event; but first let me post a picture of Milla Baldo-Ceolin giving her final remarks and inviting everybody to next year’s event. Carlo observes at her left:

Rubbia started with a prayer -which sounded more like a benign order- to theorists: stop talking about supersymmetric dark matter and think about telling us what dark energy is: because that would be extremely important.

As far as dark matter is concerned, we already have many evidences of it. The most important one is gravitational lensing: the gravitational mass of a galaxy is measured from the focussing effect induced by a distant, passing star. This evidence confirms the WMAP results of the fluctuations in the cosmic microwave radiation for a so-far unknown component of matter. It is very clear that plasma and gravitational lensing distributions in the bullet cluster of galaxies are different. This is the proof that we are dealing with a huge amount of matter which dominates the matter density in the Universe.

Dark energy is another problem. It will stay with us for a long time to come. But at least dark matter is about to be studied by direct and indirect detection experiments. Admittedly, all present evidence of dark matter is limited to gravitational effects. The main question is that if other types of interactions are connected to dark matter, like a weak coupling. One then has to consider the possible candidates on the market, and there is a long list of them: primordial black holes, split SUSY, neutralinos, branons, messenger states in GMSB, heavy neutrinos, braneworlds DM, cryptons, D-matter, mirror matter, q-balls, you name it.

Supersymmetrical (SUSY) particles are those most studied in the list. In order to protect the mass of the Higgs from higher order conrrections, we need an extremely precise graph cancellation to compensate for the divergence of known fermions. Supersymmetry can provide that cancellation. A low higgs mass tells us that the mass reange of SUSY partners must not be too far away. A discovery of a low mass Higgs, if elementary, may become an important  hint to the existence of an extremely rich realm of new physics, a real blessing for LHC.  A doubling of the number of elementary particles would be a result of gigantic magnitude.
However, if the explanation of dark matter is SUSY, we need to postulate some strictly conserved quantum number, R-symmetry. This is because the lifetime of the universe is at least 14 billions of years, but that of otherwise permitted SUSY particle decays is 10^-18 seconds: R-symmetry would need to be conserved to a fantastic degree to allow the neutralino to be the source of present-day dark matter.

The real question is the following: is the relic density of weak interacting massive particles (WIMP) the source of non-baryonic matter ?  Current experiments are providing conflicting results. We have to find a third possibility to explain why DAMA sees a signal and other experiments do not. If you take the graph of energy components of the excess from DAMA-LIBRA you see the recoil energy in keV.  Shapes look quite similar to what it should be observed from a WIMP. We are dealing with a high-statistics effect. Its source is systematical. How can we make a test ?

One test to suggest is that if DAMA were repeated in the southern emisphere, by going to South Africa or Argentina, then if the effect observed is of cosmological nature one would get the same result,  while if it is of seasonal nature (a seasonal variation in the number of neutrons, or others),  then one would see something of the opposite sign in the southern emisphere. So DAMA should take everything and carry their whole setup to a place which is on the other side of the Earth.

Several increasingly accurate astronomical observations have strenghtened the evidence that today’s Universe is dominated by an exotic energy density with negative pressure. The simplest candidate is a cosmological term in Einstein’s field equations. However, it turns out to be way too small by particle physics standards. It is thus a profound mystery. And there is a connected mystery: since the vacuum energy density is constant in time, while the matter energy density decreases as the Universe expands, why are the two comparable at about the present time, tiny in the early Universe and very large in the distant future ?

Concluding, Carlo Rubbia noted that the man of the past had discovered that earth, air, fire, and water are the elements which constitute the world. Now physicists say one should rather list baryons, neutrino, dark matter,  and dark energy. Despite that, we do not know the identity of 95% of the Universe: is it composed of dull particles, or is it something much richer than that ?

Our premier in pectore Silvio Berlusconi is known for his sense of humor, which he is usually careful to apply in the least opportune moments. As the day of his new government nears, I am trying to get accustomed to the idea of having to deal with one embarassment after another. But the man is also used to be fast, and in fact he already created a case today, weeks before he becomes a prime minister.

Vladimir Putin is visiting him in his luxurious villa in Sardinia, and a few journalists are interviewing them. A russian lady speaks to Putin, asking him about his new relationship with an ex-model. Putin does not like the question and is embarassed. Berlusconi, to help his friend in trouble, finds nothing better than pointing a fake khalasnikov to the reporter, mimicking an execution. Not particularly hilarious, but also not harmful - if it weren’t for the fact that she would not be the first journalist to die a untimely death by gun blows in today’s Russia.

What to say… Off to a good start.