42
2 Phenomenology of Jet Substructure
free parameter of the algorithm. The resulting pseudojet enters the next clustering
step and the initial pseudojets are stored as separate subjets. In case the mass jump
criterion is not fulfilled or the pseudojets are softer than p T,sub , the lighter pseudojet
or the one too soft is removed from the list. This step acts as a jet grooming and
stabilises the jet mass over a large range of p T .
The algorithm results in groomed VR jets with an effective radius R eff between
R min and R max (see the VR algorithm in Sect. 2.3.2), containing subjets with R < R eff
with a mass jump. The number of subjets found is modified by the mass jump
parameters μ, θ and p T,sub . Once the pseudojets become sufficiently heavy due to
clustering, the mass jump threshold μ results in a rejection of soft and light pseudojets.
For a fixed value of μ, the strength of this jet grooming depends on the parameters θ
and p T,sub . For θ = 1 the mass jump condition is always fulfilled and no pseudojets
are rejected (equivalent to the case μ → ∞). Conversely, the case of θ = 0 results in
a VR jet clustering which stops as soon as a jet mass of μ is reached. The algorithm
results in subjets with a maximum mass of μ. Additional jet grooming is obtained by
setting p T,sub > 0. This results in subjets with a minimum p T of p T,sub , effectively
removing soft radiation and improving the tagging performance at small p T of the
heavy object. The HOTVR algorithm is IRC safe, which has also been confirmed in
numerical studies [247].
The behaviour of the algorithm is visualised in Fig. 2.13 where two example tt
events, generated with Pythia 8 [248–250] at low p T (top row, Event 1) and at high
p T (bottom row, Event 2), are clustered with the CA algorithm (left column) and with
the HOTVR algorithm (right column). The active catchment areas of the hard jets are
obtained using ghost particles [185] and are illustrated by the coloured (orange/blue)
areas.
12 The impact of the VR part of the algorithm is nicely illustrated by the
largely different jet sizes of the two events clustered with the HOTVR algorithm
(right column). The grey regions in the right panels were rejected by the mass jump
criterion and are not part of the HOTVR jets. This criterion has largest impact in
events at low p T as exemplified in Event 1 (top, right). The HOTVR jets together
with their subjets reproduce the kinematics of the top decay adequately, both at low
and high p T , demonstrating a better adaptation to the decay topology than CA or
anti-k T jets.
2.4.4 Other Methods
There are a number of jet substructure methods that can neither be classified as
angularity/correlation variable nor as grooming/tagging algorithm. Some of the most
widely used are described below.
12 The exact borders of the jet areas depend slightly on the specific configuration of the ghost
particles.
2 Phenomenology of Jet Substructure
free parameter of the algorithm. The resulting pseudojet enters the next clustering
step and the initial pseudojets are stored as separate subjets. In case the mass jump
criterion is not fulfilled or the pseudojets are softer than p T,sub , the lighter pseudojet
or the one too soft is removed from the list. This step acts as a jet grooming and
stabilises the jet mass over a large range of p T .
The algorithm results in groomed VR jets with an effective radius R eff between
R min and R max (see the VR algorithm in Sect. 2.3.2), containing subjets with R < R eff
with a mass jump. The number of subjets found is modified by the mass jump
parameters μ, θ and p T,sub . Once the pseudojets become sufficiently heavy due to
clustering, the mass jump threshold μ results in a rejection of soft and light pseudojets.
For a fixed value of μ, the strength of this jet grooming depends on the parameters θ
and p T,sub . For θ = 1 the mass jump condition is always fulfilled and no pseudojets
are rejected (equivalent to the case μ → ∞). Conversely, the case of θ = 0 results in
a VR jet clustering which stops as soon as a jet mass of μ is reached. The algorithm
results in subjets with a maximum mass of μ. Additional jet grooming is obtained by
setting p T,sub > 0. This results in subjets with a minimum p T of p T,sub , effectively
removing soft radiation and improving the tagging performance at small p T of the
heavy object. The HOTVR algorithm is IRC safe, which has also been confirmed in
numerical studies [247].
The behaviour of the algorithm is visualised in Fig. 2.13 where two example tt
events, generated with Pythia 8 [248–250] at low p T (top row, Event 1) and at high
p T (bottom row, Event 2), are clustered with the CA algorithm (left column) and with
the HOTVR algorithm (right column). The active catchment areas of the hard jets are
obtained using ghost particles [185] and are illustrated by the coloured (orange/blue)
areas.
12 The impact of the VR part of the algorithm is nicely illustrated by the
largely different jet sizes of the two events clustered with the HOTVR algorithm
(right column). The grey regions in the right panels were rejected by the mass jump
criterion and are not part of the HOTVR jets. This criterion has largest impact in
events at low p T as exemplified in Event 1 (top, right). The HOTVR jets together
with their subjets reproduce the kinematics of the top decay adequately, both at low
and high p T , demonstrating a better adaptation to the decay topology than CA or
anti-k T jets.
2.4.4 Other Methods
There are a number of jet substructure methods that can neither be classified as
angularity/correlation variable nor as grooming/tagging algorithm. Some of the most
widely used are described below.
12 The exact borders of the jet areas depend slightly on the specific configuration of the ghost
particles.