4.1 Measurements of Jet Substructure Observables
105
the distributions in all three jet flavours are observed. These observations can be
generalised using a single observable like the energy correlation ratios C
(β)
1 . By
changing the angular exponent β, the importance of energy and angular correlations
can be adjusted. For β = 0, the distributions in C
(0)
1 for gluon and b jets are similar,
while light quark jets behave differently. For 0.2 ≤ β ≤ 1, the distributions in C
(β)
1
are different for all three jet flavours and for β ≥ 2, b and light quark jets are similar,
but gluon jets are different. Similar observations are made for the M
(β)
2 , N
(β)
2 and N
(β)
3
distributions. An interesting observation is the high sensitivity in the θ g distribution
to the value of α S used in the final state shower. This has been exploited to determine
α S (M
2
Z ) for the first time from the substructure of b jets. The value obtained is
α S (M
2
Z ) = 0.115
+0.016
−0.013 , where the dominating uncertainty of
+0.014
−0.012 originates from
scale variations in the final state shower. While the data have the precision for a
very accurate determination of α S (M
2
Z ) with an experimental uncertainty of ±0.001,
higher order corrections are needed to improve this determination.
The tt final state uniquely allows studies of the colour flow in events where the
colour configuration is known. In hadronic decays of the W boson, the qq pair is in a
colour singlet state. A measurement of the pull angle θ p between the two jets initiated
by the qq system is sensitive to the colour configuration. A first measurement by
ATLAS using 8 TeV data has shown that the colour-connected light quark jets result
in a falling distribution with a peak at θ p ≈ 0 [598]. This measurement also resulted
in an exclusion of an alternative colour-octet configuration of the qq pair by more
than three standard deviations. Despite being IRC unsafe, the pull angle can be
calculated analytically from first principles using an all-order resummation [599].
The resummed calculation and the prediction from Pythia are in agreement, but are
slightly more peaked than the observed data. The presence of two b jets from the tt
decay can be used to study the pull vector for two different colour configurations in the
same final state. An ATLAS measurement using 13 TeV data has reported unfolded
distributions of the pull angle between the light quark jets from the W decay and the
two b jets from the tt decay [600]. In contrast to the colour-connected light quark
jets, the θ p distribution for the two b jets is approximately flat. This behaviour is
qualitatively reproduced by the simulations tested, but quantitative differences are
observed. Understanding these differences is difficult because of the IRC unsafety
of the pull angle, resulting in large uncertainties in the theoretical calculations. It
has been found that the projections of the pull vector along and perpendicular to the
line joining the two centres of the jets of interest are IRC safe, allowing for all-order
calculations and more conclusive theoretical insights [228].
4.1.5 Jet Substructure in W and Top Jets
Substructure observables of W and t jets play a key role in the development and
commissioning of jet substructure taggers. Their experimental reconstruction and
resolution, performance and simulation is usually studied at the level of reconstructed
105
the distributions in all three jet flavours are observed. These observations can be
generalised using a single observable like the energy correlation ratios C
(β)
1 . By
changing the angular exponent β, the importance of energy and angular correlations
can be adjusted. For β = 0, the distributions in C
(0)
1 for gluon and b jets are similar,
while light quark jets behave differently. For 0.2 ≤ β ≤ 1, the distributions in C
(β)
1
are different for all three jet flavours and for β ≥ 2, b and light quark jets are similar,
but gluon jets are different. Similar observations are made for the M
(β)
2 , N
(β)
2 and N
(β)
3
distributions. An interesting observation is the high sensitivity in the θ g distribution
to the value of α S used in the final state shower. This has been exploited to determine
α S (M
2
Z ) for the first time from the substructure of b jets. The value obtained is
α S (M
2
Z ) = 0.115
+0.016
−0.013 , where the dominating uncertainty of
+0.014
−0.012 originates from
scale variations in the final state shower. While the data have the precision for a
very accurate determination of α S (M
2
Z ) with an experimental uncertainty of ±0.001,
higher order corrections are needed to improve this determination.
The tt final state uniquely allows studies of the colour flow in events where the
colour configuration is known. In hadronic decays of the W boson, the qq pair is in a
colour singlet state. A measurement of the pull angle θ p between the two jets initiated
by the qq system is sensitive to the colour configuration. A first measurement by
ATLAS using 8 TeV data has shown that the colour-connected light quark jets result
in a falling distribution with a peak at θ p ≈ 0 [598]. This measurement also resulted
in an exclusion of an alternative colour-octet configuration of the qq pair by more
than three standard deviations. Despite being IRC unsafe, the pull angle can be
calculated analytically from first principles using an all-order resummation [599].
The resummed calculation and the prediction from Pythia are in agreement, but are
slightly more peaked than the observed data. The presence of two b jets from the tt
decay can be used to study the pull vector for two different colour configurations in the
same final state. An ATLAS measurement using 13 TeV data has reported unfolded
distributions of the pull angle between the light quark jets from the W decay and the
two b jets from the tt decay [600]. In contrast to the colour-connected light quark
jets, the θ p distribution for the two b jets is approximately flat. This behaviour is
qualitatively reproduced by the simulations tested, but quantitative differences are
observed. Understanding these differences is difficult because of the IRC unsafety
of the pull angle, resulting in large uncertainties in the theoretical calculations. It
has been found that the projections of the pull vector along and perpendicular to the
line joining the two centres of the jets of interest are IRC safe, allowing for all-order
calculations and more conclusive theoretical insights [228].
4.1.5 Jet Substructure in W and Top Jets
Substructure observables of W and t jets play a key role in the development and
commissioning of jet substructure taggers. Their experimental reconstruction and
resolution, performance and simulation is usually studied at the level of reconstructed