Testing jet definitions: qq & gg cases
by M. Cacciari, J. Rojo, G.P. Salam and G. Soyez, arXiv:0810.1304
This page is intended to help visualize how the choice of jet definition impacts a dijet invariant mass reconstruction at LHC.

The controls fall into 4 groups:

• the jet definition
• the binning and quality measures
• the jet-type (quark, gluon) and mass scale
• pileup and subtraction

The events were simulated with Pythia 6.4 (DWT tune) and reconstructed with FastJet 2.3.

For more information, view and listen to the flash demo, or click on individual terms.
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 kt C/A anti-kt SISCone C/A-filt Q.. R = Qwf=z Q1/fw=x√M x 2 rebin = qq gg mass = pileup: none 0.05 0.25 mb-1/ev subtraction:
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kt algorithm
The inclusive, longitudinally invariant kt algorithm is a pairwise sequential recombination jet algorithm, with a distance measure that relates to the relative transverse momentum between particles.
Cambridge/Aachen algorithm
The Cambridge/Aachen algorithm is a pairwise sequential recombination jet algorithm, whose distance measure is the rapidity-azimuth distance between particles. The algorithms stops when all objects are separated by more than R.
anti-kt
The anti-kt algorithm is a pairwise sequential recombination algorithm with the property that the hard jets in an event tend to have a circular profile in the rapidity-azimuth plane.

This algorithm is a good (infrared, collinear safe) replacement for iterative and fixed-cone algorithms that implement progressive-removal (an example being the CMS iterative cone), insofar as these also produce circular jets.

SISCone
The SISCone jet algorithm finds all stable cones in an event and then runs a Tevatron Run II type split-merge procedure on them.

It is similar in many respects to the midpoint cone algorithm (used at Tevatron) and other iterative cones with split-merge steps, but without their infrared-safety issues.

Here it has been used with the split-merge overlap threshold of f=0.75 (which limits monster-jet formation), no pt threshold on stable cones, and an infinite number of passes.

Cambridge-Aachen with filtering
This consists of the Cambridge-Aachen algorithm with an additional filtering procedure: subsequent to the jet finding, each jet is unclustered down to subjets at angular scale xfiltR and one retains only the nfilt hardest of the subjets. We use xfilt=0.5 nfilt=2.

Filtering is designed to limit sensitivity to the underlying event and pileup, while retaining the bulk of perturbative radiation. The parameters of the filtering might well be an interesting subject for further study.

R
The jet-radius parameter for the jet definition.

For an event that has one hard particle and one soft one in a common neighbourhood, R corresponds to the distance in the rapidity-azimuth plane below which the two particles will be combined into a single jet.

For situations involving two hard particles in a neighbourhood, and for more complex events, the relation between R and the clustering will depend on the details of the jet algorithm.

ρL
The extra factor in luminosity that is needed to obtain a signal to background significance that is as good as that with the best jet definition (for this process and energy scale, with no pileup and no subtraction).
Quality-measure plots
In the plots of quality measures versus R, the green line indicates the best value obtained across all jet definitions for the given process and energy scale (without pileup or subtraction).
Qwf=z
A quality measure defined as the width of the smallest mass window that contains a fraction f of the generated massive objects. Smaller values indicate a better jet definition.

The value used for the fraction f depends on the process, and has been chosen so that one considers roughly 25% of the events that pass the event selection (or if "x 2" is checked, 50%).

Q1/fw=x√M
For this quality measure, one takes a mass window of width w, positioning it so as to maximise its contents. The quality measure itself is given by 1/f, the inverse of the fraction of the generated massive objects that are contained in the mass window. Smaller values indicate a better jet definition.

The value used for the window width w is 1.25√M, corresponding to a typical experimental energy resolution for jets. If "x 2" is checked, the window width is doubled.

x 2
The values for the fraction of events f in Qwf=z and for the window width w in Q1/fw=x√M are, to some extent, arbitrary choices.

When "x 2" is checked, the default choices for those values are doubled. This allows one to gauge the degree to which any physics conclusions might depend on those choices.

In the few cases where the resulting best-R value changes noticeably, an examination of the histograms usually provides insight into what is occurring.

Rebinning
One's impression of the quality of the peak can depend on the binning chosen for the histogram. If your intuition disagrees with the quality measures as to what constitutes the best peak, try choosing a binning whose width is of the same order as the width of the shaded band.
qq
The qq case allows one to examine the mass reconstruction quality for qq→Z'→qq events.

The Z', which has been given an artificially small width, serves as a physically well-defined source of mono-energetic quark jets.

gg
The gg case allows one to examine the mass reconstruction quality for gg→H→gg events.

The H, which has been given an artificially small width (and sometimes artificially high masses), serves as a physically well-defined source of mono-energetic gluon jets.

mass
Vary the mass to see how the jet-finding is affected by the energy scale of the process.

A good jet definition at one given energy scale may not be optimal at all energy scales. One reason for this is that the energy resolution for reconstructing a jet is affected by an interplay between underlying-event (UE) contamination and loss of perturbative radiation from the "parton" that induced the jet (cf. arXiv:0712.3014). The former should mostly be independent of jet energy, but the latter isn't.

pileup
Pileup degrades mass resolution because it adds extra noise to each jet.

To help appreciate the normalisation quoted for the pileup, 0.05mb-1/ev corresponds to an average of 5 minimum-bias events added to each hard event, distributed according to a Poissonian. This is foreseen to be the level during the first years of running of the LHC.

0.25mb-1/ev, corresponding to an average of 25 minimum-bias events per hard event, is the level expected for the high-luminosity phase of LHC.

Subtraction
The LHC experiments will probably attempt some form of subtraction of pileup contamination from their events. Various methods exist, some of which are specific to a given detector.

To establish the impact of subtraction, here you can turn on the (experiment-independent) area-based subtraction of arXiv:0707.1378. This uses an event-by-event estimation of the level of noise, which is then used to correct each jet individually according to its area.

Note that subtraction here also removes part of the underlying-event activity.