NLO Higgs Effective Field Theory and κ Framework

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Transcript of NLO Higgs Effective Field Theory and κ Framework

  • NLO Higgs Effective Field Theory and 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

  • higgstools

    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 H 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 s and s)

    I Provide a series of benchmark parametrizations in order totest deviations against experimental data

    http://arxiv.org/abs/1209.0040

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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

    ( BR)(ggH) = (ggH )SM (BRH)SM 2g

    2

    2H

    2g =ggH

    (ggH )SM, 2 =

    ()SM, 2H =

    H

    (H )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 s dont 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 s dont 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 s dont 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 s dont 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 Newtons 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 []() =D e iSUV [,]()

    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 = LSMdim 4

    +

    i

    ai Oi2

    dim 6

    + . . .higher dim. operators

    I ai can be Wilson coefficients or the 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 < < 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

    = Zren Mi = Zi Mi,ren Zi = 1 +g2

    162

    (dZ

    (4)i + g6dZ

    (6)i

    )

    counterterms

    X Dyson-resum the propagators. For example, Higgs self energy:

    SHH =g2

    162HH =

    g2

    162

    (

    (4)HH +

    (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

    I The amplitude for the process is:

    AHAA = THAAp2 p

    1 p1 p2

    M2H

    were we find T to be,

    THAA = ig3

    162(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 ( )

    I Find a final expression for the amplitudes in terms of s and subamplitudes!

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    Hands on EFT:

    SM EFT

    NLO Higgs EFT

    More details on the paper: 1505.03706

    http://arxiv.org/abs/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

    Introdu