Dark Matter searches at colliders – part I April 23, 2008Posted by dorigo in cosmology, personal, physics, science.
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)