5.1 Diboson Resonances
135
of 13 TeV data. These enlarge the scope of previous combinations by including the
leptonic channels [757, 758] and [759, 760], thus adding sensitivity to models
with large fermionic couplings.
The difficulty in combining different analyses in very different channels and final
states lies in ensuring full orthogonality between the analyses, i.e. statistical independence of all signal regions such that events in data are considered exactly once. The
challenge here is that sideband and control regions of one analysis might be part of
the signal region of another analysis. In addition, the same definitions of jet substructure observables and lepton identification variables have to be used in all analyses
considered, such that no unwanted and unknown correlations are introduced. Precise results also require knowledge of correlations between sources of systematic
uncertainties. The feasibility of a combination including a large number of individual results requires careful planning and coordination prior to the execution of the
individual searches. Note that when designing the analyses, the optimal sensitivity
should be achieved for the combined result and not for individual analyses. In many
cases, optimality in a single channel does not result in optimality of the combination.
The result of the latest CMS combination [756] of diboson final states is shown in
Fig. 5.5 in terms of upper cross section limits at 95% CL on the production of a heavy
W
(left) and Z
(right). At the highest masses up to 4.5 TeV, analyses in the
and all-hadronic final states have the highest sensitivity. At intermediate masses,
final states with p
miss
T
contribute, where analyses in ννqq and ννbb final states show
comparable or better sensitivity to the all-hadronic and single-lepton channels. At
resonance masses of 1 TeV and below, dilepton final states result in the best sensitivity.
The small background in multi-lepton final states has been exploited by ATLAS,
where the inclusion of the fully leptonic searches W W → eνμν [761], W Z →
[762], and Z Z → 4 [763] improves the combined limits at low masses [755].
As a result of these combinations, W
and Z
resonances below masses of 4.3 and
3.6 TeV are excluded in the HVT model. Constraints are also derived in the plane of
lepton versus diboson coupling strengths.
(GeV)
W'
m
1000
1500
2000
2500
3000
3500
4000
4500
(W') (pb)
σ
4
−
10
3
−
10
2
−
10
1
−
10
1
(13 TeV)
-1
35.9 fb
CMS
Combination
(PRD 97(2018)072006)
q
q
q
q
→
WZ
(JHEP 07(2018)075)
q
q
ν
ν
→
WZ
(JHEP 05(2018)088)
q
q
ν
l
→
WZ
(JHEP 09(2018)101)
q
llq
→
WZ
(EPJC 77(2017)636)
b
b
q
q
→
WH
(JHEP 11(2018)172)
b
b
ν
l
→
WH
(JHEP 01(2019)051)
τ
τ
q
q
→
WH
95% CL upper limits
Observed
Median expected
HVT model B
2016 diboson combination
(GeV)
Z'
m
1000
1500
2000
2500
3000
3500
4000
4500
(Z') (pb)
σ
4
−
10
3
−
10
2
−
10
1
−
10
1
(13 TeV)
-1
35.9 fb
CMS
Combination
(PRD 97(2018)072006)
q
q
q
q
→
WW
(JHEP 05(2018)088)
q
q
ν
l
→
WW
(EPJC 77(2017)636)
b
b
q
q
→
ZH
(JHEP 11(2018)172)
b
b
ν
ν
→
ZH
(JHEP 11(2018)172)
b
llb
→
ZH
(JHEP 01(2019)051)
τ
τ
q
q
→
ZH
95% CL upper limits
Observed
Median expected
HVT model B
2016 diboson combination
Fig. 5.5 Observed and expected upper limits at 95% CL on the W (left) and Z (right) cross sections
as a function of the resonance mass. The statistical combination of the V V and VH channels is
shown, together with the expected limits of the individual channels. Taken from [756]
135
of 13 TeV data. These enlarge the scope of previous combinations by including the
leptonic channels [757, 758] and [759, 760], thus adding sensitivity to models
with large fermionic couplings.
The difficulty in combining different analyses in very different channels and final
states lies in ensuring full orthogonality between the analyses, i.e. statistical independence of all signal regions such that events in data are considered exactly once. The
challenge here is that sideband and control regions of one analysis might be part of
the signal region of another analysis. In addition, the same definitions of jet substructure observables and lepton identification variables have to be used in all analyses
considered, such that no unwanted and unknown correlations are introduced. Precise results also require knowledge of correlations between sources of systematic
uncertainties. The feasibility of a combination including a large number of individual results requires careful planning and coordination prior to the execution of the
individual searches. Note that when designing the analyses, the optimal sensitivity
should be achieved for the combined result and not for individual analyses. In many
cases, optimality in a single channel does not result in optimality of the combination.
The result of the latest CMS combination [756] of diboson final states is shown in
Fig. 5.5 in terms of upper cross section limits at 95% CL on the production of a heavy
W
(left) and Z
(right). At the highest masses up to 4.5 TeV, analyses in the
and all-hadronic final states have the highest sensitivity. At intermediate masses,
final states with p
miss
T
contribute, where analyses in ννqq and ννbb final states show
comparable or better sensitivity to the all-hadronic and single-lepton channels. At
resonance masses of 1 TeV and below, dilepton final states result in the best sensitivity.
The small background in multi-lepton final states has been exploited by ATLAS,
where the inclusion of the fully leptonic searches W W → eνμν [761], W Z →
[762], and Z Z → 4 [763] improves the combined limits at low masses [755].
As a result of these combinations, W
and Z
resonances below masses of 4.3 and
3.6 TeV are excluded in the HVT model. Constraints are also derived in the plane of
lepton versus diboson coupling strengths.
(GeV)
W'
m
1000
1500
2000
2500
3000
3500
4000
4500
(W') (pb)
σ
4
−
10
3
−
10
2
−
10
1
−
10
1
(13 TeV)
-1
35.9 fb
CMS
Combination
(PRD 97(2018)072006)
q
q
q
q
→
WZ
(JHEP 07(2018)075)
q
q
ν
ν
→
WZ
(JHEP 05(2018)088)
q
q
ν
l
→
WZ
(JHEP 09(2018)101)
q
llq
→
WZ
(EPJC 77(2017)636)
b
b
q
q
→
WH
(JHEP 11(2018)172)
b
b
ν
l
→
WH
(JHEP 01(2019)051)
τ
τ
q
q
→
WH
95% CL upper limits
Observed
Median expected
HVT model B
2016 diboson combination
(GeV)
Z'
m
1000
1500
2000
2500
3000
3500
4000
4500
(Z') (pb)
σ
4
−
10
3
−
10
2
−
10
1
−
10
1
(13 TeV)
-1
35.9 fb
CMS
Combination
(PRD 97(2018)072006)
q
q
q
q
→
WW
(JHEP 05(2018)088)
q
q
ν
l
→
WW
(EPJC 77(2017)636)
b
b
q
q
→
ZH
(JHEP 11(2018)172)
b
b
ν
ν
→
ZH
(JHEP 11(2018)172)
b
llb
→
ZH
(JHEP 01(2019)051)
τ
τ
q
q
→
ZH
95% CL upper limits
Observed
Median expected
HVT model B
2016 diboson combination
Fig. 5.5 Observed and expected upper limits at 95% CL on the W (left) and Z (right) cross sections
as a function of the resonance mass. The statistical combination of the V V and VH channels is
shown, together with the expected limits of the individual channels. Taken from [756]