2.4 Identifying Particle Decays with Jet Substructure
37
Jet Shapes
Event-shape variables defined for e
+ e
− collisions can be modified to include only
particles clustered into a given jet. Originally, jet shapes have been defined for hadron
colliders as differential ρ(r ) and integrated distributions (r ), which describe the
jet energy fraction that lies within an annulus of size r ± r/2 or a cone with radius
r around the jet axis, respectively [60]. While the discrimination power of such
jet shapes is usually limited, a combination of several variables can achieve good
performance. An example are distributions of Fox-Wolfram moments [202, 203],
sphericity [43] and thrust [44–46], calculated in the rest frame of the parent particle.
Since the parent particle is usually unknown, a recent approach [229] defines four
rest frames for W , Z , H and t hypotheses and combines the obtained boosted event
shapes with an artificial neural network.
2.4.3 Jet Grooming and N-Prong Taggers
Traditionally, there has been a distinction between jet grooming techniques and N -
prong finders, or taggers, where the former are designed to reduce the impact of
non-perturbative effects on a jet, and the latter aim at labelling a jet to originate
from the collimated hadronic decay of a given heavy particle. This distinction is
somewhat misleading as grooming techniques are frequently used as taggers. By
modifying the jet substructure, a better separation between signal and background is
achieved with grooming techniques, resulting in an improved tagging performance
when selecting jets based on substructure observables. Commonly used examples
are trimming [230], as used in ATLAS, and soft drop [231], as used in CMS. The
most widely used grooming methods and taggers are reviewed in the following.
Filtering
Filtering [40] was designed to resolve large jets on a finer angular scale. This is
achieved by reclustering the jet constituents with a filter radius R sub , much smaller
than the original size of the jet R. Only the N filt hardest subjets are kept, where N filt
should be adjusted to the particular physics case. In general, for an N -prong decay,
N filt = N + 1 subjets should be kept to capture the dominant O(α S ) radiation from
the partonic decay. Filtering has been originally introduced together with a mass drop
criterion (see the mass drop tagger below) and is used in a number of applications,
most notably the HEPTopTagger [232–234].
A first analytical calculation in the leading logarithmic approximation [235] for
filtered jets from the H → bb decay, showed indeed that an optimal choice is N filt = 3
or 4 and that the parameter R filt should not be chosen too large or too small, where
values of R filt /R between 0.3 and 0.4 lead to an acceptable agreement between the
analytical fixed-order results and numerical all-order resummed results. This agreement implies not too large higher-order corrections, important for reliable predictions. Higher-order predictions in NLL accuracy and better are difficult for filtering,
because of a non-trivial slicing of the phase space.
37
Jet Shapes
Event-shape variables defined for e
+ e
− collisions can be modified to include only
particles clustered into a given jet. Originally, jet shapes have been defined for hadron
colliders as differential ρ(r ) and integrated distributions (r ), which describe the
jet energy fraction that lies within an annulus of size r ± r/2 or a cone with radius
r around the jet axis, respectively [60]. While the discrimination power of such
jet shapes is usually limited, a combination of several variables can achieve good
performance. An example are distributions of Fox-Wolfram moments [202, 203],
sphericity [43] and thrust [44–46], calculated in the rest frame of the parent particle.
Since the parent particle is usually unknown, a recent approach [229] defines four
rest frames for W , Z , H and t hypotheses and combines the obtained boosted event
shapes with an artificial neural network.
2.4.3 Jet Grooming and N-Prong Taggers
Traditionally, there has been a distinction between jet grooming techniques and N -
prong finders, or taggers, where the former are designed to reduce the impact of
non-perturbative effects on a jet, and the latter aim at labelling a jet to originate
from the collimated hadronic decay of a given heavy particle. This distinction is
somewhat misleading as grooming techniques are frequently used as taggers. By
modifying the jet substructure, a better separation between signal and background is
achieved with grooming techniques, resulting in an improved tagging performance
when selecting jets based on substructure observables. Commonly used examples
are trimming [230], as used in ATLAS, and soft drop [231], as used in CMS. The
most widely used grooming methods and taggers are reviewed in the following.
Filtering
Filtering [40] was designed to resolve large jets on a finer angular scale. This is
achieved by reclustering the jet constituents with a filter radius R sub , much smaller
than the original size of the jet R. Only the N filt hardest subjets are kept, where N filt
should be adjusted to the particular physics case. In general, for an N -prong decay,
N filt = N + 1 subjets should be kept to capture the dominant O(α S ) radiation from
the partonic decay. Filtering has been originally introduced together with a mass drop
criterion (see the mass drop tagger below) and is used in a number of applications,
most notably the HEPTopTagger [232–234].
A first analytical calculation in the leading logarithmic approximation [235] for
filtered jets from the H → bb decay, showed indeed that an optimal choice is N filt = 3
or 4 and that the parameter R filt should not be chosen too large or too small, where
values of R filt /R between 0.3 and 0.4 lead to an acceptable agreement between the
analytical fixed-order results and numerical all-order resummed results. This agreement implies not too large higher-order corrections, important for reliable predictions. Higher-order predictions in NLL accuracy and better are difficult for filtering,
because of a non-trivial slicing of the phase space.