Choosing a jet algorithm

23 April 2009


A jet is a “spray” of essentially collinear hadrons whose total momentum tracks those of the fragmenting parton (quarks or gluons). The jet can be thought of as the “footprint” of a parton, and jet algorithms collect collinear hadrons together to reflect as closely as possible the properties of the partons. In this way, we can measure the properties of the short distance degree of freedom of interactions, theoretically predicted by perturbative calculations.

On a sunny August day in Debrecen (Hungary, CTEQ-MCNET Summer school 2008), Gavin Salam, one of the main experts on jet algorithms, showed a table with the last meaningful order of perturbative calculations reached using different jet algorithms. ATLAS's cone jet algorithm is unstable if one particle in the final state splits in a collinear pair of particles or if an extra particle with really low transverse momentum is added at the final state. These instabilities permit a meaningful theoretical calculation only up to the "Leading Order" instead of "Next to Leading Order" (more accurate), which is reached with the jet algorithms used in other experiments (CDF or CMS) as shown in that table. After spending a lot of effort in measuring, reconstructing, calibrating, and understanding the jets in ATLAS, how can we compare our measurement with the state-of-the-art theory and draw conclusions on the physics that produces these sprays of particles? Should we use the ATLAS cone for our analysis?

The discussion of jet algorithms has been an area of development and debate for at least the last 20 years. Two families of jet algorithms are generally advocated for hadron colliders.

One option is to use sequential recombination jet algorithms, such as the kT jet algorithm [1, 2], which introduces a distance measure between particles, and repeatedly recombines the closest pair of particles until some stopping criterion is reached. These were used successfully in electron-positron annihilations, in electron-proton deep inelastic scatterings and, recently, even in hadron-hadron collisions.

Another option is to define a jet as an angular cone around some direction. The bulk of the measurements in hadron-hadron colliders are done using this kind of jet algorithm.

Recently new jet algorithms were developed. The SISCone (Seedless-Infrared-Safe Cone) jet algorithm is a cone algorithm that uses the sliding window idea to find all possible stable cones in an event. Seed-less cone jet algorithms were investigated even before the development of the SISCone algorithm, but the previous solutions were not practical since in events with many particles a large amount of CPU was needed. The SISCone jet algorithm solved this problem. The main difference with respect to ATLAS cone is that the latter finds only a subset of the stable cones. By finding all the stable cones, the SISCone can be used even in calculations beyond the “Next to Leading Order”. The main parameter of this algorithm is the radius of the cone R. As for the ATLAS cone algorithm, this algorithm can produce overlapping cones, and the overlaps are solved using a split-merge procedure (controlled by a second parameter). In this way, even if the starting shape is a cone, the final jets, obtained by merging or splitting the cones, could have a different shape and area.

Another algorithm developed in the last few years is the anti-kT jet algorithm. It uses sequential recombination to build the jet. In fact, the kT and anti-kT are essentially the same algorithm using a different generalised distance between two particles, which defines how the recombination is done. Different parameters produce different peculiarities between the kT algorithm and the anti-kT algorithm. The kT algorithm starts in general merging a soft object to the spatially closest one. The anti-kT algorithm usually starts recombining a hard object to the spatially closest one. In this way “soft stuff” within a certain radius R of a high kT object will be merged with this one and the final jet will have a shape almost regular (almost a circle around the high kT object).


Illustration 1: Shapes for jets algorithms reconstructing the same event. The towers in the (y,Φ) plane are colored depending on which jet they belong to. The vertical axis shows the Pt of the tower [M. Cacciari, G. P. Salam, G.Soyez, JHEP 0804:063,2008].



Algorithms resulting in jets with regular shape are particularly attractive for experiments at hadron-hadron colliders. If a jet algorithm produces always regular shape, then we can more easily know its area and its geometrical region in the detector (this can help to have a preliminary understanding of the jet measurement). Illustration 1 shows the jet shapes obtained using different algorithms to reconstruct the same event. This picture highlights that the anti-kT algorithm produces really regular circles in most cases, but not always. For the other jet algorithms, such as the kT algorithm, the definition of its shape and the calculation of its area are not trivial. To solve this problem, in association with the new algorithms, new methods of calculating the jet area were developed. These new methods to calculate the area work properly for the SISCone algorithm, the anti-kT algorithm and the kT algorithm, even if the jet has a “strange” shape. The events that we will measure and record in ATLAS are an overlap of several proton-proton interactions (pile-up). We have to correct for these overlaps, subtracting the contribution from the pile-up. The estimate of the jet area can be used for this purpose.

These two new algorithms (the SISCone and the anti-kT), fulfil most of the requirements discussed in various workshops that grouped together experimentalists and theorists in the last 20 years. Fortunately many other people in ATLAS got triggered by these interesting possibilities and by the progresses made in the theoretical understanding of the hard interactions in the last years. An interest in investigating the performances of the new jet algorithms grew in the Jet/EtMiss performance group and in many physics groups. In particular, the algorithms should be fast for the very high multiplicities of particles expected at the LHC, and robust under pile-up. Moreover they should facilitate the experimental reconstruction and calibration. These are common requirements, but in ATLAS jets are used in a lot of different analyses and therefore flexibility in reconstructing jets in different ways should also be possible.

A feature of the new jet algorithms allows us to study resonances decaying into coalescing jets such as high Pt top quarks, W/Z and Higgs bosons decays when the decay products are nearby. This is a new use-case and it needs a jet algorithm able to resolve the sub-jet structure. This highlights our need for flexibility to optimize the most suitable algorithm for a specific analysis.

In a recent Jet-EtMiss meeting, at the end of January, we concluded that, compared to the ATLAS cone, the SISCone, the anti-kT and the kT jet algorithms have a better reconstruction efficiency and they are more robust under pile-up. We also saw that the anti-kT jet algorithm produces a more regular area, which might facilitate the experimental calibration.

Waiting for the first collisions, this is a good time to investigate all the necessary aspects to work out the best analysis strategy for the first stage of data-taking. The choice of a jet algorithm is not a trivial issue, and we should take our decision by comparing the performance of the various algorithms in different analyses and scenarios. The comparisons of the different jet algorithms are on-going and at the end of April there will be another meeting to discuss new results. The use of various algorithms and parameter tuning for specific analyses can be necessary, but based on the results discussed at this meeting, it will be decided on which jet algorithm we should focus our calibration efforts. This should allow us to concentrate our activities on the understanding of the detector when the first protons collide. See you there.



Thanks to Tancredi Carli, Chiara Roda, Jimmy Proudfoot, Mike Seymour, Tom LeCompte, and Ariel Schwartzman for all their revisions and feedback.

 

 

Paolo Francavilla

INFN