Search for the supersymmetric partner of the top quark

My PhD is concerned with the search for a specific particle predicted by Supersymmetry (SUSY). I’ll probably write a number of blog posts about it in the near future, but for the moment I’ll stick to an overly-simplistic explanation of Supersymmetry : it doubles the particle content of the Standard Model. An it does so in an intriguing way, by exchanging fermions (main constituents of matter) and bosons (force carriers), such that, for example, the top quark (a fermion) is assigned a supersymmetric scalar (bosonic) partner, which goes by the names of scalar top quark or stop.

Unfortunately, there are far too many supersymmetric models, with far too many parameters to scan; so we resort to simplified models where, on the basis of theoretical arguments (more about that in a future post), we consider only a few “sparticles” to be within reach of the LHC, while all the others are assumed to have very high masses. A simplified model to look for the stop quark looks something like this : assume the stop has a mass perhaps around a couple of TeV, that there is a lightest supersymmetric particle (LSP) it can eventually decay to, and further assume that R-parity is preserved (this is a bit technical, but essentially ensures the LSP is stable, which is important for what’s coming…). A typical Feynman diagram would be :


Here we have two stop quarks $\tilde{t}$ decaying to their SM counterparts, the usual top quarks $t$, and to the LSP, the neutralino $\chi_1^0$. We request that the daughter top quarks decay to bottom quarks ($b$) and hadronic $W$ bosons, while, since R-parity is preserved, the LSP is stable and just flies off the detector. In fact, the LSP doesn’t even interact with other SM particles and essentially goes by unnoticed. Such invisible particles are detected as missing energy, since the energy sum of all the visible products don’t match anymore the (known) energy of the colliding protons. There are, of course, many other possible scenarios where one might expect to see a stop quark; as this one doesn’t involve any leptons (from the decay of the $W$ bosons), we refer to it as a stop 0 lepton search.

Study of the $t\bar{t}Z$ background

The second part of my research is looking at a rare SM decay, where we have a top-antitop quark pair and a $Z$ boson. This is particularly interesting for two reasons : it serves as a so-called precision measurement of the SM (couplings of top quarks with vector bosons), and it is also the main background for the stop 0 lepton search I described above. The leading order Feynman diagram for this process looks like this :

Main ttZ process

Of course, there are many other possible diagrams, such as :

More ttZ processes

A quick glance at the PDG table for the $Z$ boson reveals that about 70% of its decays are to hadrons, and 20% to “invisible” (e.g. neutrinos). It’s easy enough to get rid of (most of) the hadronic decays, by simply cutting on the number of final jets, or requiring that close-by jets don’t combine to an invariant mass close to that of the $Z$ boson; quid of the neutrino channel, though? As they are effectively invisible to our detector, in events where a $t\bar{t}Z(\to\nu\bar{\nu})$ process occurred, we would only see 2 top quarks and some missing energy. Which is exactly our supersymmetric signal signature. Bummer. Since we have no way of discriminating between actual signal and mere $t\bar{t}Z$ events, we call this an irreducible background.

The best we can do about irreducible backgrounds is study them in specially designed control regions, where we expect no signal contamination. We use those regions to adjust our Monte Carlo simulations to purely SM data, and we cross-check our findings by extrapolating our simulation to validation regions - closer to the signal region parameters, yet not quite there. Once everything is properly set up and we are satisfied with the data/MC agreement for our irreducible background, we finally extend it to the signal region, and basically substract the expected $t\bar{t}Z$ events from the data. It is therefore crucial to perform this background analysis correctly, if we ever are to have a shot at detecting SUSY.

Another issue is that we don’t have much $t\bar{t}Z(\to\nu\bar{\nu})$ to start with… An ingenious solution the good people in the ATLAS Top group have come up with, is to instead use the much more prolific $t\bar{t}\gamma$ events, where the photons are radiative corrections to $t\bar{t}$ processes (the relevant diagrams are pretty much the same as above). What they then do is “remove” the extra photon, so as to create fake missing energy. Since our control regions actually turn out to be quite pure (they isolate a given process with good efficiency), we can relate the expected number of $t\bar{t}Z$ events in the signal region to the (more easily studied) $t\bar{t}\gamma$ events observed in the control region as :

Coming next year… Effective Field Theory