6
2 Phenomenology of Jet Substructure
With the advent of the LHC it was realised that decays of hypothetical, very heavy
resonances can lead to highly Lorentz-boosted heavy SM particles, W , Z , H bosons
and top quarks [37–41]. Since these particles feature the largest branching fractions
into hadrons, final states with fully-hadronic decays have high sensitivity in LHC
analyses. The large boost leads to very collimated decays, where particle masses of
O(100) GeV are not large enough for the outgoing quarks to be sufficiently separated
relative to each other to be resolved into individual jets. It is the small opening angle
between the decay products that leads to fully-merged particle decays. This chapter
describes techniques for measuring jets as proxies for hadronic decays of W , Z , H
bosons and top quarks, as well as the discrimination of quark and gluon jets.
Since the first evidence for jets in e
+ e
− collisions at SPEAR [42], jets have had a
significant impact on the research programme of every particle collider since DORIS
through the LHC, and beyond to the design of future colliders. There is no single,
universal definition of a jet—which particles belong to a jet depend on the algorithm
used to combine particles into jets. In the beginning of jets from the mid 1970’s,
there were no jet clustering algorithms; information from the whole event was used
instead of localised energy flows. The sphericity tensor [43] was typically used to
obtain a jet axis for events with a back-to-back dijet topology. Quantitative statements
about data were obtained from event shapes, like the sphericity or thrust [44–46].
Sphericity is a measure for the isotropy of the particles produced and thrust is a
measure of the directed energy flow along an axis that maximises this flow in an
event. These event shapes can be used to characterise how compatible events are
with the assumption of two oppositely directed, collimated jets. A clear theoretical
advantage of these event shapes is that they are calculable in perturbative Quantum
Chromodynamics (pQCD). This was realised early on and the calculability, together
with experimental data, ultimately resulted in the confirmation of the parton model
and, with data from experiments at higher
√
s, the discovery of the gluon in three jet
events at PETRA [27–30].
When studying the dynamics of quark and gluon scattering, it became necessary
to perform quantitative analyses and calculations that go beyond event shapes. For
these to be possible, it was realised that it is mandatory to define a deterministic
set of rules on how particles are combined into jets. A schematic drawing depicting
this problem is shown in Fig. 2.1. While the sphericity axis is uniquely defined and
easily calculable, the direction and magnitude of the jet axes depend on which particles should be combined into a given jet, and how the particles are combined to
obtain the axes. An intuitive definition for a jet algorithm consists of summing the
momenta of all particles within a cone with fixed size [47]. Naive cone algorithms
are not infrared and collinear (IRC) safe—the requirement that the resulting jets be
insensitive to arbitrarily low energy particles and collinear splittings. IRC safety is a
useful theoretical requirement for making calculations in pQCD and is also a convenient language for describing the experimental robustness to noise and detector
granularity.
There exist many variants of cone-type algorithms, developed in the attempt to
solve the IRC unsafety of naive cone jet algorithms. This stems from the necessity of
an initial axis, which was eventually solved with the formulation of the SISCone algo-
2 Phenomenology of Jet Substructure
With the advent of the LHC it was realised that decays of hypothetical, very heavy
resonances can lead to highly Lorentz-boosted heavy SM particles, W , Z , H bosons
and top quarks [37–41]. Since these particles feature the largest branching fractions
into hadrons, final states with fully-hadronic decays have high sensitivity in LHC
analyses. The large boost leads to very collimated decays, where particle masses of
O(100) GeV are not large enough for the outgoing quarks to be sufficiently separated
relative to each other to be resolved into individual jets. It is the small opening angle
between the decay products that leads to fully-merged particle decays. This chapter
describes techniques for measuring jets as proxies for hadronic decays of W , Z , H
bosons and top quarks, as well as the discrimination of quark and gluon jets.
Since the first evidence for jets in e
+ e
− collisions at SPEAR [42], jets have had a
significant impact on the research programme of every particle collider since DORIS
through the LHC, and beyond to the design of future colliders. There is no single,
universal definition of a jet—which particles belong to a jet depend on the algorithm
used to combine particles into jets. In the beginning of jets from the mid 1970’s,
there were no jet clustering algorithms; information from the whole event was used
instead of localised energy flows. The sphericity tensor [43] was typically used to
obtain a jet axis for events with a back-to-back dijet topology. Quantitative statements
about data were obtained from event shapes, like the sphericity or thrust [44–46].
Sphericity is a measure for the isotropy of the particles produced and thrust is a
measure of the directed energy flow along an axis that maximises this flow in an
event. These event shapes can be used to characterise how compatible events are
with the assumption of two oppositely directed, collimated jets. A clear theoretical
advantage of these event shapes is that they are calculable in perturbative Quantum
Chromodynamics (pQCD). This was realised early on and the calculability, together
with experimental data, ultimately resulted in the confirmation of the parton model
and, with data from experiments at higher
√
s, the discovery of the gluon in three jet
events at PETRA [27–30].
When studying the dynamics of quark and gluon scattering, it became necessary
to perform quantitative analyses and calculations that go beyond event shapes. For
these to be possible, it was realised that it is mandatory to define a deterministic
set of rules on how particles are combined into jets. A schematic drawing depicting
this problem is shown in Fig. 2.1. While the sphericity axis is uniquely defined and
easily calculable, the direction and magnitude of the jet axes depend on which particles should be combined into a given jet, and how the particles are combined to
obtain the axes. An intuitive definition for a jet algorithm consists of summing the
momenta of all particles within a cone with fixed size [47]. Naive cone algorithms
are not infrared and collinear (IRC) safe—the requirement that the resulting jets be
insensitive to arbitrarily low energy particles and collinear splittings. IRC safety is a
useful theoretical requirement for making calculations in pQCD and is also a convenient language for describing the experimental robustness to noise and detector
granularity.
There exist many variants of cone-type algorithms, developed in the attempt to
solve the IRC unsafety of naive cone jet algorithms. This stems from the necessity of
an initial axis, which was eventually solved with the formulation of the SISCone algo-