2.3 Jet Algorithms
27
Despite the fact that the k T , anti-k T and CA algorithms are identical except for the
choice of the parameter k, each of them exhibits a very different behaviour.
The k T algorithm starts with clustering soft and collinear objects, harder objects
are clustered at later iteration steps. This leads to irregular jet boundaries with on
average larger jet areas [184] than those of other algorithms with the same value of
R [185].
The anti-k T algorithm starts with the hardest object and accumulates all objects
within a distance smaller than R into a jet. If there is no harder jet within the jet’s
vicinity with a distance smaller than R, the resulting jet is circular in the y − φ plane
and has an area of exactly π R
2 .
7 Anti-k T jets also exhibit the smallest amount of
back-reaction [59] among the three clustering algorithms discussed here. Because of
these features anti-k T jets became the standard choice for jet analyses at the LHC.
Since the softest particles are clustered last in the anti-k T algorithm, it is unsuited for
substructure taggers which include decomposition steps.
The CA algorithm is insensitive to the objects’ transverse momenta and builds jets
using geometrical proximity in the y − φ plane as the only criterion. Like the k T algorithm, the resulting jets are somewhat irregular, but the angular hierarchy makes the
clustering sequence very useful for substructure techniques, where different angular
scales can reveal the underlying dynamics.
2.3.2 Variable R Algorithm
The optimal choice of the distance parameter R used in an analysis depends on
the physics case under consideration. In general, perturbative and non-perturbative
effects influence jet observables. The relative size of these contributions depends
on the choice of R. The transverse momentum of a jet with a given value of R is
modified by perturbative effects proportional to ln R, while hadronisation effects lead
to a change proportional to R
−1 , and corrections due to the underlying event grow as
R
2 [186]. The same hierarchy holds for the jet mass, albeit modified by two powers
of R (see Sect. 2.4.1). The average squared jet mass is modified by perturbative
corrections proportional to α s R
2 p
2
T [161], whereas hadronisation corrections grow
linearly with Rp T and the underlying event affects the jet mass proportional to R
4 p T
at leading order [186].
This leads to a predicament for jet substructure analyses. At low values of p T of
the decaying object, a large value of R must be chosen to combine all decay products
in a single jet. At low values of p T the non-perturbative effects on the jet substructure
are still manageable. At large values of p T the influence of non-perturbative effects
on the jet mass and other substructure observables is much larger, resulting in a
performance loss of substructure techniques. A possible solution to this dilemma is
7 The jet axis will change between the different clustering steps because of combining particles i
and j, resulting in a slight deviation from the exact value of π R 2 .
27
Despite the fact that the k T , anti-k T and CA algorithms are identical except for the
choice of the parameter k, each of them exhibits a very different behaviour.
The k T algorithm starts with clustering soft and collinear objects, harder objects
are clustered at later iteration steps. This leads to irregular jet boundaries with on
average larger jet areas [184] than those of other algorithms with the same value of
R [185].
The anti-k T algorithm starts with the hardest object and accumulates all objects
within a distance smaller than R into a jet. If there is no harder jet within the jet’s
vicinity with a distance smaller than R, the resulting jet is circular in the y − φ plane
and has an area of exactly π R
2 .
7 Anti-k T jets also exhibit the smallest amount of
back-reaction [59] among the three clustering algorithms discussed here. Because of
these features anti-k T jets became the standard choice for jet analyses at the LHC.
Since the softest particles are clustered last in the anti-k T algorithm, it is unsuited for
substructure taggers which include decomposition steps.
The CA algorithm is insensitive to the objects’ transverse momenta and builds jets
using geometrical proximity in the y − φ plane as the only criterion. Like the k T algorithm, the resulting jets are somewhat irregular, but the angular hierarchy makes the
clustering sequence very useful for substructure techniques, where different angular
scales can reveal the underlying dynamics.
2.3.2 Variable R Algorithm
The optimal choice of the distance parameter R used in an analysis depends on
the physics case under consideration. In general, perturbative and non-perturbative
effects influence jet observables. The relative size of these contributions depends
on the choice of R. The transverse momentum of a jet with a given value of R is
modified by perturbative effects proportional to ln R, while hadronisation effects lead
to a change proportional to R
−1 , and corrections due to the underlying event grow as
R
2 [186]. The same hierarchy holds for the jet mass, albeit modified by two powers
of R (see Sect. 2.4.1). The average squared jet mass is modified by perturbative
corrections proportional to α s R
2 p
2
T [161], whereas hadronisation corrections grow
linearly with Rp T and the underlying event affects the jet mass proportional to R
4 p T
at leading order [186].
This leads to a predicament for jet substructure analyses. At low values of p T of
the decaying object, a large value of R must be chosen to combine all decay products
in a single jet. At low values of p T the non-perturbative effects on the jet substructure
are still manageable. At large values of p T the influence of non-perturbative effects
on the jet mass and other substructure observables is much larger, resulting in a
performance loss of substructure techniques. A possible solution to this dilemma is
7 The jet axis will change between the different clustering steps because of combining particles i
and j, resulting in a slight deviation from the exact value of π R 2 .