1. NLO-QCD bottom corrections to Higgs boson production in the MSSM
Giuseppe Degrassi
Università di Roma Tre, I.N.F.N. Sezione di Roma Tre
SUSY 2010
Bonn, 23rd-28th August 2010
based on: arXiv: in collaboration with P. Slavich

2. Outline
Status of the gluon fusion production cross section in the SM and
in the MSSM
Effective approximation
NLO-QCD bottom correction to in the MSSM
Conclusions

3. Higgs production at LHC
VBF
Ass. with
Ass. with W,Z

4. Gluon fusion Higgs production in the SMLO
Georgi, Glashow, Machacek, Nanopoulos (78)
QCD corrections exact
NLO corrections at large
Ellis et al.(88), Baur, Glover (90)
NLO corrections to production rate
(LO X-sect % )
Djouadi et al. (91-95), Dawson (91),
QCD corrections
NNLO corrections to production rate (NLO X-sect % )
Harlander, Kilgore (01-02), Catani, de Florian, Grazzini (01), Anastasiou, Melnikov (02),
Ravindran, Smith, van Neerven (03), Harlander, Ozeren (09), Pak, Rogal Steinhauser (09),
Marzani et al. (08)
NNLO corrections +softgluon NNLL resummation (NNLO X-sect. 6-15% )
Catani, de Florian, Grazzini, Nason (03), Moch, Vogt (05)
Higher order and rapidity distributions
de Florian, Grazzini, Kunszt (99), Del Duca et al. (01), Bozzi, Catani, de Florian, Grazzini (03-07), Anastasiou, Dixon, Melnikov (03), Anastasiou, Melnikov, Petriello (03), Catani, Grazzini (07)
Electroweak corrections exact
NLO Light fermion + top (NNLO QCD X-sect. 5% )
Aglietti, Bonciani, Vicini, G.D. (04), F.. Maltoni, G.D. (04), Actis, Passarino, Sturm, Uccirati (07-08)

5. Form factor for coupling:
Coefficient function:
LO:
NLO:

6. Effective approximation
Kraemer, Laenen, Spira (98)
evaluated via E.T. or L.E.T.
exact

7. The effective approximation does not work fine when the bottom
contribution becomes important

8. in the MSSM Higgs sector:
Higgs coupling to gluons mediated by quarks and squarks
partonic X-sect.:
related to the structure of the Higgs-(s)quark-(s)quark couplings
Yukawa
D-term

9. @ NLO in the MSSM Dawson, Djouadi, Spira (96)
Gluon-squark virtual & real contribution in the vanishing Higgs-mass limit (VHML)
Dawson, Djouadi, Spira (96)
Gluon-squark virtual & real contribution complete (analytic)
Anastasiou, Beerli, Bucherer, Daleo, Kunszt (07), Aglietti, Bonciani, Vicini, G.D. (07)
Muehlleitner, Spira (07), Bonciani, Vicini, G.D. (07)
Gluino-top-stop virtual contribution in the VHML (not applicable to the bottom case)
evalcsusy.f: Harlander, Steinhauser (03-04);
explict analytic: Slavich, G.D. (08)
Gluino-quark-squark virtual contribution complete
semianalytic, not yet available to the public as computer code
Anastasiou, Beerli,Daleo (08)
see also talk by H. Rzehak at this conference
Gluino-bottom-sbottom contribution can be evaluated analytically via an asymptotic expansion in the large supersummetric masses obtaining a
@ NLO at the level of the effective approximation
Slavich, G.D. (10)

10. @ NLO in the MSSM
virtual
real

11. Classifying the contributions
Controlled by the Higgs-bottom coupling
Controlled by the Higgs-sbottom coupling
at the tree level by SUSY but they may differ at the 1-loop level.
In the sbottom sector we also need renormalization prescriptions for

12. Two-loop contributions controlled by the Higgs-bottom coupling
-scheme with parameters renormalized at the scale
red gluon, blue gluino
SUSY contribution to the bottom self-energy

13. Large two-loop corrections depend on the choice of renormalization prescriptions
for the bottom mass and Yukawa coupling
Large Terms
scheme
YES
YES
On-shell scheme
YES No
Mixed scheme No
YES

14. Two-loop contributions controlled by the Higgs-sbottom coupling
Typically smallish, as they do not contain enhanced terms
However, large terms might still be induced by an unwise choice of OS
renormalization conditions for the parameters in the sbottom sector
Typical scheme for the top: OS definition for and treat
as a derived quantity through
Doing the same for the bottom sector would result in huge counterterm
contributions (also the Higgs mass matrix):
Alternative OS scheme for the sbottom sector:
OS defintion for and treat
as a derived quantity
Brignole, Slavich, Zwirner, G.D. (02)
is connected to the proper vertex of the interaction and
is NOT enhanced

15. A numerical example (I): Higgs masses and mixing

16. A numerical example (II): size of two-loop contributions for h

17. A numerical example (III): size of two-loop contributions for H

18. Summary
Analytic results for the NLO bottom contribution to light-Higgs production
in the MSSM are avaliable.
These results can be easily implemented in computer code
(e.g. FeynHiggs).
The bottom contribution is usually dominated by the from
diagrams controlled by the Higgs-bottom coupling.
The contributions controlled by the Higgs-sbottom couplings are usually
small if the OS renormalization prescription is chosen wisely.
Finally, when the contributions controlled by the Higgs-sbottom couplings
are small there is a simple recipe in order to absorb the bulk of the
2-loop contribution in the 1-loop part:
is the HRS term