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
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Warning THIS IS NOT A TALK ON ILC PHYSICS
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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

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NP of non decoupling type
Extra Z
A heavy Higgs needs
Isosplitted particles
More difficult (light sleptons)
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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

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SM Higgs production at LHC
Gluon fusion
VBF
Associate production with
Associate production with W,Z
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SM Higgs decays (BR)
huge QCD background
small BR exp. clean
dominant
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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)
• NNLOsoftgluon 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
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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)

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Two-loop EW Corrections to
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Decay width
Amplitude
Lowest order
does not exist in BFG
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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 -gt 12 2l 4200 -gt 1700
• finite

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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
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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
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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)

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Light fermion Contributions
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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
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Cancellation between EW and QCD
contributions Similar results obtained via a
fully numerical approach Passarino, Sturm,
Uccirati (07)
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Two-loop EW Corrections to
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• 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.
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Colored scalar contribution to
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• Colored scalar particles present in
• the MSSM, (squarks).
• Try to make a (as much as possible)
• model independent analysis

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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

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QCD Corrections
renormalized O.S., renormalized
Similar analysis by Anastasiou et al.
(06) Numerical check against Muehlleitner, Spira
(06)
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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

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

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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.