Dark Matter Searches at Colliders – part II

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…)