1. 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

2. 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

3. 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

4. NP of non decoupling type
Two radiative parameters:
Extra Z
A heavy Higgs
needs:
Isosplitted particles
More difficult
(light sleptons)

5. 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

6. SM Higgs production at LHC
Gluon
fusion
VBF
Associate
production
with
Associate
production
with W,Z

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

8. Gluon fusion Higgs production in the SM
LO completely known
Georgi, Glashow, Machacek, Nanopoulos (78)
QCD Corrections
NLO completely known (LO Xsect % )
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

9. 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)

10. Two-loop EW Corrections to

11. Decay width:
Amplitude:
Lowest order:
does not exist in BFG

12. 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: > 1700
finite

13. 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

14. 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

15. 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)

16. Light fermion Contributions

17. 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

18. Corrections to Cancellation between EW and QCD contributions
Similar results obtained via a fully numerical approach
Passarino, Sturm, Uccirati (07)

19. Two-loop EW Corrections to

20. 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.

21. Colored scalar contribution to

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

23. 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

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

25. 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:

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

27. 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.