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

To be prepared for ANY kind of new physics LHC Warning THIS IS NOT A TALK ON ILC PHYSICS 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

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

NP of non decoupling type Two radiative parameters: 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

SM Higgs decays (BR) dominant huge QCD background small BR exp. clean

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) 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

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

QCD Corrections and are unrelated: different renormalizations 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 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.