30
2 Phenomenology of Jet Substructure
two-prong H → bb decays [180]. The N -jettiness factorisation theorem provides a
basis for precision calculations (see e.g. [196–198]) which can also be performed for
jet substructure observables [195], making this algorithm an interesting choice for
future studies.
2.3.4 The Georgi Algorithm
A very different approach to jet finding, based on maximising a fixed function of the
total four-momentum, has been suggested by H. Georgi [181] for e
+ e
− collisions.
The algorithm is based on a jet function depending on the total energy and the mass
squared divided by the energy. One particular choice is given by
J β = E − β P μ P
μ
/E ,
(2.28)
where β > 1 and P denotes the total four-momentum, obtained by adding the jet
constituents’ four-momenta. The jet function monotonically increases in energy and
decreases in jet mass squared. It is closely related to parton shower kinematics and
can be modified to obtain Lorentz-invariant jet finding [199]. Maximising (2.28) by
subsequently adding particles to the jet, leads to conical a jet with a cone size that
goes to 1/
√ β for large values of β. Removing all particles associated to the jet from
the input list and iterating the procedure leads to non-overlapping, IRC safe jets.
For hadron-hadron collisions, the energy E in (2.28) is replaced by the transverse
energy E T , resulting in the J E T algorithm [182]. The jets feature a shrinking jet cone
size as the jets are closer to the beam direction. A first analytical calculation at NLO
on parton level [200] established a similar cross section for inclusive jet production
in hadron-hadron collisions as for the k T algorithm. In fact, it can been shown that
maximising the jet function, minimising N -jettiness (XCone), and stable cone finding
(SISCone) can be reduced to a more fundamental optimisation problem [201],
explaining the similar behaviour of the cross section.
A promising feature of the J E T algorithm for substructure applications is its global
strategy, which leads to a better reconstruction efficiency for hadronically decaying
W bosons into a single jet, compared to the anti-k T algorithm [182]. A modification
to the algorithm has been proposed [183], where an additional term related to FoxWolfram moments [202, 203] is added to the jet function. This results in a better
performance in terms of signal acceptance versus background efficiency for reconstructing boosted hadronically decaying W bosons when compared to strategies using
sequential recombination algorithms together with filtering [40] and pruning [204].
These studies should be extended, exploiting also other substructure techniques, in
order to establish the usefulness of this algorithm.
2 Phenomenology of Jet Substructure
two-prong H → bb decays [180]. The N -jettiness factorisation theorem provides a
basis for precision calculations (see e.g. [196–198]) which can also be performed for
jet substructure observables [195], making this algorithm an interesting choice for
future studies.
2.3.4 The Georgi Algorithm
A very different approach to jet finding, based on maximising a fixed function of the
total four-momentum, has been suggested by H. Georgi [181] for e
+ e
− collisions.
The algorithm is based on a jet function depending on the total energy and the mass
squared divided by the energy. One particular choice is given by
J β = E − β P μ P
μ
/E ,
(2.28)
where β > 1 and P denotes the total four-momentum, obtained by adding the jet
constituents’ four-momenta. The jet function monotonically increases in energy and
decreases in jet mass squared. It is closely related to parton shower kinematics and
can be modified to obtain Lorentz-invariant jet finding [199]. Maximising (2.28) by
subsequently adding particles to the jet, leads to conical a jet with a cone size that
goes to 1/
√ β for large values of β. Removing all particles associated to the jet from
the input list and iterating the procedure leads to non-overlapping, IRC safe jets.
For hadron-hadron collisions, the energy E in (2.28) is replaced by the transverse
energy E T , resulting in the J E T algorithm [182]. The jets feature a shrinking jet cone
size as the jets are closer to the beam direction. A first analytical calculation at NLO
on parton level [200] established a similar cross section for inclusive jet production
in hadron-hadron collisions as for the k T algorithm. In fact, it can been shown that
maximising the jet function, minimising N -jettiness (XCone), and stable cone finding
(SISCone) can be reduced to a more fundamental optimisation problem [201],
explaining the similar behaviour of the cross section.
A promising feature of the J E T algorithm for substructure applications is its global
strategy, which leads to a better reconstruction efficiency for hadronically decaying
W bosons into a single jet, compared to the anti-k T algorithm [182]. A modification
to the algorithm has been proposed [183], where an additional term related to FoxWolfram moments [202, 203] is added to the jet function. This results in a better
performance in terms of signal acceptance versus background efficiency for reconstructing boosted hadronically decaying W bosons when compared to strategies using
sequential recombination algorithms together with filtering [40] and pruning [204].
These studies should be extended, exploiting also other substructure techniques, in
order to establish the usefulness of this algorithm.