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Electroweak Corrections to Higgs Production and decays

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Electroweak Corrections to Higgs Production and decays

Giuseppe Degrassi

Università di Roma Tre

I.N.F.N. Sezione di Roma Tre

ILC Physics in Florence

Florence, September 12-14, 2007

My PERSONAL opinion on ILC

If LHC does not discover anything or discovers only the Higgs (of any mass) ILC has a very little chance to be built

The best things non ILC people can do for ILC

To be prepared for ANY kind of new physics LHC

could discover

Warning

THIS IS NOT A TALK ON ILC PHYSICS

What kind of new physics?

2007

2002

- A Higgs boson heavier than 220 GeV requires
- NP of non decoupling type
- A Higgs boson ligther than 220 GeV may be
- accompanied by NP of decoupling type

Two radiative parameters:

NP of non decoupling type

Extra Z

A heavy Higgs

needs:

Isosplitted particles

More difficult

(light sleptons)

Outline

- Higgs production and decay in SM.
- NP can play a role in
- EW correction to
- in the SM
- NP contributions in :
- colored scalars, QCD corrections
- Conclusions

SM Higgs production at LHC

Gluon

fusion

VBF

Associate

production

with

Associate

production

with W,Z

dominant

SM Higgs decays (BR)

huge QCD background

small BR

exp. clean

dominant

Gluon fusion Higgs production in the SM

- LO completely known
- Georgi, Glashow, Machacek, Nanopoulos (78)
- QCD Corrections
- NLO completely known (LO Xsect. 60-70% )
- Dawson (91), Djouadi, Graudens, Spira, Zerwas (91-95),
- Ellis et al. (88), Bauer, Glover (90)
- NNLO known
- Harlander, Kilgore (01-02),
- Catani, de Florian, Grazzini (01),
- Anastasiou, Melnikov (02),
- Ravindran, Smith, van Neerven (03)
- NNLO+softgluon resummation (NLO Xsect. 6-15% )
- Catani, de Florian, Grazzini, Nason (03)

Error on QCD correction at the level of 10%

EW corrections could be important

Higgs decay in two photons in the SM

- Lowest order (one-loop) completely known
- largest contribution is bosonic (W exchange)
- Ellis, Gaillard, Nanopoulos (76), Shifman et al. (79)
- QCD Corrections
- Corrections to the top-bottom contribution
- completely known
- Zheng,Wu (90),Djouadi, Spira, Zerwas, van der Bij, Graudens (91-94),
- Dawson , Kauffman (93), Melnikov, Yakolev (93), Steinhauser (96)
- Analytic results available
- Fleischer, Tarasov, Tarasov (04), Harlander, Kant (05),
- Anastasiou et al. (06), Aglietti, Bonciani, Vicini, G.D. (06)
- EW Corrections
- Large limit
- Liao, Li (97), Fugel, Kniehl, Steinhauser (04)
- Large limit
- Korner, Melnikov, Yakovlev (96)

Two-loop EW Corrections to

Decay width:

Amplitude:

Lowest order:

does not exist in BFG

Background Field Method

- Technique for quantizing gauge field theories without
- losing explicit gauge invariance. Fields are splitted
- in classical (background) and quantum components.
- Green functions of classical fields satisfy simple
- QED-like W.I.
- Larger number of Feynman rules. Implemented in
- FeynArts
- Denner, Dittmaier, Weiglein (95), T. Hahn (01)
- In the Feynman BFG the vertex is absent
- Reduction in the number of diagrams
- 1l: 28 -> 12; 2l: 4200 -> 1700
- finite

Two-loop contributions:

two mass scales

diagrams

one mass scale

diagrams

We look for a result valid at least in the intermediate

Higgs mass regime

Structure of the diagram cuts

- Helicity structure does not allow
- a cut at
- First cut is at when
- q is massless (in ) .
- Next cut at
- (in )

To cover the intermediated higgs mass region

must be computed exactly

can be computed via a Taylor expansion

Light fermion Contributions

Aglietti, Bonciani, Vicini, G.D. (04)

- Reduction of loop integrals
- to MI via IBP (LI)
- (Laporta algorithm)
- Computation of MI
- via differential equations
- Analytic solution of MI in
- terms of Generalized Harmonic
- Polylogarithms GHPLs thresholds at
- Goncharov (98), Broadhurst (99), Remiddi, Vermaseren (00)
- Gehrmann, Remiddi, (01), Maitre (06)
- Aglietti, Bonciani (03-04)

Light fermion Contributions

Bosonic and top Contributions

F. Maltoni, G.D. (05)

- Reduction of Taylor expanded amplitudes to bubble
- integrals
- O.V. Tarasov (95)
- Evaluation of two-loop massive bubble integrals
- Daviydychev, Tausk (93)
- Vertex function finite and vanishing for .
- Renormalization of .

finite, O.S. limit

Corrections to

Cancellation between EW and QCD contributions

Similar results obtained via a fully numerical approach

Passarino, Sturm, Uccirati (07)

Two-loop EW Corrections to

- Calculation at the partonic level similar to
- L.F. contribution computed exactly, top contribution
- via Taylor expansion

Enhancement of the cross section of about 6-8% in

the intermediate higgs mass range.

Colored scalar contribution to

Form factor in

- Colored scalar particles present in
- the MSSM, (squarks).
- Try to make a (as much as possible)
- model independent analysis

QCD Corrections

Aglietti, Bonciani, Vicini, G.D. (06)

- and are unrelated: different renormalizations
- are possible.
- An analytic result, following the same steps as for
- the L.F. contributions, can be derived.
- Analytic result expressed in terms of HPL
- thresholds at

QCD Corrections

renormalized O.S., renormalized

Similar analysis by Anastasiou et al. (06)

Numerical check against Muehlleitner, Spira (06)

The Manohar-Wise Model

Manohar, Wise. (06)

- Scalar sector of the SM augmented with a (8,2)1/2
- scalar multiplet.
- (1,2)1/2, (8,2)1/2 are the only representations which have
- couplings to quarks with natural flavor conservation
- Fields:
- Scalar Potential :
- Spectrum: Couplings:

Corrections to

- Colored scalars can change up to 25% the SM result
- QCD corrections to the scalar contribution are about
- 10%

Conclusions

- Theoretical predictions for the Higgs boson at
- LHC are in good shape.
- QCD corrections are known at the NNLO level.
- The theoretical error is at the level of 10%.
- EW corrections start to be important. We have it for:

Bredenstein, Denner, Dittmaier, Weber (06)

Ciccolini, Denner, Dittmaier (07)

- are affected by NP. We must be
- prepared for any kind of NP that can modify the
- gluon-fusion Higgs production cross section or
- the decays in two photons.