Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Searches for new physics at LHC within the Higgs sector.Step 2: Defining the tools

Raquel Gomez-Ambrosio (Turin Univ. & INFN)1

HiggsCouplings 2016 @ SLAC

November 10, 2016

1Work done in collaboration with G. Passarino

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Motivation

After the success of RUN-I of LHC, with the Higgs boson discovery, the door is opento search for new physics. During RUN-II the pheno community needs to move forwardtoo, and define tools and strategies to follow.

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Higgs Production and Decay channels

Look at Production:

Gluon-gluon fusion → Biggest statistics

Weak boson fusion (WBF) → Most important for Pertubative Unitarity

”Higgs-Strahlung” (VH production) → Most important for Pertubative Unitarity

Why study these processes:

1 Higgs couplings are relatively unconstrained (20%)

2 The kinematics of the final state can depend on the structure on the UVcompletion. → look at high energy “tails”

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Effective Field Theory: The bottom-up approach

Augment the SM with operators of dim > 4, suppressed by factors of a new scale Λd−4

Leff = LSM︸︷︷︸dim 4

+1

Λ2

∑k

αkO(6)k︸ ︷︷ ︸

dim 6

+1

Λ4

∑k

αkO(8)k︸ ︷︷ ︸

dim 8

+ . . .︸︷︷︸higher dim. operators

αk is the Wilson coefficient of the kth operator. → assume they allow to use PT

For the current experimental resolution we can truncate this expansion at d = 6

Choose a basis of dim-6 operators, with SU(2)× SU(3)× U(1) andlepton/baryon conservation, and assuming flavor universality.

We chose the “Warsaw Basis” → arXiv: 1008.4884 → containing 59 operators.

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

A word on renormalization of the EFT

The EFT is renormalizable order by order. We have to calculate the new CTsthough: Φ = ZΦ · Φren, p = Zp · pren

Zi = 1 +g2

16π2

(dZ

(4)i + g6dZ

(6)i

)

Note: In the case of EFT, one has to be careful when combining MSrenormalization and on-shell. see [arXiv: 1607.07352] (A. Denner et. al)

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Applicability of the EFT

The EFT introduces a new scale on the theory, Λ, or possibly more:

We assume the new heavy particles are well separated from the SM ones

Λ is related to the mass of the heavy particles in the UV completion.

But we don’t know how they mix with the Higgs: Λ± gν, sin(θ)

The cut-off of the effective theory at LHC:

| σ×BR(σ×BR)SM

− 1| =g2m2

hΛ2 ' 0.1 → Λ <

√10gmh ≈ 400GeV . . . 1.4TeV︸ ︷︷ ︸

(for g = 1 . . .√

4π)

See [arXiv:1510.03443], J. Brehmer, A. Freitas, D. Lopez-Val, T. Plehnand [arxiv:1603.03660], M. Boggia, R.G-A, G. Passarino

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Amplitudes

Amplitudes

EFT Amplitudes

A =∞∑

n=N

gnA(4)n +

∞∑n=N6

n∑`=0

∞∑k=`

gng`4+2kA(4+2k)n`k , g4+2k =

1

(√

2GF Λ2)k

More concretely:

|A|2 = |ASM |2 + |ASM ×A(6)|︸ ︷︷ ︸O( 1

Λ2 )

+ |A(6)|2︸ ︷︷ ︸O( 1

Λ4 )

+ |ASM ×A(8)|︸ ︷︷ ︸O( 1

Λ4 )

+ . . .

Where do we truncate the amplitude expansion?How do we estimate theoretical uncertainties?

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Amplitudes

Amplitudes

EFT Amplitudes

A =∞∑

n=N

gnA(4)n +

∞∑n=N6

n∑`=0

∞∑k=`

gng`4+2kA(4+2k)n`k , g4+2k =

1

(√

2GF Λ2)k

More concretely:

|A|2 = |ASM |2 + |ASM ×A(6)|︸ ︷︷ ︸“linear EFT”

+ |A(6)|2︸ ︷︷ ︸“quadratic EFT”

+ |ASM ×A(8)|︸ ︷︷ ︸not available (th.uncertainty)

+ . . .

Where do we truncate the amplitude expansion?How do we estimate theoretical uncertainties?

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Amplitudes

Higher order corrections: Power counting

The hierarchy of corrections is driven by the value of Λ. Without knowing Λ we cannot know if NLO dim 6 corrections are bigger or smaller than LO dim 8 ones.

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Amplitudes

NLO EFT Example:

some diagrams for pp → ZH, contributing up to O( 1Λ2 )

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Some Results: Helicity Amplitudes

pp → HZ helicity amplitudes, large M(HZ) behaviour

helicity SM one insertion two insertionsq q Z

– + – MZ/M(HZ) g6M(HZ)/MZ g26 M(HZ)/MZ

Wilson — azz , a(3)φq , a

(1)φq aAA, aAZ , aZZ , aφD , aφ�, a

(3)φq , a

(1)φq

– + 0 const g6M2(HZ)/M2Z g2

6

Wilson — a(3)φq , a

(1)φq aAA, aAZ , aZZ , aφD , aφ�, a

(3)φq , a

(1)φq

– + + MZ/M(HZ) g6M(HZ)/MZ g26 M(HZ)/MZ

Wilson — azz , a(3)φq , a

(1)φq aAA, aAZ , aZZ , aφD , aφ�, a

(3)φq , a

(1)φq

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Some results: Tails of kinematic distributions

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 = 10−1aPTG = 10−1

Λ = 1 TeVΛ = 1 TeVΛ = 1 TeV

Λ = 2 TeVΛ = 2 TeVΛ = 2 TeV

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 = 10−1aPTG = 10−1

Λ = 2 TeVΛ = 2 TeVΛ = 2 TeV

Λ = 1 TeVΛ = 1 TeVΛ = 1 TeV

p⊥(Z)[ GeV]p⊥(Z)[ GeV]p⊥(Z)[ GeV]

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

−3 −2 −1 0 +3

0

+0.05

+0.1

σ/σSM − 1σ/σSM − 1σ/σSM − 1

events/5000

pp → HZpp → HZpp → HZ

Linear

Quadratic

Λ = 1 TeVΛ = 1 TeVΛ = 1 TeV

M(HZ) = 400 GeVM(HZ) = 400 GeVM(HZ) = 400 GeV

aPTG ∈ unif(−1 , 1)aPTG ∈ unif(−1 , 1)aPTG ∈ unif(−1 , 1)

16 π2 aLG ∈ unif(−1 , 1)16 π2 aLG ∈ unif(−1 , 1)16 π2 aLG ∈ unif(−1 , 1)

Sigma goes negative if we onlyinclude linear

The quadratic corrections areapparently bigger than the lin-ear

A study of partial waves (per-turbative unitarity) can helpus understand the validity ofthe theory.

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Pseudo Observables: The bridge between theory and experiment

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Pseudo Observables

In RUN-I, POs where the κ’s in the kappa framework. Just some parametersmeasuring ad-hoc deviations on the effective couplings

σ(ii → h + X )× BR(h→ ff) =κ2

iiκ2ff

κ2h

σSM × BRSM

From the QFT point of view, we need a more rigorous description: The κ-frameworkis ill-defined beyond leading order

To bypass this problem: POs can be definded to be residues of the poles of theon-shell amplitudes.

See [arXiv:1412.6038] M. Gonzalez-Alonso, A.Greljo, G. Isidori, D. Marzocca and,[arXiv:1512.06135] A. Greljo, G. Isidori, J.M. Lindert, D. Marzocca

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Pseudo observables

POs can be written as linear combination of Wilson coefficients, this applies both forthe SM Lagrangian and for the EFT Lagrangian. Also beyond LO

A paradigmatic example: H → γµ(p1)γν(p2)

PO : AµνHAA = iFHAATµν = −i2

MFM2H

εγγ︸︷︷︸PO

Tµν

EFT : FLOHAA = FSM + gFg6

M2H

MWaAA︸︷︷︸

Wilson coeff.

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Conclusions (and suggestions)

1 We should try not to go on a gold rush looking for new particles. But insteaddefine and agree on some tools.

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Conclusions (and suggestions)

1 We should try not to go on a gold rush looking for new particles. But insteaddefine and agree on some tools.

2 The bottom-up effective field theory is a powerful model-independent option.

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Conclusions (and suggestions)

1 We should try not to go on a gold rush looking for new particles. But insteaddefine and agree on some tools.

2 The bottom-up effective field theory is a powerful model-independent option.

3 Work still to be done to understand the hierarchy of scales introduced by theEFT.

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Conclusions (and suggestions)

1 We should try not to go on a gold rush looking for new particles. But insteaddefine and agree on some tools.

2 The bottom-up effective field theory is a powerful model-independent option.

3 Work still to be done to understand the hierarchy of scales introduced by theEFT.

4 Violation of unitarity gives us hope for understanding this hierarchy andeventually finding hints of New Physics.

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Conclusions (and suggestions)

1 We should try not to go on a gold rush looking for new particles. But insteaddefine and agree on some tools.

2 The bottom-up effective field theory is a powerful model-independent option.

3 Work still to be done to understand the hierarchy of scales introduced by theEFT.

4 Violation of unitarity gives us hope for understanding this hierarchy andeventually finding hints of New Physics.

5 Pseudo Observables seem the best tool to bring EFT to the experiments.

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC

Introduction Effective Field Theory Some results Pseudo Observables Production POs Vs decay POs

Thank you

R. Gomez-Ambrosio Torino Univ. & INFN

EFT@LHC