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 G´omez-Ambrosio (Turin Univ. & INFN) 1 HiggsCouplings 2016 @ SLAC November 10, 2016 1 Work done in collaboration with G. Passarino R. Gomez-Ambrosio Torino Univ. & INFN EFT@LHC
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Searches for new physics at LHC within the Higgs sector. Step 2: Defining the tools.
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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