Studies of gauge couplings at LHC using Effective Field Theory approach

Studies of gauge couplings at LHC:
the Eﬀective Field Theory approach
Raquel Gomez Ambrosio
PhD Defence
October 16th
2017
Raquel Gomez Ambrosio (PhD Defence) October 16th 2017 1 / 66

Summary of my PhD: 4 main projects
Theoretical: Eﬀective Field Theories
Renormalization of the SMEFT ⇒ arXiv:1505.03706 and JHEP
Novel method for top-down EFTs ⇒ arXiv:1603.03660 and JHEP
Experimental
Validation of Monte Carlo generators for VBS ⇒ new CMS task
Matrix element study for the CMS VBS analysis ⇒ arXiv:1708.02812
Side Project: started the study for the implementation on EFT in the VBS Monte Carlo
Generators. ⇒ arXiv:1610.07491 (Rencontres de Blois, proceedings)

Part I:
Eﬀective Field Theories

Introduction

Introduction
After the Higgs boson discovery in 2012, the SM was completed. The next natural step
is to search for the so-called new-physics. There are two approaches for such searches in
the phenomenology community:
Direct Searches
Exotic particles
Supersymmetric particles
Indirect Searches
Kappa-framework
Eﬀective Field Theory

SMEFT
The SMEFT is born as an attempt to extend the Standard Model in the most general
possible way. Any Lagrangian for SMEFT can be written as:
Leff = LSM +
a5
Λ
O(5)
+
i
ai
Λ2
O
(6)
i +
j
aj
Λ4
O
(8)
j + . . . (1)
O(5)
is the Weinberg operator
O
(6)
i is an operator with mass dimension 6 built out of Standard Model fields
The coefficients ai are arbitrary Wilson coefficients
In general we can add to the expansion an infinite number of operators with growing
mass dimension: O(n)
, n > 4.
The goal, for the “new physics” searches, is to preform a fit the ai coefficients, to
understand the contribution of each of the Oi operators.

SMEFT
The reasons why we can write such a Lagrangian are the following,
1) Applequist-Carazzone theorem (Decoupling theorem)
For two coupled systems with different energy scales (m2 > m1) and described by a
renormalizable theory, there is always a condition under which the effects of the physics
at scale m2 can be effectively included in the theory with the smaller scale m1 by
modifying the parameters of the corresponding theory.
2) Minimal set of assumptions on the UV completion
There is a SM-like Higgs doublet, in a linear representation
The heavy degrees of freedom decouple
There are no new light degrees of freedom

SMEFT
Equivalence theorem (1972, Kallosh, t ’Hooft, Veltman)
“In a renormalizable theory, a reparametrization of the fields leaves renormalized
quantities invariant.” This theorem is fundamental on proving the SM renormalizability,
since gauge invariance is a particular case of field reparametrization.
Application for EFTs:
As a consequence: observables (S-matrix elements) of a QFT are unchanged under an
operator replacement if the difference between the new operator and the replaced one
vanishes on-shell.
“Two operators Q,Q are said to be equivalent, if their difference can be expressed as
Q − Q =
φ
Uφ
δS
δφ
+ h.c. (2)
where the sum runs over all the fields in the theory and Uφ is a polynomial of those and
possibly derivatives. And δS
δφ
are the equations of motion of the action S.”
It can be used to build the minimal basis of non-redundant operators at a given
dimension. Which is very important, in order to work with a minimal set of Wilson
coefficients.

Equivalence theorem, an example.
Lφ =
1
2
(∂φ)2
−
m2
2
φ2
+
λ
4
φ4
V (φ)
⇒ EoM: ∂2
φ = −V (φ) (3)
when considering dim = 6 extensions to this model the candidates are: {φ6
, (∂2
φ)2
,
φ2
(∂φ)2
}. It is possible to write:
(∂2
φ)2
− (V (φ))2
= ∂2
φ + V (φ)
EoM
∂2
φ − V (φ)
Uφ
(4)
The equivalence theorem indicates that the operator (∂2
φ)2
is equivalent to the operator
(V (φ))2
, since their diﬀerence is proportional to the EoM. If we expand V (φ) this
means,
(∂2
φ)2
≡ m4
φ2
+ 2λm2
φ4
+ λ2
φ6
(5)

SMEFT. The Warsaw basis
The most general set of dimension-6 operators respecting the SM symmetries has 81
operators (76 if we impose Baryon number conservation). These can be reduced to
59 using the equivalence theorem.
These 59 operators, have 76 free parameters, if we consider only one generation of
fermions. If we consider three independent generations, the number grows up to
2499 free parameters.
The minimal basis of gauge-invariant non-redundant operators is called the “Warsaw
Basis” arXiv: 1008.4884

Warsaw Basis. Bosonic Sector

Warsaw Basis. Fermionic Sector

Canonical Normalization
Through the introduction of terms such as (Φ†
Φ)3
we also get dimension 4
contributions, due to the Higgs vev ∼ v4
h2
, v2
h4
, v3
h3
, v2
(φ0
)2
h2
. . . that affect
the mass terms in LSM as well as the SM interactions. Other dimension 6 operators,
including covariant derivatives of Φ, modify the kinetic terms directly.
p = ¯p 1 + dRp
M2
Λ2
, Φ = 1 + dRΦ
M2
Λ2
¯Φ, (6)
where ¯p are the SM parameters (M2
h, cw , . . . ) and ¯Φ are the SM fields, with the
“hat” denoting the properly rescaled ones.
This is again a consequence of reparametrization invariance
Tadpoles and the Gauge fixing terms in the Lagrangian, get modified too,
ξi = 1 + dRξi
M2
Λ2
, dRξi
M2
Λ2
= g6∆Rξi i = A, Z, W , ±, 0 (7)
These are the main results of arXiv:1505.03706.

SMEFT Amplitudes
Amplitude for a 1 → 2 process
ASMEFT(1 → 2) =
∞
n=N
gn
A(4)
n +
∞
n=N6
n
l=0
∞
k=l
gn
gl
4+2k A
(4+2k)
nlk , (8)
where g is the SU(2) coupling constant and we deﬁne g4+2k = 1/(
√
2GF Λ2
)k
, therefore
k = 1 for dimension 6, k = 2 for dimension 8, etc. Further, N is the LO of the SM
process (N=1 for H → VV , N = 3 for H → γγ, etc) and N6 = N for tree level processes
while N6 = N − 2 for loop induced ones.
EFT couplings
g6 =
1
√
2GF Λ2
g6 = 0.0606
TeV
Λ
2
1 and g8 =
1
2G2
F Λ4
≡ g2
6 g8 << 1
(9)

SMEFT Amplitudes
SMEFT amplitudes can be used as a tool to study the validity regime of the EFT
perturbative expansion
(1 → 2 process)
Higher dim. →
Higher order ↓ gA
(4)
1 gg6A
(6)
1,1,1 gg8A
(8)
1,1,2 . . .
g3
A
(4)
3 g3
g6A
(6)
3,1,1 g3
g8A
(8)
3,2,1 . . .
. . . . . . . . . . . .
The leading order for an EFT amplitude is unambiguous: A = ASM + g6A
(1)
6 where A
(1)
6
has only one dimension-6 operator. When adding higher orders in PT to A we can use
the following hierarchy:
AEFT = ASM + g6A
(1)
6
LO EFT
+ g2
6 A
(1)
6 + g8A
(1)
8
NLO EFT
+ . . . (10)

SMEFT Amplitudes
The ambiguities reappear when squaring the amplitude:
|AEFT|2
=|ASM|2
+ g6 |ASM × A
(1)
6 |+
+ g2
6 |A
(1)
6 |2
+ g2
6 |ASM × A
(2)
6 | + g8 |ASM × A
(1)
8 | + . . .
where we ﬁnd three terms at order g2
6 with very diﬀerent origins. Our convention is to
consider the g2
6 |A
(1)
6 |2
, also called “quadratic EFT” in the literature, and take the other
terms, when known, as an estimate for the theoretical uncertainty.
|AEFT|2
= |ASM |2
+ |ASM × A
(1)
6 |
“linear EFT”
+ |A
(1)
6 |2
“quadratic EFT”
+ |ASM × A
(2)
6 | + |ASM × A
(1)
8 |
not available (th.uncertainty)
+ . . .

Example pp → ZH
A = A(s), ALO EFT = A(s, t, apq, apu, apW , apD , ap , apWB ) (11)
Ongoing work: Double insertions, NLO EFT and QCD-EFT corrections...

Example pp → ZH
100100100 200200200 300300300 400400400 500500500
−3.5
0
+3.5
pp → HZ 14 TeVpp → HZ 14 TeVpp → HZ 14 TeV LO
Linear SMEFT / SM
Quadratic SMEFT / SM
aLG = 10−1
/(16 π2
)aLG = 10−1
/(16 π2
)aLG = 10−1
/(16 π2
)
aPTG = 10−1aPTG = 10−1
aPTG = 10−1
Λ = 2 TeVΛ = 2 TeVΛ = 2 TeV
p⊥(Z)[ GeV]p⊥(Z)[ GeV]p⊥(Z)[ GeV]
2002
/s2002
/s2002
/s 5002
/s5002
/s5002
/s 8002
/s8002
/s8002
/s
M2
(HZ)/sM2
(HZ)/sM2
(HZ)/s
−1.5
0
+0.9
+1.5
pp → HZ 14 TeVpp → HZ 14 TeVpp → HZ 14 TeV LO
Linear SMEFT / SM
Quadratic SMEFT / SM
aLG = 10−1
/(16 π2
)aLG = 10−1
/(16 π2
)aLG = 10−1
/(16 π2
)
aPTG = 10−1aPTG = 10−1
aPTG = 10−1

SMEFT NLO and Renormalization
The next natural step is to go to NLO-EFT calculations
The main reasons to do this are:
Understand the validity of the perturbative expansion.
Understand the size of the QCD-EFT corrections.
To have a precise estimate of the theoretical uncertainty induced by the missing
higher orders.

The SMEFT renormalization is performed analogously to the SM one:
{p0}
bare
= Z{p} {p}
ren.
, {Φ0}
bare
= Z
1/2
{Φ} {Φ}
ren.
(12)
with counterterms,
Zi = 1 +
g2
16π2
dZ
(4)
i + g6dZ
(6)
i ∆UV (13)
The Zi ’s, can be extracted from the self energies of the theory and with them we can
write down Dyson resummed propagators. In the previous equation we introduced a
useful quantity,
∆UV =
2
− γE − ln π − ln
µ2
R
µ2
, ∆UV(x) =
2
− γE − ln π − ln
x
µ2
(14)
where = 4 − d, d is the space-time dimension, µ is an auxiliary scale that appears in
the integral measure (µ4−d
dn
q) but not in the ﬁnal results, γE = 0.5772 is the
Euler-Mascheroni constant and µR is the renormalization scale.
These are the main results of arXiv:1505.03706.

SMEFT Finite renormalization
For the SMEFT, we use on-shell renormalization for the SM parameters, and MS
renormalization for the Wilson Coefficients.
Caveat: The MS is a non-physical renormalization scheme and the decoupling
theorem does not hold any more, i.e. it has to be enforced (matching conditions).
On-shell renormalization
If m0 is the bare mass for the field V,
m2
0 = M2
OS 1 +
g2
16π2
ReΣVV ;fin
s=MOS
= M2
OS + g2
∆M2
(15)
where MOS is the on-shell massa
and Σ is the self energy extracted from the required 1PI
Green function.
a
Strictly speaking, this procedure is only valid at one loop, to be completely rigorous and to be
able to go beyond one loop, we should introduce a complex component in the on-shell mass

On-shell Renormalization
The value of the bare mass can then be substituted in the results. After UV poles have
been removed and bare masses replaced, we introduce,
MV ;ren = MV ;OS +
g2
16π2
dZ
(4)
MV
+ g6dZ
(6)
MV
(16)
we substituted the counterterms Z for Z and required that s = MV ;OS is a zero of the
real part of the inverse V propagator, up to O(g2
g6). At this stage one has to choose a
ﬁnite-renormalization scheme
Finite renormalization:
GF renormalization scheme: The input parameter set is {GF , Mw , Mz }
gren. = gexp. +
g2
exp
16π2
dZ(4)
g + g6dZ(6)
g (17)
α renormalization scheme: The input parameter set is {α, GF , Mz }
g2
s2
θ = 4πα 1 −
α
4π
ΠAA(0)
s2
θ
(18)

There is a particular feature of EFTs: when renormalizing 3-point functions, new
relations between the Wilson Coefficients appear.
Ci =
j
ZW
ij Cren.
j , ZW
ij = δij +
g2
16π2
dZW
ij ∆UV (19)
We believe that these relations might play an important role when designing the strategy
for global fits for EFTs at LHC. These effect introduces new dependencies between the
Wilson coefficients, that should be taken into account.
For instance we should not set an operator to zero just because a priori it is not entering
the LO calculation, its WC might be contributing to another relevant operator.
In arXiv:1505.03706, we calculated the canonical normalization and renormalization for
the SMEFT Lagrangian. This is, all the tadpoles and self-energies of the theory. We also
calculated several 3-point Green’s functions in order to extract the ZW
ij matrix, and the
NLO EFT corrections to the S, T and U EW parameters.

SMEFT: Infrared behaviour
In principle, by the Applequist-Carazzone theorem, the IR structure of a theory should
not be altered by the inclusion of UV eﬀects. Hence the SMEFT should conserve the IR
behaviour of the SM.
Example: Z decay to two charged leptons: Z →
Z
Z
LO EFT
Zγ γ Z γ
NLO EFT
γ γZ γZ
Z Zγ γ Z γZ γ
Ongoing work: QCD-EFT corrections

SMEFT: Infrared behaviour
Example: Z decay to two charged leptons: Z →
After UV renormalization the LO amplitude for Z → is,
Aµ = g A(4)
µ + gg6 A(6)
µ (20)
The virtual and real contributions cancel exactly:
Γ(Z → ¯ll) div
= −
g4
384π3
MZ s2
ωFvirt
Γ
(4)
0 1 + g6 ∆Γ + g6 Γ
(6)
0 , (21)
Γ(Z → ¯llγ) div
=
g4
384π3
MZ s2
ωFreal
Γ
(4)
0 1 + g6 ∆Γ + g6 Γ
(6)
0 (22)
Leading to an IR-safe ﬁnal expression:
Γ1
QED =
3α
4π
GF M3
Z
24
√
2π
(v2
l + 1) 1 + g6 δ
(6)
QED + g6 ∆
(6)
QED (23)
where vl = 1 − 4 s2
θ, δ
(6)
QED, ∆
(6)
QED contain the ﬁnite contributions from dim = 6
operators.

The top-down approach
These are the main results of arXiv:1603.03660, where we discuss an alternative to the
SMEFT: the top-down approach.
In the top-down approach, the heavy fields are integrated out from a concrete UV
theory.
Classically, the top-down approach is performed using functional methods: the
background field method and the covariant derivative expansion method.
These techniques have some flaws, that we overcome by using a mix of functional
and diagrammatic methods.

Top-down approach, graphical interpretation
Tree Level
One Loop Level

The top-down approach
Starting from a concrete UV model, integrate out the heavy degrees of freedom
The initial set-up is similar to the SMEFT case:
LBSM = LSM + ∆L(4)
+ L
(4)
H (24)
L
(4)
H =
h
i1=0
· · ·
Ik −1
ik =0
· · ·
In−2
in−1=0
Fh
i1...in
Hi1
1 . . . H
In−1
n + h.c. (25)
where Ik = {h − i1 − · · · − ik−1}, ∆L(4)
contains light fields and non-SM couplings
(SM couplings modified by the BSM effects) and Fh
is a function of the light fields
with canonical dimension 4 − h.

Low energy behaviour of SM extensions
Identification of the scale
In this approach, the identification of the energy scale (Λ in the SMEFT case) is not
trivial.
First, if there is more than one heavy particle to be integrated out, the hierarchy of
the masses and the mixings between particles must be carefully addressed.
Additionally, if we work in the mass eigenbasis, the scale gets “shifted” as:
M2
H = Λ2
∞
n=0
ξn
M2
Λ2
2
(26)
where M is the W mass and ξn are model-dependent parameters.
It has been shown for a series of UV models that different choices of the “new
physics” scale, lead to different low-energy predictions (arXiv:1607.08251)

Most general UV generating functional and Lagrangian,
Γ = DH ei d4
x LH
, LH = −
1
2
∂µH∂µ
H −
1
2
M2
H H2
+
4
n=1
FnHn
(27)
Form here we extract the effective Lagrangian,
Γ = Γ0 e i d4
x Leff
, Leff = LT
eff +
1
16π2
LL
eff (28)
at tree level,
LT
eff =
1
2
F2
10
ξ0
+
1
ξ3
0Λ2
F3
10F30 +
ξ0
2
2F2
10F20 − M2
ξ1F2
10 − ∂µF10∂µ
F10 + ξ2
0F10F11

At loop level the situation is more complicated, 3 kinds of contributions:
Heavy loop-generated operators. ⇒ Solvable by functional methods
Mixed heavy-light loop-generated operators. ⇒ Need diagrammatic methods
Tadpole-generated operators ⇒ Need diagrammatic methods
NOTE: The last two contributions are strictly model dependent.
In arXiv:1603.03660, we addressed diﬀerent models (SM singlet extension, THDM and
non-linear Higgs) where we calculated the one-loop eﬀective Lagrangian in a model-by
model basis.

SM Singlet extension
We consider the simplest SM extension: a heavy SU(2)-singlet,
LUV = LSM + LS , LS = (∂µS)(∂µ
S) − µ2
1S2
− λ1S4
− λ12S2
(Φ†
Φ) (29)
In the mass eigenbasis, the singlet field (h1) mixes with the SM Higgs (h), leading to two
new fields: h (light) and H (heavy),
h = cαh − sαh1, H = sαh + cαh1 (30)
Using the previously outlined technique, we found an effective Lagrangian, valid up
to one-loop, independent of H and h1.
This Lagrangian has more terms that the ones presented usually in the literature.
In this case, we didn’t assume decoupling of the heavy fields

Singlet Extension: Example of heavy-light loop-generated operators
the contribution to the hhZZ vertex from the bottom right diagram is:
QhhZZ
µν =
1
16π2
1
8
C
(2)
0 (Mh) V 2
h V 11
hZZ + V 10
hh V 21
ZZ V 10
hh
1
t1Λ2
δµν (31)
where,
V 2
h = 2gMt3 1 −
t3
t1
, V 11
hZZ = −g2 M
c2
w
t3
t1
, V 10
hh = −2gt3, V 21
zz = −
g2
4
M2
c2
w
t2
3
t2
1
and C
(2)
0 = C0(Mh, MH, MH)

SM Singlet extension
Canonical Normalization
the ﬁelds have to be reparametrized to restore the correct structure of the kinetic terms,
h → Zh h ⇒ Zh = 1 −
g2
16π2
M2
Λ2
1
6
t2
3
t3
1
(t1 − t3)2
(32)
further we can reparametrize the masses to keep them as bare parameters in the
Lagrangian,
Mh = ¯Mh 1 +
1
2
g2
16π2
∆M
(0)
h
Λ2
M2
+ ∆M
(1)
h
+ ∆M
(2)
h
M2
Λ2
M = ¯M 1 +
1
2
g2
16π2
∆M(1) + ∆M(2)
M2
Λ2
Gauge Invariance
h = h +
1
2
gcα Γz
φ0
cw
+ φ+
Γ−
+ φ−
Γ+
(33)
H = H +
1
2
gsα Γz
φ0
cw
+ φ+
Γ−
+ φ−
Γ+

Part II:
Vector Boson Scattering at LHC

Vector Boson Scattering: Theoretical background
Theorist deﬁnition
t-channel exchange of two weak bosons between two quarks
Experimentalist deﬁnition
Processes that pass the VBS cuts

Unitarity violation
Longitudinal scattering of same sign weak bosons is the paradigmatic example of
unitarity violation, in the absence of the Higgs:

Delayed Unitarity
An interesting phenomenon that should be carefully studied in the context of VBS
and EFT is that of delayed unitarity: it is proven that the Higgs stabilizes the WW
scattering amplitudes, and that a set of very concrete cancellations between
divergent terms makes the total cross-section ﬁnite in the high energy regime.
An extension of the SM Lagrangian with a gauge-invariant heavy sector could make
such amplitudes (concretely the one for e+
e−
→ W +
L W −
L ) to grow at intermediate
energies, specially through the radiative corrections to the gauge boson vertices.
If this is the case, we can say that unitarity is delayed, predicting an enhancement of
the total cross section for the process, that could be measured in experiment as a
hint for new physics. This too would be a natural scenario for EFT studies.
This one reason why VBS is very important in the context of new physics searches ...

Searches for VBS in the experiment: ZZ → 4
Low σ × BR
Large irreducible background (B ≈ 20 S)
Final state selection:
Two charged-lepton pairs
Two tagged jets
Additionally, VBS cuts:
mjj > 100 GeV
Z on-shell
Very similar to H → ZZ → 4 analysis.
This is the analysis presented in arXiv:1708.02812

VBS-ZZ Signal and Background
Main Signal
Main Background

Validation Study
• Before carrying out the physics analysis, we performed a validation study for diﬀerent
signal and background samples, using Rivet .
• Such a study is independent of LHC physics, and can be used for either of CMS or
ATLAS detectors, as well as for general theoretical questions.
Background samples: q¯q → ZZjj → 4 jj
Madgraph5 aMC@NLO , LO: generate pp > l+
l−
l+
l−
, QED=4
The cross section for this sample is: σ = (1.003 ± 0.004)pb
Madgraph5 aMC@NLO , NLO: generate pp > l+
l−
l+
l−
, QED=4
POWHEG NLO inclusive: + − + −

Validation Study: Background

Baseline Selection: Fiducial region
To define the fiducial region we chose a standard CMS set of cuts.
Transverse momentum of the final state leptons: To match the resolution of the
detector
pT ( 1) > 20 GeV pT ( 2) > 10 GeV
pT ( 3,4) > 7 GeV(e) pT ( 3,4) > 5 GeV(µ)
Cuts in pseudo-rapidity: To adapt to the fiducial volume of the detector
η(e) < 2.5, η(µ) < 2.4
Transverse momentum of the jets:
pT (j) > 30 GeV

Baseline Selection: VBS region
Select leptons coming from decay of on-shell Z bosons, to remove the Higgs signal:
M ∈ [60, 120] GeV
Number of jets in the ﬁnal state, to match the event topology
njet ≥ 2
Invariant mass of the two leading jets: To remove the “triboson” production
contributions,
mjj > 100 GeV
⊕ the previous ﬁducial cuts

Background plots: Leading Lepton pT
We ﬁnd a small disagreement between POWHEG and Madgraph5 aMC@NLO
This disagreement was known prior to this study.
It is larger in the VBS region, still it is smaller that the disagreement seen in
previous VBS studies (other channels)

Validation Study: Signal
The validation of the signal samples plays a double role: not only it serves to cross check
diﬀerent MC generators, but also, we use it to study diﬀerent kinematic variables, and
choose the most useful ones for the analysis.
Signal samples
Madgraph5 aMC@NLO LO: generate pp > l+
l−
l+
l−
j j, QED=6
The cross-section for this sample is: σ = (0.01008 ± 0.00008)pb
PHANTOM LO:
The cross-section for this sample is: σ = (0.0004273 ± 0.0000002)pb . It is much
smaller than the Madgraph5 aMC@NLO cross section for the same process due to
some more restrictive cuts that are applied at the generator level.
Ongoing work: production and study of equivalent SHERPA samples

Signal plots

VBS signatures
VBS has a very small cross section, but very particular experimental signatures, that
allow us to extract the signal at LHC from the dominant backgrounds.
In general, variables related to the di-jet system will be the most useful ones to extract
signal from background.

Signal Vs. Background plots
Rapidity and invariant mass of the di-jet system

Conclusions and Comments
Conclusions
We found a relatively good agreement for the bkg samples
We found a diﬃculty when normalizing the signal samples in Rivet
Rivet proved to be very useful and theorist friendly
Comments
Currently working with the PHANTOM authors and CMS experts to understand this
disagreement
As a result of this work I have been asked to do the validation of the VBS SHERPA
samples for the next CMS production campaign.

VBS in the ZZ channel: The Analysis
Experimental analysis, with the same cuts used in the validation study
The main irreducible backgrounds are much larger than the signal. Additionally to
the baseline cuts, we had to use multivariate techniques for the signal extraction.
For the ﬁnal analysis, signal, background and interferences were generated with
Madgraph5 aMC@NLO

Control Plots
These are oﬃcial CMS plots from the analysis presented in arXiv:1708.02812

Multivariate Analysis: MELA

Multivariate Analysis: MELA
Use a signal-background kinematic discrimiant
KD =
Psig
Psig + Pbkg
(34)
“sig” and “bkg” are the two processes we want to isolate
P are their relative probabilities, normalized to one
For a given 4 total mass there are 7 independent variables for which P are
aggregated probabilities, taken correlations into account.
Results:
We performed a sig./
√
sig. + bkg. cut optimization
The optimal KD cut was found to be KD > 0.66

Results: ROC curve
Advantages and disadvantages of MELA
(+) Solid theoretical background (wrt. BDT)
(+) Very good results with a “small” eﬀort
(–) Depends on the MELA authors
(–) Only useful to discriminate 2 processes, not more
Results:
Expected signiﬁcance
σnosyst. = 1.43
σsyst. = 1.24
Very close to the BDT 1.6σ result.

Systematic errors and final results
Systematic errors
Monte Carlo 0.5 - 2.7 % MC statistics
PDF Variation 1. - 9.3 % NNPDF envelope (PDF4LHC)
Scale Variation 1. - 31 % µR , µF = ×0.5, ×2
31% due to LO samples
Jet Energy Scale 1.1 - 7.3 % partons Vs. jets
Final results
The electroweak production of two Z bosons in association with two jets was measured
with an observed (expected) significance of 2.7 (1.6) standard deviations, using a BDT.
Additionally an expected significance of 1.2 standard deviations was found using matrix
elements techniques. The fiducial cross section was found to be,
σEW (pp → ZZjj → jj) = 0.40+0.21
−0.16(stat)+0.13
−0.09(syst)fb (35)
consistent with the standard model prediction of 0.29+0.02
−0.03fb, but still suffering from big
statistical uncertainties.

Vector Boson Scattering in experiment. State of the art

Conclusions and Future prospects
Conclusions
“What I expect from the LHC? That’s a big problem. What I would like to see is the
unexpected. If it gives me what the Standard Model predicted ﬂat out – the Higgs with a
low mass – that would be dull. I would like something more exciting than that”
Martinus Veltman, in “The Unexpected”
Future prospects
Continue developing the NLO EFT
Preliminary studies of EFT in VBS
Studies of the introduction of EFT in the Monte Carlo generators
Validation of SHERPA samples in CMS

Thank you!

And thank you...

Additional Slides

Our choice of Warsaw Basis and Wilson Coeﬃcients

Counting of the free parameters
The Warsaw Basis has 76 or 2499 free parameters, if we consider 1 generation of
fermions or 3 respectively.

“Integrating out” operators Vs. “Completely removing” them
When we integrate out, we use functional or diagrammatic methods, as explained before.
When we “completely remove” we do a direct matching between diﬀerent Green’s
functions of both theories

Searches for VBS in the experiment: Same sign WW
Large σ × BR
Low irreducible background ( B ≈ S)
Final state selection:
Two charged leptons
Two tagged jets
Observed in CMS Run 2 data:
5.5 σ observed (5.7 expected)

Studies of gauge couplings at LHC using Effective Field Theory approach

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