SciPost Phys. 6, 024 (2019)

The global Higgs picture at 27 TeV
Anke Biekötter1 , Dorival Gonçalves2 , Tilman Plehn1 ,Michihisa Takeuchi3 and Dirk Zerwas4
1 Institut für Theoretische Physik, Universität Heidelberg, Germany
2 PITT PACC, Department of Physics and Astronomy, University of Pittsburgh, USA
3 Kavli IPMU (WPI), UTIAS, University of Tokyo, Kashiwa, Japan
4 LAL, IN2P3/CNRS/ Orsay, France? biekoetter@thphys.uni-heidelberg.de

Abstract
We estimate the reach of global Higgs analyses at a 27 TeV hadron collider in termsof Higgs couplings and in terms of a gauge-invariant effective Lagrangian, including
invisible Higgs decays and the Higgs self-coupling. The new collider will indirectly probe
new physics in the TeV range and allow for a meaningful test of the Higgs self-coupling
also embedded in a global analysis.
Copyright A. Biekötter et al.
This work is licensed under the Creative Commons
Attribution 4.0 International License.
Published by the SciPost Foundation.

Received 22-11-2018
Accepted 11-02-2019
Check forupdatesPublished 25-02-2019
doi:10.21468/SciPostPhys.6.2.024

Content
1 Introduction

1

2 Global Higgs analysis

3

3 Higgs-gauge analysis

5

4 Higgs self-interaction

7

5 Outlook9

References

101

Introduction

In record time Higgs physics has moved from a spectacular discovery of a new particle to asystematic and comprehensive study of its properties [1]. The general development of hadroncollider physics into precision physics has been fueled by the understanding of the LHC detectors, the control of perturbative QCD, the ability to precisely simulate even complex LHC
1

SciPost Phys. 6, 024 (2019)

processes, and the theoretical understanding of a perturbative electroweak Lagrangian as aninterpretation framework. This naturally leads to the question what kind of precision we canreach with a 27 TeV hadron collider with an attobarn-level integrated luminosity.
If we assume that the observed scalar is really Higgs-like, specifically that it is responsible for electroweak symmetry breaking and hence forms a doublet with the weak Goldstone
modes, we can interpret the LHC results in terms of an effective Lagrangian with linearly realized electroweak symmetry breaking [2–11]. This defines the framework of some of the mostinteresting global Higgs analyses based on Run I [12–15] and even Run II [16] data. Because
this effective Lagrangian firmly links the Higgs and electroweak sectors, the global analysis
has to incorporate anomalous triple gauge boson measurements from LEP [17, 18] and the
LHC [12, 18–23]. At the 13 TeV LHC the Higgs self-coupling can be neglected at the typicalprecision of a global Higgs analysis [24]. In contrast, a 27 TeV hadron collider is expected tocontribute a meaningful measurement of Higgs pair production [25–28], for example testing
a possible first-order electroweak phase transition as an ingredient to baryogenesis [29, 30].
Finally, we include invisible Higgs decays in terms of an invisible branching ratio following
Ref. [31].
For our brief study we start from the established Run I limits of the LHC [12, 32] and extrapolate them to an upgraded LHC setup∗ . This provides a reliable benchmark for such anenergy upgrade with a large integrated luminosity. First, we discuss the 27 TeV projectionsin terms of Higgs coupling modifiers, motivated by an effective Lagrangian with a non-linear
realization of electroweak symmetry breaking, in Sec. 2. In Sec. 3 we then use a linear realization to combine the global Higgs analysis with di-boson data. In Sec. 4 we discuss the benefits
from including a differential measurement of Higgs pair production in detail.
Eventually, this analysis should be combined with anomalous gauge couplings to fermions,as well as electroweak precision data [16,22,23,34–36]. We leave such a more detailed analysis also including a larger set of kinematic distributions [37] and an appropriate validation on
ATLAS and CMS results for the future. For now, this extrapolation based on our established andvalidated 8 TeV analysis will provide a reliable first estimate. Such a conservative treatment
is in order, because dependent on the interpretation framework the global Higgs analyses at a
27 TeV collider will rapidly enter systematics-limited and theory-limited territory.
Table 1: Relative theory uncertainties for the different production and decay channels
contributing to the global analysis. The numbers correspond to those quoted in Ref.
[38].
production

[%]

decay

[%]

GF
qqH
WH
ZH
t t̄ H
HH

10.2
3.0
3.2
5.7
12.8
18.

WW
ZZ
γγ
b b̄
Zγ
ττ

2.63
2.63
3.31
2.17
7.33
2.78

2

SciPost Phys. 6, 024 (2019)27 TeV, 68% CL
0.15

1.5 ab-1
15 ab-1

σsyst+theo=half
σsyst+theo=full

0.1

0.05

0

-0.05

-0.1

BR
v

in

/W

∆b

P

/Z

/τ

∆b

∆W

+N
SM

∆g P

+N
SM

∆γ

∆g

∆γ

∆τ

∆b

∆t

∆Z

∆W

Figure 1: Result from the global Higgs analysis in terms of coupling modifiers or nonlinearly realized electroweak symmetry breaking. All limits are shown as profiled
over all other couplings.

2

Global Higgs analysis

Historically [33,39,40], new physics effects on the SM-like Higgs couplings have been parameterized as coupling modifiers
g x = g SM
x (1 + ∆ x )
SM+NP
SM
SM
),
g g,γ = g SM
g,γ (1 + ∆ g,γ + ∆ g,γ ) ≡ g g,γ (1 + ∆ g,γ(1)

where the ∆ x can be directly translated into the experimentally used κ notation
κ x = (1 + ∆ x )(2)

at least modulo the treatment of the tree-level couplings contributing to the loop-induced
operators. The corresponding global Higgs analysis is the main reason why we can now claimthat the observed Higgs boson closely follows the Standard Model predictions. In terms of a
Lagrangian we can write this hypothesis as [12]L = LSM + ∆W g mW h W µ Wµ + ∆ Z+ ∆ g FGXmfgm Z h Z µ Zµ −h f¯R f L + h.c.
∆f
2cW
v
τ,b,t

h
h
Gµν G µν + ∆γ FA Aµν Aµν + invisible decays .
v
v

(3)

This Lagrangian shifts all numerical values of the SM-like Higgs couplings and breaks electroweak gauge invariance. The modified dimension-4 coupling terms obviously affect all loopinduced Higgs couplings. In addition, the Lagrangian includes new higher-dimensional operators coupling the Higgs to photons and gluons. They arise from potential new particles in
the loop and are normalized to their Standard Model values FG and FA. In the limit of heavy(∞)
top masses these normalization constants read FG → αs /(12π). We refrain from including
Many aspects of our 27 TeV study are described in detail in these 8 TeV legacy papers [12, 32], including avalidation of the 8 TeV results. The SFITTER error treatment is discussed in Ref. [33].
∗3

SciPost Phys. 6, 024 (2019)a more complete set of operators, to be consistent with existing analyses. The form of Eq.(3)can be trivially mapped onto an effective Lagrangian with a non-linear representation of the
Higgs and Goldstone fields, resulting in a broken SU(2) doublet structure [17, 41–43].
Including invisible Higgs decays in terms of an effective Lagrangian would force us to either
define a new particle with unknown quantum numbers, or to re-scale the decay H → 4νto ridiculous branching ratios. Instead, we include invisible Higgs decays in terms of thecorresponding partial width or, equivalently, the invisible branching ratio. The total Higgs
width is consistently constructed out of all observed partial width, with an assumed scaling of
the second and third generation of Yukawa couplings, as described in Ref. [12].
In principle it would be possible to include the Higgs self-coupling in the global, nonlinear Higgs analysis. However, we know that di-Higgs measurements will not improve any ofthe parameters given in Eq.(3) and that the Higgs self-coupling does not affect single-Higgs
production in a relevant way. Because the extration of the Higgs self-coupling crucially depends
on kinematic distributions [24, 25] we postpone this aspect to Sec. 3, where we also include afull set of di-boson and single Higgs distributions.
The global Higgs analysis in terms of Eq.(3) only describes total cross sections in the Higgs
sector. We therefore just re-scale the number of signal and background events in the 8 TeV
analysis [12] to 27 TeV, assuming two experiments. This affects all statistical uncertainties, aswell as the systematics, which we assume to be related to measurements in control regions.
For all measurements we assume the SM predictions, which means that our best-fit points will
always be the SM values. For the invisible Higgs searches we use an in-house extrapolationof the WBF analysis from Ref. [31] to 27 TeV. The current theory uncertainties of all measurements are listed in Tab. 1, including uncertainties on the parton distributions. For these,
we simply assume that dedicated fits will determine the PDFs at a 27 TeV collider will fullluminosity at the same level as they are determined for the LHC now. To illustrate the pointthat precision predictions and PDF extraction are crucial we will show results with the current
theory uncertainties as well as an assumed improvement of theory and systematics by a factor
two.
In Fig. 1 we show the expected precision of the SM-like Higgs coupling measurements fora 27 TeV LHC upgrade. Asymmetric uncertainty bands arise because of correlations, but also
reflect numerical uncertainties. Different colors correspond to assumed integrated luminositiesof 1.5 ab−1 and 15 ab−1 . For all coupling deviations, with the exception of ∆ b , we observe
an improvement with increased luminosity. However, this improvement is much smaller than
the rough factor three which one could expect from a scaling of the limits with the squareroot of the luminosity, indicating that the limits are systematics and theory limited. Ratiosof couplings, like ∆W /Z , see little improvement from an increased luminosity. To confirm
the domination by systematics and theory uncertainties, we also compare today’s theory andsystematic uncertainties with an improvement to half the current uncertainties indicated byfull and shaded bands. For example for ∆ b and ∆ g , as well as for the coupling ratios weindeed see a significant improvement. Altogether, the typical precision in measuring Higgs
couplings can reach 3% to 5% at a 27 TeV hadron collider with a realistic improvement of
the systematic and theory uncertainties. The ratio of the W and Z couplings to the Higgs, forexample, will benefit from correlated uncertainties and will therefore be measured a factor
two more precisely than the individual couplings. Invisible Higgs decays will be constrainedat the branching ratio level of 1% to 2%. Compared to the high-luminosity LHC predictions inRef. [44] the 27 TeV with its projected final luminosity will double the precision on many of
the Higgs coupling modifications.

4

SciPost Phys. 6, 024 (2019)3

Higgs-gauge analysis

An effective Lagrangian is defined by its particle content and its symmetries, with the dimensionality of the individual operators, or inverse powers of a large matching scale as the expansion parameter. Truncated to dimension six it has the form [6, 9]

L=

X f
x

x

Λ2

Ox ,

(4)

where Λ  v is the scale of the assumed UV-complete model. It can be extended to the fullStandard Model particle content, defining the Standard Model Effective Field Theory [11]. The
minimum independent set of dimension-6 operators with the SM particle content, compatible
with the SM gauge symmetries, and compatible with baryon number conservation contains
59 operators [9]. We impose C and P invariance [45] on the operator set of Ref. [6], use
the equations of motion including all necessary fermionic operators to avoid blind directions
from electroweak precision data, and neglect all operators that will not be constrained by
LHC Higgs measurements. For the Higgs couplings to fermions we assume a Yukawa coupling
structure, noting that current LHC analyses are unlikely to test the Lorentz structure of a
possible deviation from the Standard Model. This gives us the Lagrangian
αs f GGfffff
OGG + BB2 OBB + W2W OW W + B2 OB + W2 OW + W W2 W OW W W
2
8π Λ
Λ
Λ
Λ
Λ
Λ
fφ3
fφ2
f b mbf t mtf τ mτ
Oeφ,33 +Odφ,33 +Ouφ,33+ 2 Oφ2 + 2 Oφ3 +
Λ
Λ
vΛ2
vΛ2
vΛ2
+ invisible decays ,Leff = −(5)

with the operators defined as in Ref. [32],aG aµν
OGG = φ † φ Gµν

OB = (Dµ φ)† B̂ µν (Dν φ)

OBB = φ † B̂µν B̂ µν φ
OW = (Dµ φ)† Ŵ µν (Dν φ)

1
Oφ3 = −(φ † φ)3 /3
Oφ2 = ∂ µ (φ † φ)∂µ (φ † φ)2
Oeφ,33 = φ † φ L̄3 φeR,3
Odφ,33 = φ † φ Q̄ 3 φdR,3OW W = φ † Ŵµν Ŵ µν φOW W W = Tr Ŵµν Ŵ νρ Ŵρµ(6)

Ouφ,33 = φ † φ Q̄ 3 φ̃uR,3 .

The pure gauge operator OW W W is needed to fully describe anomalous triple gauge couplings
in a gauge-invariant framework. Any LHC analysis also needs to include an anomalous triple
gluon interaction, but this operator is constrained by multi-jet production at 13 TeV much
more strongly than any Higgs analysis will achieve [46], and we assume that this pattern willbe the same at a 27 TeV collider. Recent studies [23, 36, 47] have shown the relevance offermionic operators through their induced f f¯V , f f¯V V and f f¯V H couplings, which require
a combination of the Higgs–gauge analysis with electoweak precision data. Such an analysis
is beyond the scope of this projection, but eventually the fermionic operators should be partof a global SMEFT fit.
Because the effective Lagrangian of Eq.(5) includes new Lorentz structures, especially valuable information comes from kinematic distributions probing interactions with a large momentum flow. We therefore include four single Higgs and four di-boson distributions in our analysis [32]. For the 8 TeV analysis they are validated with existing data [32,48,49]. We use MAD GRAPH5-2.3.2.2 [50], PYTHIA6-2.4.5 [51], and DELPHES3.1.2 [52] for two ATLAS/CMS-like experiments. For distributions, where different cuts define different phase space regions, we only
use the high-momentum regime. Finally, we include Higgs pair production pp → H H → b b̄γγ
including kinematic information in terms of mH H , as pioneered in Ref. [53], now accounting
5

SciPost Phys. 6, 024 (2019)

for two different jet multiplicities [25]. All distributions entering our analysis are summarizedin Tab. 2, the details of the Higgs pair production process will be discussed in Sec. 4.
Comparing the reach of the main kinematic distributions in Tab. 2 we see that the V Vchannels probe a much larger momentum flow than the V H channels. This can be traced to
the larger signal rates, namely σW Z = 61.1 pb vs σW H = 2.8 pb at 27 TeV and to leading
order [50], combined with higher tails through the momentum-dependent W W Z coupling.
For example comparing W Z production with W H production, the reach in p TV is defined by
the highest bins with a sizeable number of signal events. Specifically, we ignore phase space
regions with fewer than three signal events for an integrated luminosity of 15 ab−1 .
In Fig. 2 we show the results of the global Higgs analysis in terms of dimension-6 SMEFT
operators, including the quadratic terms of the EFT expansion. The right axis indicates the
new-physics scale Λ assuming reasonably strongly interacting new physics f x = 1. The 27 TeV
analysis is typically sensitive to new-physics scales well above 1 TeV. This number should becompared to the range of distributions given in Tab. 2, indicating that our Higgs analysis does
not have any serious EFT validity issues provided we do not see a pole in the diboson channels.
The asymmetric error bands for some of the Wilson coefficients will be discussed in the next
section.
The balance of statistical, systematic, and theory uncertainties in the SMEFT analysis issignificantly different from the non-linear coupling modifiers shown in Fig. 1. Effective operators benefit from an increased statistics, because larger luminosity extends the reach of
kinematic distributions, which in their tails are always statistically limited. In contrast, theYukawa couplings f b,τ , which do not change the Lorentz structure, are mostly limited by theassumed systematic and theory uncertainties. Consequently, the reach for operators which
modify the Lorentz structure of some Higgs interaction exceeds the reach for the Yukawa-like
operators or the reach for the operator Oφ2 , which introduces a wave function renormalization for the Higgs field and only changes the kinematics of Higgs
p pair production. For theformer the kinematic distributions drive the limits towards Λ/ f ≈ 3 TeV and beyond, forhigh luminosity and improved systematics and theory uncertainties. This aspect is where wealso expect significant improvements from a dedicated 27 TeV study developing analysis ideas
not realized at 8 TeV.
The asymmetric limits on f B give us some insight into the structure of the effective theory. This operator is largely constrained through V H production at high momentum transfer,specifically the p TV distributions from Tab. 2. In its highest available bins we probe sizeable
Table 2: Distributions included in the analysis. The number of bins includes an overflow bin for all channels.
channelW W → (`ν)(`ν)
W W → (`ν)(`ν)
W Z → (`ν)(``)
W Z → (`ν)(``)
WBF, H → γγV H → (0`)(b b̄)
V H → (1`)(b b̄)
V H → (2`)(b b̄)
H H → (b b̄)(γγ), 2 j
H H → (b b̄)(γγ), 3 jobservable# binsrange [GeV]

m``0
`
p T1
WZ
mT
Z
p``
T (p T )
`
p T1
p TV
p TV
p TV
mH H
mH H

10
8
11
9
9
7
7
7
9
9

0 − 4500
0 − 1750
0 − 5000
0 − 2400
0 − 2400
150 − 750
150 − 750
150 − 750
200 − 1000
200 − 1000

6

SciPost Phys. 6, 024 (2019)

f/Λ2[TeV-2]27 TeV, 68% CLΛ/√|f|[TeV]σsyst+theo=half
σsyst+theo=full

1.5 ab-1
-1
15 ab

BR
[%]
2.5

2

0.7

1

1

2

0

2
∞
2

1.5

-1

1

1

-2

0.7

0.5

-3
0

BR
v

in

W

W

/9
f φ3

fτ

fb

ft

fW

f φ2

fB

fW

W

f BB

fW

f GG

Figure 2: Result from the global Higgs analysis in terms of dimension-6 operators.
All limits are shown as profiled over all other Wilson coefficients.
ratios p T /Λ, but with sizeable statistical uncertainties. If we include the dimension-6 squared
terms a second solution predicting the same event count within the statistical uncertainties
appears for f B /Λ > 0. For this second solution the squared term compensates a small destructive interference with the SM contribution. Because the precise position of this secondary
solution differs for different values of p T,V , it induces a slightly asymmetric measurement off B /Λ. Note that a visible dimension-6-squared term in a specific observable does by no means
signal the breakdown of the effective Lagrangian [54]. The validity of an effective field theory
representing classes of underlying UV-complete models can only be judged once we identify
on-shell contributions of the new particles [55]. Second, truncating the expansion of our observables after the linear term in f /Λ2 would lead to a symmetric and more narrow likelihood
distribution and underestimate of the errors. In general, we do not include uncertainties on
the EFT framework in our global analysis, as we consider them to be uncertainties on thematching and interpretation of our results in terms of a UV complete model [56, 57].

4

Higgs self-interaction

An enhanced Higgs self-coupling as a simple modification of the SM Higgs potential is especially interesting for example in relation to vacuum stability and baryogenesis [29, 30]. Including it in our global Higgs analysis is a significant improvement as compared to the Run I
legacy analysis [32]. It is made possible by the fact that a 27 TeV collider with a large integrated luminosity will allow for a dedicated measurement of the Higgs self-coupling. The
self-coupling with its unique relation to the Higgs potential is not yet included in most global
analyses of SM-like Higgs couplings because of the modest reach of the LHC. However, for a
27 TeV collider with an integrated luminosity of 15 ab−1 we quote the expected reach [25]¨
1 ± 15% 68% C.L.
λ3H
=
(7)
(SM)
1 ± 30% 95% C.L.
λ3H

7

.5 −1 −0.5

SciPost Phys. 6, 024 (2019)

We can translate this range into the conventions of Eq.(5) if we assume that the underlying
new physics does not generate any other dimension-6 operator. In that case we assume
V = µ2fφ3 (v + H)6(v + H)2(v + H)4
+λ
+
,
2
4
3Λ2
8

(8)

and find for the reach of the dedicated self-coupling analysis [58]λ3H = λ(SM)3H22v 2 fφ3 v
1+
3m2H Λ2



¨
1 TeV
Λ
¦
Æ
700 GeVfφ3

and

68% C.L.
95% C.L.

(9)

While we are free to define a modified Higgs potential as our physics hypothesis [30], thissetup is in direct violation of the effective Lagrangian approach. Here all operators consistent
with the symmetry assumptions have to be included. Consequently, Oφ2 also affects the Higgs
pair production process with a momentum-dependent self-coupling [58, 59].

30

25

20

fφ3/ Λ2 [TeV-2]

The full kinematic information from Higgs pair production encoded in the mH H distribution
allows us to separate the effects of Oφ2 and Oφ3 [24,25]. In addition, we can use single Higgs
production to constrain OGG and Ouφ,33 , as seen in Sec. 3. All corresponding error bands haveto be propagated into Higgs pair production, and given the size of the uncertainties we cansafely assume that in the presence of Oφ3 Higgs pair production will hardly help with anyof the operators already constrained by single Higgs production. Following Refs. [60, 61] andespecially Ref. [62] we also neglect the loop effects of Oφ3 on single Higgs production, because
they will hardly affect a global Higgs analysis. Finally, looking at different uncertainties it isalso obvious that a study of the mH H distribution will be statistically limited even at the 27 TeV
collider, in contrast to the typical total rate measurements discussed before.
In Fig. 3 we illustrate the correlation of Oφ2 and Oφ3 through the full expression for a modified self-coupling [58]. We also know that positive and negative deviations of the Higgs selfcoupling affect different phase space regions [24]: while a reduced value of the self-coupling
can be tested around the threshold mH H ≈ 2mH , an increase in the self-coupling requires us
to look for large values of mH H and to deal with large effects from Oφ2 . All of this leads to an
asymmetric uncertainty band on Oφ3 especially once we allow for an agreement of the SMlike measurements with the SM predictions at two sigma and integrate the asymmetric tails
25

35

20
30

15
10

25

5

20

0

15

15

10

−5

10

−10
5

5

−15
0

0.5

1

1.5

2

2.5

fB/ Λ2 [TeV-2]

0

−20
−4

−3

−2

−1

0

1

2

3

4

0

fφ2/ Λ2 [TeV-2]

Figure 3: Correlations between the leading operators describing Higgs pair production.

8

SciPost Phys. 6, 024 (2019)2

27 TeV, 15 iab, σsyst+theo=half

Λ/
√|f|
[TeV]

BR
[%]

2

0.7

2

1

1

0

2
∞
2

-1

1

-2

0.7

f/Λ
-2
[TeV ]

68% CL
95% CL

1.5

1

0.5

-3
0

BR
v

in

W

W

/9
f φ3

fτ

fb

ft

fW

f φ2

fB

fW

W

f BB

fW

f GG

Figure 4: Result from the global Higgs analysis in terms of dimension-6 operators,
complementing the high-luminosity and improved-error scenario of Fig. 2 with results for 95% C.L. or two standard deviations.
further. From Fig. 4 we read off the limitsΛÆÆ| fφ3 |
Λ| fφ3 |

> 430 GeV
> 245 GeV ( fφ3 > 0) and

68% C.L.
ΛÆ| fφ3 |

> 300 GeV

( fφ3 < 0)

95% C.L.

(10)

These limits are diluted from the one-parameter analysis quoted in Eq.(9), largely because of
the combination with Oφ2 . As a matter of fact, we can directly compare the effects from Oφ2
and Oφ3 for similar values of f /Λ2 as a function of the momentum flowing through the tripleHiggs vertex or mH H . In that case we find that the momentum dependence in Oφ2 matches
the effects from Oφ3 for mH H ¦ 1 TeV, with either relative sign. This additional source of amodified self-coupling characterized by the interplay between Oφ2 and Oφ3 is not accounted
for in the usual Higgs pair analyses.

5

Outlook

Following the established Run I legacy results [12, 32] we estimate the reach of a 27 TeV
hadron collider in a global analysis of the Higgs-gauge sector. We include not only invisible
Higgs decays, but also Higgs pair production, sensitive to the Higgs self-coupling.
First, we interpret the extrapolated measurement in terms of modified SM-like Higgs couplings, motivated by an effective theory with non-linearly realized electroweak symmetry
breaking. We find that a 27 TeV hadron collider will be sensitive to 3 ... 5% deviations from the
SM coupling values. Systematics and theory uncertainties rapidly limit the reach for modified
Higgs couplings beyond attobarn-level integrated luminosities.
Using a gauge-invariant effective theory in terms of the Higgs doublet allows us to include
di-boson rates and kinematic distributions in the global Higgs analysis. Invisible branchingratios can be extracted from a global Higgs analysis to better than one per-cent. For the gaugeinvariant interpretation framework we also include a modified Higgs potential at dimension
six. The additional Wilson coefficient can be constrained by a kinematic analysis of Higgs pair9

SciPost Phys. 6, 024 (2019)

production [25] if we control the correlation with the operator Oφ2 .
We find a TeV-scale reach for new physics given order-one Wilson coefficients for mostdimension-6 operators. Those operators which change the Lorentz structure of Higgs couplings can be strongly constrained beyond the 3 TeV level. Comparing those numbers withthe current reach of the LHC Run II [16, 35, 36], we find that the reach of a 27 TeV hadroncollider could increase the bounds on the new physics scale by more than 50%. The global
analysis obviously reduces the reach for the Higgs self-coupling modification compared to oneparameter analysis, but still indicates that a 27 TeV hadron collider will for the first time delivera meaningful measurement of this fundamental physics parameter.

Acknowledgments
First and foremost we are grateful to Michael Rauch, not only because of his significant contribution in the early phase of this project, but also because of his long-term leading role inall SFitter analyses. If our field decides to let technically cutting-edge people like him go, weshould not be surprised that large parts of BSM theory are losing contact to LHC data and are
becoming increasingly irrelevant to LHC physics as a whole.
We would like to thank Jennie Thompson for providing the numbers for the invisible Higgs
analysis. AB is funded by the DFG through the Graduiertenkolleg Particle physics beyond theStandard Model (GRK 1940) and the IMPRS-PTFS. The authors acknowledge support by thestate of Baden-Württemberg through bwHPC and the German Research Foundation (DFG)
through grant no INST 39/963-1 FUGG (bwForCluster NEMO). MT is supported in part by
the JSPS Grant-in-Aid for Scientific Research Numbers 16H03991, 16H02176, 17H05399,
18K03611, and the World Premier International Research Center Initiative, MEXT, Japan.

References[1] S. Dawson, C. Englert and T. Plehn, Higgs Physics: It ain’t over till it’s over (2018),
arXiv:1808.01324.
[2] C. N. Leung, S. T. Love, and S. Rao, Low-energy manifestations of a new interactions scale:Operator analysis, Z. Phys C 31, 433 (1986), doi:10.1007/BF01588041.
[3] W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor
conservation, Nucl. Phys. B 268, 621 (1986), doi:10.1016/0550-3213(86)90262-2.
[4] A. De Rújula, M. B. Gavela, P. Hernandez, and E. Massó, The self-couplings of vectorbosons: does LEP-1 obviate LEP-2?, Nucl. Phys. B 384, 3 (1992), doi:10.1016/05503213(92)90460-S.
[5] K. Hagiwara, R. Szalapski and D. Zeppenfeld, Anomalous Higgs boson production anddecay, Phys. Lett. B 318, 155 (1993), doi:10.1016/0370-2693(93)91799-S.
[6] K. Hagiwara, S. Ishihara, R. Szalapski, and D. Zeppenfeld, Low energy effects of
new interactions in the electroweak boson sector, Phys. Rev. D 48, 2182 (1993),
doi:10.1103/PhysRevD.48.2182.
[7] K. Hagiwara, S. Matsumoto and R. Szalapski, Constraints on new physics in the electroweakbosonic sector from current data and future experiments, Phys. Lett. B 357, 411 (1995),
doi:10.1016/0370-2693(95)00925-B.

10

SciPost Phys. 6, 024 (2019)[8] M. C. Gonzalez-Garcia, Anomalous Higgs couplings, Int. J. Mod. Phys. A 14, 3121 (1999),
doi:10.1142/S0217751X99001494.
[9] B. Grzadkowski, M. Iskrzyński, M. Misiak and J. Rosiek, Dimension-six terms
in the Standard Model Lagrangian, J. High Energ. Phys. 10, 085 (2010),
doi:10.1007/JHEP10(2010)085.
[10] G. Passarino, NLO inspired effective Lagrangians for Higgs physics, Nucl. Phys. B 868, 416(2013), doi:10.1016/j.nuclphysb.2012.11.018.
[11] I. Brivio and M. Trott, The standard model as an effective field theory, Phys. Rep. 793, 1(2019), doi:10.1016/j.physrep.2018.11.002.
[12] T. Corbett, O. J. P. Eboli, D. Goncalves, J. Gonzalez-Fraile, T. Plehn and M. Rauch, The
Higgs legacy of the LHC Run I (2015), arXiv:1505.05516.
[13] T. Corbett, O. J. P. Éboli, J. Gonzalez-Fraile and M. C. Gonzalez-Garcia, Robust determination of the Higgs couplings: Power to the data, Phys. Rev. D 87, 015022 (2013),
doi:10.1103/PhysRevD.87.015022.
[14] S. Banerjee, S. Mukhopadhyay and B. Mukhopadhyaya, Higher dimensional operatorsand the LHC Higgs data: The role of modified kinematics, Phys. Rev. D 89, 053010 (2014),
doi:10.1103/PhysRevD.89.053010.
[15] J. Ellis, V. Sanz and T. You, The Effective Standard Model after LHC Run I (2014),
arXiv:1410.7703.
[16] J. Ellis, C. W. Murphy, V. Sanz and T. You, Updated global SMEFT fit to Higgs, diboson andelectroweak data, J. High Energ. Phys. 06, 146 (2018), doi:10.1007/JHEP06(2018)146.
[17] I. Brivio, T. Corbett, O. J. P. Éboli, M. B. Gavela, J. Gonzalez-Fraile, M. C. Gonzalez-Garcia,
L. Merlo and S. Rigolin, Disentangling a dynamical Higgs, J. High Energ. Phys. 03, 024(2014), doi:10.1007/JHEP03(2014)024.
[18] A. Falkowski, M. González-Alonso, A. Greljo and D. Marzocca, Global constraints on
anomalous triple gauge couplings in the effective field theory approach, Phys. Rev. Lett.
116, 011801 (2016), doi:10.1103/PhysRevLett.116.011801.
[19] A. Falkowski, M. González-Alonso, A. Greljo, D. Marzocca and M. Son, Anomalous triple
gauge couplings in the effective field theory approach at the LHC, J. High Energ. Phys. 02,
115 (2017), doi:10.1007/JHEP02(2017)115.
[20] L. Berthier, M. Bjørn and M. Trott, Incorporating doubly resonant W ± data in a global
fit of SMEFT parameters to lift flat directions, J. High Energ. Phys. 09, 157 (2016),
doi:10.1007/JHEP09(2016)157.
[21] D. Liu and L.-T. Wang, Precision measurement with Diboson at the LHC (2018),
arXiv:1804.08688.
[22] J. Baglio, S. Dawson and I. M. Lewis, NLO QCD effective field theory analysis of W + W −production at the LHC including fermionic operators, Phys. Rev. D 96, 073003 (2017),
doi:10.1103/PhysRevD.96.073003.
[23] R. Franceschini, G. Panico, A. Pomarol, F. Riva and A. Wulzer, Electroweak precision tests in high-energy diboson processes, J. High Energ. Phys. 02, 111 (2018),
doi:10.1007/JHEP02(2018)111.
11

SciPost Phys. 6, 024 (2019)[24] F. Kling, T. Plehn and P. Schichtel, Maximizing the significance in Higgs boson pair analyses,
Phys. Rev. D 95, 035026 (2017), doi:10.1103/PhysRevD.95.035026.
[25] D. Gonçalves, T. Han, F. Kling, T. Plehn and M. Takeuchi, Higgs boson pair production at
future hadron colliders: From kinematics to dynamics, Phys. Rev. D 97, 113004 (2018),
doi:10.1103/PhysRevD.97.113004.
[26] W. Kilian, S. Sun, Q.-S. Yan, X. Zhao and Z. Zhao, Multi-Higgs production and unitarity invector-boson fusion at future hadron colliders (2018), arXiv:1808.05534.
[27] W. Bizoń, U. Haisch and L. Rottoli, Constraints on the quartic Higgs self-coupling fromdouble-Higgs production at future hadron colliders (2018), arXiv:1810.04665.
[28] S. Homiller and P. Meade, Measurement of the Triple Higgs Coupling at a HE-LHC (2018),
arXiv:1811.02572.
[29] C. Grojean, G. Servant and J. D. Wells, First-order electroweak phase transition in the standard model with a low cutoff, Phys. Rev. D 71, 036001 (2005),
doi:10.1103/PhysRevD.71.036001.
[30] M. Reichert, A. Eichhorn, H. Gies, J. M. Pawlowski, T. Plehn and M. M. Scherer, Probing baryogenesis through the Higgs boson self-coupling, Phys. Rev. D 97, 075008 (2018),
doi:10.1103/PhysRevD.97.075008.
[31] A. Biekötter, F. Keilbach, R. Moutafis, T. Plehn and J. Thompson, Tagging Jets in invisible
Higgs Searches, SciPost Phys. 4, 035 (2018), doi:10.21468/SciPostPhys.4.6.035.
[32] A. Butter, O. J.P. Éboli, J. Gonzalez-Fraile, M. C. Gonzalez-Garcia, T. Plehn and M.
Rauch, The gauge-Higgs legacy of the LHC Run I, J. High Energ. Phys. 07, 152 (2016),
doi:10.1007/JHEP07(2016)152.
[33] R. Lafaye, T. Plehn, M. Rauch, D. Zerwas and M. Dührssen, Measuring the Higgs sector,
J. High Energ. Phys. 08, 009 (2009), doi:10.1088/1126-6708/2009/08/009.
[34] J. de Blas, M. Ciuchini, E. Franco, S. Mishima, M. Pierini, L. Reina and L. Silvestrini, Electroweak precision observables and Higgs-boson signal strengths in the Standard Model and beyond: present and future, J. High Energ. Phys. 12, 135 (2016),
doi:10.1007/JHEP12(2016)135.
[35] A. Alves, N. R. Agostinho, O. J. P. Éboli and M. C. Gonzalez–Garcia, Effect of fermionicoperators on the gauge legacy of the LHC Run I, Phys. Rev. D 98, 013006 (2018),
doi:10.1103/PhysRevD.98.013006.
[36] A. Biekötter, T. Corbett and T. Plehn, The Gauge-Higgs legacy of the LHC Run II (2018),
arXiv:1812.07587.
[37] C. Englert, R. Kogler, H. Schulz and M. Spannowsky, Higgs coupling measurements at the
LHC, Eur. Phys. J. C 76, 393 (2016), doi:10.1140/epjc/s10052-016-4227-1.
[38] D. de Florian et al., Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the
Higgs sector, CERN Yellow Rep.: Monogr. 2 (2017), doi:10.23731/CYRM-2017-002.
[39] D. Zeppenfeld, R. Kinnunen, A. Nikitenko and E. Richter-Was, Measuring
Higgs boson couplings at the CERN LHC, Phys. Rev. D 62, 013009 (2000),
doi:10.1103/PhysRevD.62.013009.

12

SciPost Phys. 6, 024 (2019)[40] M. Duhrssen, S. Heinemeyer, H. Logan, D. Rainwater, G. Weiglein and D. Zeppenfeld,
Extracting Higgs boson couplings from CERN LHC data, Phys. Rev. D 70, 113009 (2004),
doi:10.1103/PhysRevD.70.113009.
[41] G. Buchalla and O. Catà, Effective theory of a dynamically broken electroweak Standard
Model at NLO, J. High Energ. Phys. 07, 101 (2012), doi:10.1007/JHEP07(2012)101.
[42] G. Buchalla, O. Catà and C. Krause, On the power counting in effective field theories, Phys.
Lett. B 731, 80 (2014), doi:10.1016/j.physletb.2014.02.015.
[43] I. Brivio, J. Gonzalez-Fraile, M. C. Gonzalez-Garcia and L. Merlo, The complete HEFT
Lagrangian after the LHC Run I, Eur. Phys. J. C 76, 416 (2016), doi:10.1140/epjc/s10052016-4211-9.
[44] M. Klute, R. Lafaye, T. Plehn, M. Rauch and D. Zerwas, Measuring Higgs couplings at alinear collider, Europhys. Lett. 101, 51001 (2013), doi:10.1209/0295-5075/101/51001.
[45] T. Corbett, O. J. P. Éboli, J. Gonzalez-Fraile and M. C. Gonzalez-Garcia, Constraining anomalous Higgs boson interactions, Phys. Rev. D 86, 075013 (2012),
doi:10.1103/PhysRevD.86.075013.
[46] F. Krauss, S. Kuttimalai and T. Plehn, LHC multijet events as a probe foranomalous dimension-six gluon interactions, Phys. Rev. D 95, 035024 (2017),
doi:10.1103/PhysRevD.95.035024.
[47] S. Banerjee, C. Englert, R. S. Gupta and M. Spannowsky, Probing electroweak precision physics via boosted Higgs-strahlung at the LHC, Phys. Rev. D 98, 095012 (2018),
doi:10.1103/PhysRevD.98.095012.
[48] G. Aad et al. [ATLAS Collaboration], Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC, Phys. Lett. B 726, 88(2013), doi:10.1016/j.physletb.2013.08.010.
[49] S. Chatrchyan et al. [CMS Collaboration], Observation of a new boson with mass nearp
125 GeV in pp collisions at s = 7 and 8 TeV, J. High Energ. Phys. 06, 081 (2013),
doi:10.1007/JHEP06(2013)081.
[50] J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, J. High Energ. Phys.
07, 079 (2014), doi:10.1007/JHEP07(2014)079.
[51] T. Sjöstrand, S. Mrenna and P. Skands, PYTHIA 6.4 physics and manual, J. High Energ.
Phys. 05, 026 (2006), doi:10.1088/1126-6708/2006/05/026.
[52] J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lemaître, A. Mertens and M.
Selvaggi, DELPHES 3: a modular framework for fast simulation of a generic collider experiment, J. High Energ. Phys. 02, 057 (2014), doi:10.1007/JHEP02(2014)057.
[53] U. Baur, T. Plehn and D. Rainwater, Probing the Higgs self-coupling at hadron colliders
using rare decays, Phys. Rev. D 69, 053004 (2004), doi:10.1103/PhysRevD.69.053004.
[54] R. Contino, A. Falkowski, F. Goertz, C. Grojean and F. Riva, On the validity of the effective field theory approach to SM precision tests, J. High Energ. Phys. 07, 144 (2016),
doi:10.1007/JHEP07(2016)144.

13

SciPost Phys. 6, 024 (2019)[55] A. Biekötter, J. Brehmer and T. Plehn, Extending the limits of Higgs effective theory, Phys.
Rev. D 94, 055032 (2016), doi:10.1103/PhysRevD.94.055032.
[56] J. Brehmer, A. Freitas, D. López-Val and T. Plehn, Pushing Higgs effective theory to its
limits, Phys. Rev. D 93, 075014 (2016), doi:10.1103/PhysRevD.93.075014.
[57] A. Helset and M. Trott, Equations of motion, symmetry currents and EFT below the electroweak scale (2018), arXiv:1812.02991.
[58] T. Plehn, Lectures on LHC Physics, Springer Berlin Heidelberg, Berlin, Heidelberg (2012),
doi:10.1007/978-3-642-24040-9.
[59] V. Barger, T. Han, P. Langacker, B. McElrath and P. Zerwas, Effects of genuine dimension-six
Higgs operators, Phys. Rev. D 67, 115001 (2003), doi:10.1103/PhysRevD.67.115001.
[60] W. Bizoń, M. Gorbahn, U. Haisch and G. Zanderighi, Constraints on the trilinear Higgs
coupling from vector boson fusion and associated Higgs production at the LHC, J. HighEnerg. Phys. 07, 083 (2017), doi:10.1007/JHEP07(2017)083.
[61] F. Maltoni, D. Pagani, A. Shivaji and X. Zhao, Trilinear Higgs coupling determination
via single-Higgs differential measurements at the LHC, Eur. Phys. J. C 77, 887 (2017),
doi:10.1140/epjc/s10052-017-5410-8.
[62] S. Di Vita, C. Grojean, G. Panico, M. Riembau and T. Vantalon, A global view on the Higgs
self-coupling, J. High Energ. Phys. 09, 069 (2017), doi:10.1007/JHEP09(2017)069.

14