No CHAMPS in CDF data

A recent search for long-lived charged massive particles in CDF data has found no signal in 1.0 inverse femtobarns of proton-antiproton collisions produced by the Tevatron collider at Fermilab.

Most subnuclear particles we know have very short lifetimes: they disintegrate into lighter bodies by the action of strong, or electromagnetic, or weak interactions. In the first case the particle is by necessity a hadron- one composed of quarks and gluons-, and the strength of the interaction that disintegrates it is evident by the fact that the life of the particle is extremely short:  we are talking about a billionth of a trillionth of a second, or even less time. In the second case, the electromagnetic decay takes longer, but still in most instances a ridiculously small time; the neutral pion, for instance, decays to two photons () in about seconds: eighty billionths of a billionth of a second. In the third case, however, the weakness of the interaction manifests itself in decay times that are typically long enough that the particle is indeed capable of traveling for a while.

Currently, the longest-living subnuclear particle is the neutron, which lives about 15 minutes before undergoing the weak decay , the well-studied beta-decay process which is at the basis of a host of radioactive phenomena. The neutron is very lucky, however, because its long life is not only due to the weakness of virtual W-boson exchange, but also by the fact that this particle happens to have a mass just a tiny bit larger than the sum of the bodies it must decay into: this translates in a very, very small “phase space” for the decay products, and a small phase space means a small decay rate.

Of course, we have only discussed unstable particles so far: but the landscape of particle physics includes also stable particles, i.e. the proton, the electron, the photon, and (as far as we know) the neutrinos. We would be very surprised if this latter set included particles we have not discovered yet, but we should be more possibilistic.

A stable, electrically-neutral massive particle would be less easy to detect than we could naively think. In fact, most dark-matter searches aimed at detecting a signal of a stable massive particle are tuned to be sensitive to very small signals: if a gas of neutralinos pervaded the universe, we might be unaware of their presence until we looked at rotation curves of galaxies and other non-trivial data, and even then, a direct signal in a detector would require extremely good sensitivity, since a stable neutral particle would be typically very weakly interacting, which means that swarms of such bodies could easily  fly through whatever detector we cook up unscathed. Despite that, we of course are looking for such things, with CDMS, DAMA, and other dark-matter-dedicated experiments.

The existence of a charged massive stable particle (CHAMP for friends), however, is harder to buy. An electrically-charged particle does not go unseen for long: its electromagnetic interaction is liable to betray it easily. However, there is no need to require that a CHAMP is by force THE reason of missing mass in the universe. These particles could be rare, or even non-existent in the Universe today, and in that case our only chance to see them would be in hadron-collision experiments, where we could produce them if the energy and collision rate are sufficient.

What would happen in the event of a creation of a CHAMP in a hadron collision is that the particle would slowly traverse the detector, leaving a ionization trail. A weak-interacting CHAMP (and to some extent even a strongly-interacting one) would not interact strongly with the heavy layers of iron and lead making up the calorimeter systems of which collider experiments are equipped, and so it would be able to punch through, leaving a signal in the muon chambers before drifting away. What we could see, if we looked carefully, would be a muon track which ionizes the gas much more than muons usually do -because massive CHAMPS are heavy, and so they kick atoms around as they traverse the gas. Also, the low velocity of the particle (be it clear, here “low” means “only few tenths of the speed of light”!) would manifest itself in a delay in the detector signals as the particle traverses them in succession.

CDF has searched for such evidence in its data, by selecting muon candidates and determining whether their crossing time and ionization is compatible with muon tracks or not. More specifically, by directly measuring the time needed for the track to cross the 1.5 meter-radius of the inner tracker, and the particle momentum, the mass of the particle can be inferred. That is easier said than done, however: a muon takes about 5 nanoseconds to traverse the 1.5 meters of the tracker, and to discern a particle moving half that fast, one is requred to measure this time interval with a resolution better than a couple of nanoseconds.

The CDF Time-Of-Flight system (TOF) is capable of doing that. One just needs to determine the production time with enough precision, and then the scintillation bars which are mounted just outside of the tracking chamber (the COT, for central outer tracker) will measure the time delay. The problem with this technique, however, is that the time resolution has a distinctly non-Gaussian behaviour, which may introduce large backgrounds when one selects tracks compatible with a long travel time. The redundancy of CDF comes to the rescue: one can measure the travel time of the particles through the tracker by looking at the residuals of the track fit. Let me explain.

A charged particle crossing the COT leaves a ionization trail. These ions are detected by 96 planes of sense wires along the path, and from the pattern of hit wires the trajectory can be reconstructed. However, each wire will have recorded the released charge at a different time, because they are located at different distances from the track, and the ions take some time to drift in the electric field before their signal is collected. The hit time is used in the fit that determines the particle trajectory: residuals of these time measurements after the track is fit provide a measurement of the particle velocity. In fact, a particle moving slowly creates ionization signals that are progressively delayed as a function of radius; these residuals can be used to determine the travel time.

The resulting measurement has a three-times-worse precision than that coming from the dedicated TOF system (fortunately, I would say, otherwise the TOF itself would be a rather useless tool); however, the uncertainty on this latter measurement has a much more Gaussian behaviour! This is an important asset, since by requiring that the two time measurements are consistent with one another, one can effectively remove the non-Gaussian behavior of the TOF measurement.

By combining crossing time -i.e. velocity- and track momentum measurement, one may then derive a mass estimate for the particle. The distribution of reconstructed masses for CHAMP candidates is shown in the graph below. Overimposed to the data, the distribution expected for a 220-GeV CHAMP signal has been overlaid. It is clear to see that the mass resolution provided by the method is rather poor: despite of that, a high-mass charged particle would be easy to spot if it were there.

One note of warning about this graph: the distribution above shows masses ranging all the way from 0 to 100 GeV, but that does not mean that these tracks have similar masses: the vast majority of tracks are real muons, for which the velocity is underestimated due to instrumental effects: in a sense, the very shape of the curve describes the resolution of the time measurement provided by the analysis.

The absence of tracks compatible with a mass larger than 120 GeV in the data allows to place model-independent limits on the CHAMP mass. Weak-interacting CHAMPS are excluded, in the kinematic region covered by the muon chambers, and with , if they are produced with a cross section larger than 10 fb. For strongly-interacting CHAMPS the search considers the case of a scalar top R-hadron, a particle which is predicted by Supersymmetric theories when the stable stop quark binds together with an ordinary quark. In that case, the 95% CL limit can be set at a mass of 249 GeV.

It is interesting to note that this analysis, while not using the magnitude of the ionization left by the track in the gas chamber (the so-called on which most past searches of CHAMPS have been based, e.g. in CDF (Run I) and ALEPH) to identify the CHAMP signal candidates, still does use the to infer the (background) particle species when determining the resolution of the time measurement from COT residuals. So the measurement shows once more how collider detectors really benefit from the high redundancy of their design!

[Post scriptum: I discuss in simple terms the ionization energy loss in the second half of this recent post.]

It only remains to congratulate with the main authors of this search, Thomas Phillips (from Duke University) and Rick Snider (Fermilab), for their nice result, which is being sent for publication as we speak. The public web page of the analysis, which contains more plots and an abstract, can be browsed here.