Centrality refers to the sum of the Pt of the particles considered, over the sum of the P of the same particles. This thus contains information about the relative locations of these particles, as well as the location relative to the transverse direction. This combination is particularly potent at separating out different event types. Plots of various centrality variables for 1 and 2 b-tagged jet selection can be seen below. For an example, we will show the 1 b-tagged jet selection, isolated for 3 jets.
If we examine the centrality of the last jet and the lepton, for instance, after single-top preselection cuts, we find that there is a peak of W+jets background around 0.2 for the 1 b-tagged jet selection. If some cuts are taken on lepton eta, pt and last jet p, we find that this background bump flattens out if events with a large P for the lepton and the light quark jet, which are both close to the beam are removed. The W+jets drops off after this 0.2 or so region since the particles stay near the beam and the overall Pt won't get much higher, since the Pt of the misreconstructed light quark is pretty high already. That the Pt is as high as it is, is a result of the single-top preselection cuts.
Thus, this variable helps to isolate W+Jet like events with misreconstructed q's that pass our cuts, which is a large background, especially for 1 b-tagged jets. We can see this if we simply apply a cut to require lepton eta < 1 (not near the beam). Even with this relatively blunt cut, there is clearly a reduction in background for a low centrality region. All of the centrality variables are affected, but the AllJetsLeptonCentrality shape mimics that of Jet1Jet2Centrality. Moreover, having Jet1Jet2Centrality and LastJetLeptonCentrality allows you to look at the physics of different particles in the event, rather than lumping it all together into one variable, so the combination of Jet1Jet2Centrality and LastJetLeptonCentrality is preferred.
Centrality variables seem complementary to other, more basic, variables because of the effect these have on reducing background in different regions of centrality and enabling useful cuts.
There is also some impact on ttbar, which has one b-quark mis-identified as a light quark for the 1 b-tagged jet selection and potential mis-identifications of a second lepton. This case is a little more complicated, but in general ttbar tends to have slightly higher centrality values, although no obvious peak like W+Jets. For the centrality of the last jet and lepton, if a cut is taken requiring the lepton has eta < 1, implying that the combination of the lepton and last jet momentum is almost all in the transverse direction, the centrality values tend to be on the high side, as they are for any remaining W+Jets background, again illustrating the usefulness of this variable even with a rough cut on lepton eta. This was a useful variable for separating ttbar and w+jets in ttbar analyses. It holds this use for single-top analyses (other cuts may do better with one background instead of the other, so isolating one may be useful), as well as for separating single-top itself from these backgrounds.
You could also argue for the use of deltaR variables instead. Although these do contain some of the location information, they are missing information related to deviation from the transverse direction, and the momentum relation. Graphically, the shape of deltaR is not as useful for signal and background separation as the centrality variable is. The information about both the relative and transverse propositioning of the particles is particularly useful for separating event types.
Overall, the centrality seems like a useful variable to use when separating signal and background, particularly in a multivariate analysis when it can be used in coordination with various pt and eta cuts of different particles. We particularly favor the use of Jet1Jet2Centrality and LastJetLeptonCentrality for their good background separation and ability to look at the locations of two separate sets and types of particles in an event.
- 11 May 2009