44
2 Phenomenology of Jet Substructure
to introduce a variable transformation of the form ν
DDT
i j
= ν i j − c log(ρ SD ), which
results in an unaltered shape of the m SD distribution after a cut on the decorrelated
variable ν
DDT
i j
. The scaling variable is given by ρ SD = m SD / p T,SD and the constant c
is determined from the ρ SD dependence of the ν i j distribution in bins of p T . While the
decorrelation is usually obtained from studies using MC event generators, it is also
possible to obtain the decorrelated shapes from analytical calculations [252, 253],
where both approaches agree within uncertainties. The performance of a DDT tagger
is similar to the uncorrelated version if no selection on the jet mass is applied. In case
of a jet mass selection, the tagging performance using ν
DDT
i j
can be better than using
the plain shape ν i j , as less background events are reconstructed within the selected
jet mass window (see for example [254]).
Qjets
Quantum jets [255], or Qjets, are based on the stochastic nature of parton showers.
While the radiation pattern of quarks and gluons is inherently random within the
physically allowed boundaries, N -prong decays adhere to kinematic constraints in
addition to stochastic showering. When constructing jets, this can be used to discriminate N -prong decays from quark and gluon jets by building multiple variants of a
single jet, where the jet constituents are weighted by an appropriate metric during
the clustering. Then each jet in each event produces a distribution for an observable.
This can lead to new discriminating variables, like the relative width of the ensemble
of jet masses for a single jet, or to an improvement of the statistical stability of an
observable [256]. Note that this only works in combination with a grooming step,
which discards selected particles in the clustering, where pruning is used in the originally proposed version of Qjets. Due to the random modification of the distance
measure d i j in (2.20), different particles are discarded in each iteration, resulting in
wider distributions for light quark and gluon jets than for jets with N definite hard
prongs.
Shower Deconstruction
Shower Deconstruction [257, 258] is based on calculating conditional probabilities
that a given set of N final state particles { p N } = ( p 1 , . . . , p N ) originates from a
signal, P(S|{ p N }), or a background hypothesis, P(B|{ p N }). The likelihood ratio
χ =
P(S|{ p N })
P(B|{ p N })
(2.43)
can then be used as a discriminator in an analysis. The signal and background probabilities are computed using an all-order QCD calculation, where all possible splittings
into initial- or final-state radiation are taken into account. For each such splitting all
possible shower histories are considered that could lead to the final state { p N }. A
weight is computed for each history, where each vertex receives a factor from the
partonic splitting probability and a Sudakov form factor. The LO matrix elements
for the decays of W , Z , H bosons and t quarks are used. By retaining the full mass
dependency for the partons, leading-logarithmic accuracy is achieved. Shower decon-
2 Phenomenology of Jet Substructure
to introduce a variable transformation of the form ν
DDT
i j
= ν i j − c log(ρ SD ), which
results in an unaltered shape of the m SD distribution after a cut on the decorrelated
variable ν
DDT
i j
. The scaling variable is given by ρ SD = m SD / p T,SD and the constant c
is determined from the ρ SD dependence of the ν i j distribution in bins of p T . While the
decorrelation is usually obtained from studies using MC event generators, it is also
possible to obtain the decorrelated shapes from analytical calculations [252, 253],
where both approaches agree within uncertainties. The performance of a DDT tagger
is similar to the uncorrelated version if no selection on the jet mass is applied. In case
of a jet mass selection, the tagging performance using ν
DDT
i j
can be better than using
the plain shape ν i j , as less background events are reconstructed within the selected
jet mass window (see for example [254]).
Qjets
Quantum jets [255], or Qjets, are based on the stochastic nature of parton showers.
While the radiation pattern of quarks and gluons is inherently random within the
physically allowed boundaries, N -prong decays adhere to kinematic constraints in
addition to stochastic showering. When constructing jets, this can be used to discriminate N -prong decays from quark and gluon jets by building multiple variants of a
single jet, where the jet constituents are weighted by an appropriate metric during
the clustering. Then each jet in each event produces a distribution for an observable.
This can lead to new discriminating variables, like the relative width of the ensemble
of jet masses for a single jet, or to an improvement of the statistical stability of an
observable [256]. Note that this only works in combination with a grooming step,
which discards selected particles in the clustering, where pruning is used in the originally proposed version of Qjets. Due to the random modification of the distance
measure d i j in (2.20), different particles are discarded in each iteration, resulting in
wider distributions for light quark and gluon jets than for jets with N definite hard
prongs.
Shower Deconstruction
Shower Deconstruction [257, 258] is based on calculating conditional probabilities
that a given set of N final state particles { p N } = ( p 1 , . . . , p N ) originates from a
signal, P(S|{ p N }), or a background hypothesis, P(B|{ p N }). The likelihood ratio
χ =
P(S|{ p N })
P(B|{ p N })
(2.43)
can then be used as a discriminator in an analysis. The signal and background probabilities are computed using an all-order QCD calculation, where all possible splittings
into initial- or final-state radiation are taken into account. For each such splitting all
possible shower histories are considered that could lead to the final state { p N }. A
weight is computed for each history, where each vertex receives a factor from the
partonic splitting probability and a Sudakov form factor. The LO matrix elements
for the decays of W , Z , H bosons and t quarks are used. By retaining the full mass
dependency for the partons, leading-logarithmic accuracy is achieved. Shower decon-