What Happens When Energy Goes Missing?

Title: “Performance of algorithms that reconstruct missing transverse momentum in s = √8 TeV proton–proton collisions in the ATLAS detector”
Authors: ATLAS Collaboration

Reference: arXiv:1609.09324

Check out the public version of this post on the official ATLAS blog here!

The ATLAS experiment recently released a note detailing the nature and performance of algorithms designed to calculate what is perhaps the most difficult quantity in any LHC event: missing transverse energy. Missing energy is difficult because by its very nature, it is missing, thus making it unobservable in the detector. So where does this missing energy come from, and why do we even need it?

The LHC accelerate protons towards one another on the same axis, so they will collide head on. Therefore, the incoming partons have net momentum along the direction of the beamline, but no net momentum in the transverse direction (see Figure 1). MET is then defined as the negative vectorial sum (in the transverse plane) of all recorded particles. Any nonzero MET indicates a particle that escaped the detector. This escaping particle could be a regular Standard Model neutrino, or something much more exotic, such as the lightest supersymmetric particle or a dark matter candidate.

Figure 2 shows an event display where the calculated MET balances the visible objects in the detector. In this case, these visible objects are jets, but they could also be muons, photons, electrons, or taus. This constitutes the “hard term” in the MET calculation. Often there are also contributions of energy in the detector that are not associated to a particular physics object, but may still be necessary to get an accurate measurement of MET. This momenta is known as the “soft term”.

In the course of looking at all the energy in the detector for a given event, inevitably some pileup will sneak in. The pileup could be contributions from additional proton-proton collisions in the same bunch crossing, or from scattering of protons upstream of the interaction point. Either way, the MET reconstruction algorithms have to take this into account. Adding up energy from pileup could lead to more MET than was actually in the collision, which could mean the difference between an observation of dark matter and just another Standard Model event.

One of the ways to suppress pile up is to use a quantity called jet vertex fraction (JVF), which uses the additional information of tracks associated to jets. If the tracks do not point back to the initial hard scatter, they can be tagged as pileup and not included in the calculation. This is the idea behind the Track Soft Term (TST) algorithm. Another way to remove pileup is to estimate the average energy density in the detector due to pileup using event-by-event measurements, then subtracting this baseline energy. This is used in the Extrapolated Jet Area with Filter, or EJAF algorithm.

Once these algorithms are designed, they are tested in two different types of events. One of these is in W to lepton + neutrino decay signatures. These events should all have some amount of real missing energy from the neutrino, so they can easily reveal how well the reconstruction is working. The second group is Z boson to two lepton events. These events should not have any real missing energy (no neutrinos), so with these events, it is possible to see if and how the algorithm reconstructs fake missing energy. Fake MET often comes from miscalibration or mismeasurement of physics objects in the detector. Figures 3 and 4 show the calorimeter soft MET distributions in these two samples; here it is easy to see the shape difference between real and fake missing energy.

This note evaluates the performance of these algorithms in 8 TeV proton proton collision data collected in 2012. Perhaps the most important metric in MET reconstruction performance is the resolution, since this tells you how well you know your MET value. Intuitively, the resolution depends on detector resolution of the objects that went into the calculation, and because of pile up, it gets worse as the number of vertices gets larger. The resolution is technically defined as the RMS of the combined distribution of MET in the x and y directions, covering the full transverse plane of the detector. Figure 5 shows the resolution as a function of the number of vertices in Z to μμ data for several reconstruction algorithms. Here you can see that the TST algorithm has a very small dependence on the number of vertices, implying a good stability of the resolution with pileup.

Another important quantity to measure is the angular resolution, which is important in the reconstruction of kinematic variables such as the transverse mass of the W. It can be measured in W to μν simulation by comparing the direction of the MET, as reconstructed by the algorithm, to the direction of the true MET. The resolution is then defined as the RMS of the distribution of the phi difference between these two vectors. Figure 6 shows the angular resolution of the same five algorithms as a function of the true missing transverse energy. Note the feature between 40 and 60 GeV, where there is a transition region into events with high pT calibrated jets. Again, the TST algorithm has the best angular resolution for this topology across the entire range of true missing energy.

As the High Luminosity LHC looms larger and larger, the issue of MET reconstruction will become a hot topic in the ATLAS collaboration. In particular, the HLLHC will be a very high pile up environment, and many new pile up subtraction studies are underway. Additionally, there is no lack of exciting theories predicting new particles in Run 3 that are invisible to the detector. As long as these hypothetical invisible particles are being discussed, the MET teams will be working hard to catch them.

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