The anti-k_t jet clustering algorithm (0802.1189v2)

Abstract: The k_t and Cambridge/Aachen inclusive jet finding algorithms for hadron-hadron collisions can be seen as belonging to a broader class of sequential recombination jet algorithms, parametrised by the power of the energy scale in the distance measure. We examine some properties of a new member of this class, for which the power is negative. This anti-k_t'' algorithm essentially behaves like an idealised cone algorithm, in that jets with only soft fragmentation are conical, active and passive areas are equal, the area anomalous dimensions are zero, the non-global logarithms are those of a rigid boundary and the Milan factor is universal. None of these properties hold for existing sequential recombination algorithms, nor for cone algorithms with split--merge steps, such as SISCone. They are however the identifying characteristics of the collinear unsafe plainiterative cone'' algorithm, for which the anti-k_t algorithm provides a natural, fast, infrared and collinear safe replacement.

• The paper introduces the anti-k_t algorithm that uses a negative energy exponent to produce stable jet boundaries in high-energy collisions.
• It demonstrates robustness to soft radiation and pileup by generating predictably conical jet shapes ideal for collider experiments.
• The algorithm simplifies perturbative QCD calculations, enhancing precision in analyses such as top quark and Higgs physics at the LHC.

The Anti-$k_t$ Jet Clustering Algorithm

This paper introduces the anti-$k_t$ jet clustering algorithm, a novel member of the sequential recombination class of jet algorithms. Traditionally, jet algorithms are pivotal in interpreting data from hadronic collisions, where the complexity of final states, especially at facilities like the Large Hadron Collider (LHC), necessitates robustness in jet definition and identification.

Motivation and Context

The discourse around jet algorithms revolves mainly around the sequential recombination and cone algorithms. The sequential recombination algorithms like $k_t$ and Cambridge/Aachen involve clustering based on a distance measure involving particles' momenta and spatial separation in the pseudorapidity-azimuth ($y-\phi$) plane. Cone algorithms identify jets within fixed geometric cones, potentially leading to irregular boundaries influenced by soft radiation.

The anti-$k_t$ algorithm alters this paradigm by assigning a negative power to the energy scale in its distance measure calculation. This radical approach creates jet shapes that remain unaffected by soft radiations, offering potential advantages in maintaining regular, conical jet shapes, unlike other IRC-safe counterparts.

Characteristics and Results

The anti-$k_t$ algorithm's defining property is its "soft-resistant" boundary, meaning its jet regions do not deform with soft radiation. This property ensures that passive and active jet areas—metrics of a jet's susceptibility to radiation—remain equal and predictable. Furthermore, usual factors such as anomalous area dimensions and non-global logarithms maintain theoretical simplicity, aligning with those of cone algorithms having rigid boundaries.

Notably, the anti-$k_t$ algorithm is characterized by reduced susceptibility to phenomena such as pileup and underlying event contamination, enhancing momentum resolution precision. The equivalency of active and passive areas simplifies analytical calculations necessary for perturbative QCD studies, allowing explicit order-by-order computations without the complications typical with non-uniform boundaries in other algorithms.

Practical Implications and Potential Applications

A significant application of anti-$k_t$ is in scenarios requiring precision in jet identification and calibration, such as top quark and Higgs physics at the LHC. Its compatibility with existing data-analysis frameworks, offering fast processing times and resilience to noise, underpins its potential utility in experimental setups.

Additionally, its robust handling of non-global logarithms—simplifying their computation to align with ideal unexpected boundaries—holds implications for theoretical predictions and the understanding of jet dynamics without necessitating complex recalibrations during experimental fluctuations or detector effects.

Concluding Remarks and Future Directions

The anti-$k_t$ algorithm provides a methodological advance in jet clustering, aligning with experimental and theoretical needs without sacrificing safety from collinear and infrared errors. Its adoption in experimental analyses could enhance data integrity in high-luminosity conditions synonymous with modern collider environments.

Future work may explore the nuanced balance between hard and soft adaptability within negative power frameworks, potentially optimizing algorithmic parameters for diverse event conditions. Moreover, assessing the algorithm's adaptability to multi-scale processes could further establish its utility across a broader spectrum of jet-related analyses. This exploration will likely enrich algorithmic choice, reinforcing the toolkit available to particle physicists at cutting-edge facilities.