NLO Higgs Effective Field Theory and κ FrameworkarXiv:1505.03706. M. Ghezzi, R.G. , G.Passarino, S.Uccirati
Raquel Gomez-AmbrosioHiggsTools @Universita & INFN @Torino & CMS @CERN
Planck Conference 2015, Ionannina, GR
May 27, 2015
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Outline
Introduction:The Search of BSM physicsThe kappa framework
Effective Field theoryWhat is Effective Field TheoryWhy choose Effective Field Theory
Hands on EFT:HowToSM EFT
Summary & Open Questions
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Introduction:
The Search of BSM physics
Introduction: Why are we here?
The Standard Model Today:
I Higgs-like particle with JCP = 0++,MH = 125.09± 0.24 GeV found in 2012.
No new physics found yet:
I Neutrino masses
I Dark Matter
I Graviton
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Introduction:
The Search of BSM physics
CMS results: “Constraints on the Higgs boson width . . . ” (1405.3455)
MH can be extracted from the peak, for ΓH we have to look at the off-shell region
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Introduction:
The kappa framework
Search for BSM physics: The kappa framework
I First proposed by the LHC-HXSWG in 1209.0040
I Idea: Introduce ad-hoc deviations for some SM observables(Higgs’ σ’s and Γ’s)
I Provide a series of benchmark parametrizations in order totest deviations against experimental data
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Introduction:
The kappa framework
Search for BSM physics: The kappa framework
The simplest example:
Gamma-Gamma state originated from Gluon-Gluon fusion
(σ · BR)(gg→H→γγ) = (σggH )SM · (BRHγγ)SM ·κ2
gκ2γ
κ2H
κ2g =
σggH
(σggH )SM, κ2
γ =Γγγ
(Γγγ)SM, κ2
H =ΓH
(ΓH )SM
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Introduction:
The kappa framework
Search for BSM physics: The kappa framework
Disadvantages . . .
I Ad-hoc deviations are not compatible with QFT(they break gauge invariance and unitarity)
I The κ’s don’t have a direct physical interpretation
I With the available amount of data and theoreticalpredictions, no deviation has been found
I Need to go to higher orders in perturbation theory(NLO for signal AND background processes)
I Need higher experimental accuracy
I Or, maybe, need another approach . . .
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Introduction:
The kappa framework
Search for BSM physics: The kappa framework
Disadvantages . . .
I Ad-hoc deviations are not compatible with QFT(they break gauge invariance and unitarity)
I The κ’s don’t have a direct physical interpretation
I With the available amount of data and theoreticalpredictions, no deviation has been found
I Need to go to higher orders in perturbation theory(NLO for signal AND background processes)
I Need higher experimental accuracy
I Or, maybe, need another approach . . .
higgstools
Introduction:
The kappa framework
Search for BSM physics: The kappa framework
Disadvantages . . .
I Ad-hoc deviations are not compatible with QFT(they break gauge invariance and unitarity)
I The κ’s don’t have a direct physical interpretation
I With the available amount of data and theoreticalpredictions, no deviation has been found
I Need to go to higher orders in perturbation theory(NLO for signal AND background processes)
I Need higher experimental accuracy
I Or, maybe, need another approach . . .
higgstools
Introduction:
The kappa framework
Search for BSM physics: The kappa framework
Disadvantages . . .
I Ad-hoc deviations are not compatible with QFT(they break gauge invariance and unitarity)
I The κ’s don’t have a direct physical interpretation
I With the available amount of data and theoreticalpredictions, no deviation has been found
I Need to go to higher orders in perturbation theory(NLO for signal AND background processes)
I Need higher experimental accuracy
I Or, maybe, need another approach . . .
higgstools
Effective Field theory
What is Effective Field Theory
Alternative strategy: Effective field theory
Definition:
An effective field theory (EFT) is a field theory, designed to reproduce the
behaviour of some underlying physical theory in some limited regime. It focuses
on the degrees of freedom relevant to that regime, simplifying the problem but
letting aside some physics.
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Effective Field theory
Why choose Effective Field Theory
Why choose EFT?
I Historically legitimated: Large scale physics, as we know it, is made of EFTs: fluiddynamics, solid state and condensed matter physics.
I Newton’s theory of gravity is an effective low-energy theory of general relativity,which is itself some low-energy effective theory of a quantum theory of gravity.
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Hands on EFT:
HowTo
Things the apprentice has to know: Top-down Vs. Bottom-up approach
I In the Top-down approach: (model dependent)
I Start from a complete high energy theory.
I Integrate out heavy fields: e iSeff [φ](µ) =∫DΦ e iSUV [φ,Φ](µ)
I Use RG-flow to study the resulting theory in its low-energy regime
I In the Bottom-up approach: (model independent)
I Start from a low-energy known theory (the SM).
I Add operators consistent with the symmetries(recall Wilson: only dim > 4 makes sense)
I Calculate (pseudo)-observables and compare with experiments
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Hands on EFT:
HowTo
SM EFT (bottom-up approach)
Leff = LSM︸︷︷︸dim 4
+∑
i
ai Oi
Λ2︸ ︷︷ ︸dim 6
+ . . .︸︷︷︸higher dim. operators
I ai can be Wilson coefficients or the κ’s introduced previously
I For current experimental thresholds, dim 6 operators are enough.
I Using eqs. of motion and gauge symmetries, one can build a 59-operator
basis (for one generation of particles! for three → 2499 operators)
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Hands on EFT:
SM EFT
SM EFT
Some Assumptions
I There is one Higgs doublet with a linear representation
I The EFT does not add new light degrees of freedom
I The heavy degrees of freedom of the EFT decouple
I The heavy degrees of freedom do not mix with the Higgs doublet
I The UV completion is weakly coupled and renormalizable
Also: Restrict to dim 6 and NLO
I As a consequence: 5 TeV < Λ < 7 TeV
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Hands on EFT:
SM EFT
Hands on: The Strategy to follow
1. Start from the SM L
2. Add all possible dim 6 operators(“a basis”)
3. Redefine fields and parameters torecover the wanted expression:
L = LSM + Ldim 6
4. Write down Feynman rules andrenormalize this L
5. Do your calculations!
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Hands on EFT:
SM EFT
Redefiniton and Renormalization
X Include wave-function factors and counterterms
Φ = ZΦΦren Mi = Zi Mi,ren Zi = 1 +g2
16π2
(dZ
(4)i + g6dZ
(6)i
)︸ ︷︷ ︸
counterterms
X Dyson-resum the propagators. For example, Higgs self energy:
SHH =g2
16π2ΣHH =
g2
16π2
(Σ
(4)HH + Σ
(6)HH
)X Add counterterms. Remove UV divergencies.
X Use Ward-Slavnov-Taylor identities to check consistency.
X OBS: Counterterms remove O(4) UV divergencies, not the O(6):
Wilson coefficients mix!
X Finite renormalization instead of RG flow: Connect with pseudo observables
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Hands on EFT:
SM EFT
The message
X We want to do precision physics: We are looking for tiny deviations from the SM,and the energy scale of our theory is relatively narrow
× Therefore cannot use the renormalization group equations
X We want to isolate the O(6) contributions to the amplitudes from the O(4)
X If you manage to do this, it should be easy to measure SM deviations in Higgsproduction and decays (through the couplings)
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Hands on EFT:
SM EFT
Step 5. Calculations: Higgs decays and all that
Example: H → γγ
I The amplitude for the process is:
AµνHAA = THAApµ2 pν1 − p1 · p2δ
µν
M2H
were we find T to be,
THAA = ig3
16π2(T (4)
HAA + g6 T (6),bHAA︸ ︷︷ ︸
UV divergent
) + igg6 T (6),aHAA︸ ︷︷ ︸
UV finite
(1)
I Need to renormalize T (6),bHAA → mixing of Wilson coefficients ( ≡ κ)
I Find a final expression for the amplitudes in terms of κ’s and subamplitudes!
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Hands on EFT:
SM EFT
NLO Higgs EFT
More details on the paper: 1505.03706
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Summary & Open Questions
Summary & Open Questions
I We present an effective field theory approach to BSM physics
I EFT is a very good choice,regarding model independence.
I It also goes beyond LO:Starting from the kappa-framework, propose an NLO extension for it.
I We can identify the deviations inside the amplitudesand therefore compare with LHC data
Open Questions
I What is the range of validity of the effective theory?
I Which kind of theory we find at (even) higher energies?
I How to combine the bottom-up and top-down approaches of EFT?
I Do SM deviations have a SM basis?
I What happens to PDFs & theoretical uncertainties?
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Summary & Open Questions
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Backup
Backup
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Backup
List of relevant dim 6 operators
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Backup
Realtion with the Wilson coefficients
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