22
2 Phenomenology of Jet Substructure
Table 2.2 Numerical values of ρ 90 and α for the calculation of the 90th percentile 90 , as given
in (2.16). The top part is obtained without a kinematic requirement on the decay quarks, the bottom
part is obtained for p T,q > 20 GeV
[GeV]
T
p
200
400
600
800
1000 1200 1400
')
q
R(q
Δ
0
0.5
1
'
q
q
→
T
W
> 20 GeV:
T,q
Percentiles for p
70%
80%
90%
MPV
1
−
T
p
W
2M
1
−
T
(370 GeV) p
[GeV]
T
p
200
400
600
800
1000 1200 1400
)
b
R(b
Δ
0
0.5
1
b
b
→
H
> 20 GeV:
T,q
Percentiles for p
70%
80%
90%
MPV
1
−
T
p
H
2M
1
−
T
(500 GeV) p
Fig. 2.8 Angular distance between the two quarks from the decay of transversely polarised
W (left) and a H bosons (right), as a function of the boson p T . The transverse momenta of the two
quarks from the decay are required to be p T,q > 20 GeV. The fraction of events contained within a
given interval in are shown by shaded areas, the most probable value (MPV) is depicted by a
dashed line. For comparison, also shown are the naive expectations 2M W / p T and 2M H / p T (solid
lines), and the functions (370 GeV)/ p T and (500 GeV)/ p T (dotted lines)
see (2.16), parametrisations can be found that describe the shapes of the percentiles
well. An example is given in the bottom part of Table 2.2, where the parameters for
the 90 percentiles are given for the requirement p T,q > 20 GeV. Another observation from Fig. 2.8 is that the minimum value of can be accurately predicted by
(2.14), which also coincides with the MPV. Only for H decays with p T < 300 GeV
the approximation (2.14) starts to deviate from the realistic shape, since for small
values of p T the approximation of small angles in (2.12) is not valid any more.
2.2.8 Kinematics of Top Quark Decays
In the SM, the top quark decays to bW with a branching fraction larger than 99.9%.
The subsequent hadronic decay of the W boson leads to the decay chain t → bW →
bqq
, with three quarks in the final state. The narrow width approximation, where
the top quark and the W boson are on-shell, is sufficiently accurate to study the
kinematics of this decay for substructure related applications. Thus, the decay can
2 Phenomenology of Jet Substructure
Table 2.2 Numerical values of ρ 90 and α for the calculation of the 90th percentile 90 , as given
in (2.16). The top part is obtained without a kinematic requirement on the decay quarks, the bottom
part is obtained for p T,q > 20 GeV
[GeV]
T
p
200
400
600
800
1000 1200 1400
')
q
R(q
Δ
0
0.5
1
'
q
q
→
T
W
> 20 GeV:
T,q
Percentiles for p
70%
80%
90%
MPV
1
−
T
p
W
2M
1
−
T
(370 GeV) p
[GeV]
T
p
200
400
600
800
1000 1200 1400
)
b
R(b
Δ
0
0.5
1
b
b
→
H
> 20 GeV:
T,q
Percentiles for p
70%
80%
90%
MPV
1
−
T
p
H
2M
1
−
T
(500 GeV) p
Fig. 2.8 Angular distance between the two quarks from the decay of transversely polarised
W (left) and a H bosons (right), as a function of the boson p T . The transverse momenta of the two
quarks from the decay are required to be p T,q > 20 GeV. The fraction of events contained within a
given interval in are shown by shaded areas, the most probable value (MPV) is depicted by a
dashed line. For comparison, also shown are the naive expectations 2M W / p T and 2M H / p T (solid
lines), and the functions (370 GeV)/ p T and (500 GeV)/ p T (dotted lines)
see (2.16), parametrisations can be found that describe the shapes of the percentiles
well. An example is given in the bottom part of Table 2.2, where the parameters for
the 90 percentiles are given for the requirement p T,q > 20 GeV. Another observation from Fig. 2.8 is that the minimum value of can be accurately predicted by
(2.14), which also coincides with the MPV. Only for H decays with p T < 300 GeV
the approximation (2.14) starts to deviate from the realistic shape, since for small
values of p T the approximation of small angles in (2.12) is not valid any more.
2.2.8 Kinematics of Top Quark Decays
In the SM, the top quark decays to bW with a branching fraction larger than 99.9%.
The subsequent hadronic decay of the W boson leads to the decay chain t → bW →
bqq
, with three quarks in the final state. The narrow width approximation, where
the top quark and the W boson are on-shell, is sufficiently accurate to study the
kinematics of this decay for substructure related applications. Thus, the decay can