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:1007.3465 in collaboration with P. Slavich

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

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

Gluon fusion Higgs production in the SM LO 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. 60-70% ) Djouadi et al. (91-95), Dawson (91), QCD corrections NNLO corrections to production rate (NLO X-sect. 15-20% ) 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)

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

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

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

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

@ 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)

@ NLO in the MSSM virtual real

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

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

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

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

A numerical example (I): Higgs masses and mixing

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

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

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