1. Precise predictions for a light Higgs Giuseppe Degrassi Università di Roma Tre I.N.F.N. Sezione di Roma III SUSY 2005 The Millennium Window to Particle Physics Durham 18-23 July 2005

2. Summary The nineties legacy: a light Higgs. How solid is the evidence for a light Higgs? Recent SUSY results for a light Higgs on: Mass determination Production Conclusions

3. The LEP legacy SM Higgs: HZZ coupling = gM Z with = 1/c w

4. A strong hint for a light Higgs 60%

5. Swinging top Tevatron: Run I Run I Run I-II (prel. 99) (fin. 04) (prel. 05) Light Higgs indication reenforced: 95% C.L. 285 210 GeV Old considerations are back SM fit is OK (  2  d.of. =18.6/13) it will improve if hadronic asymmetries are excluded pushed down, (depend on )

6. NO, but we need new physics of a particular kind that can compensate for the heavy Higgs Is an heavy Higgs ruled out? To increase the fitted : (smaller ) Most sensitive observable, ( )

7. Buchmuller, Wyler (86); Hall, Kolda (99); Barbieri, Strumia (99); Han, Skiba (04) dimension 6 that can relax the Higgs bound: SM as an effective theory: linear realization of SU(2)xU(1) The other dimension 6 operators should be suppressed! WHY?

8. No Higgs scenario: non linear realization of SU(2)xU(1) Kniehl, Sirlin (99); Bagger, Falk, Swartz (99) Theory is not renormalizable; cutoff cutoff is (TeV) only if K <0 It is not easy to find models that give K<0

9. What we learnt from the nineties Mechanism of EWSB with a light Higgs are clearly favored. The success of the SM fit places strong constraint on new physics. New physics of the decoupling type ( ) avoids “naturally” ( ) the SM fit constraints (SMFC). Non decoupling physics can exist, i.e. effects that do not vanish as. However it needs same “conspiracy” to pass the SMFC.

10. Supersymmetry Is a NP of the decoupling type. No problem with the SMFC. Predicts the quartic Higgs coupling. A light Higgs must be in the spectrum.  Favors the gauge coupling unification. Has a dark matter candidate. It has to be broken. 

11. Higgs sector of the MSSM Two SU(2)xU(1) doublets: Higgs potential: responsible for EWSB

12. Spectrum: five physical states. neutral CP-even neutral CP-odd charged Tree-level mass matrix for the CP-even sector: exploiting the minimization condition for can be expressed in terms of decoupling limit: ;

13. Radiative corrections to the MSSM Higgs sector ruled out by LEP! Quantum corrections push above. = effective potential approximation = external momentum contributions solutions of

14. SUSY breaking  incomplete cancellation between loop of particle and susy partners. Main effect: top and stop loops One-loop corrections to : scale as ; depend upon have a logarithmic sensitivity to the stop masses. Large tan  scenario: completely known Okada, Yamaguchi, Yanagida (91); Ellis, Ridolfi, Zwirner (91); Haber, Hempfling (91); Chankowski et al. (92); Brignole (92).........

15. Beyond one-loop: Split SUSY Around TEV spectrum: SM + gauginos + higgsinos. Sfermions are very heavy. Mixing is unimportant No bottom corrections. The logarithmic correction is very large. It has to be resummed via Split-RGE. Gauge effects can be relevant. Barbieri, Frigeni, Caravaglios (91); Okada, Yamaguchi, Yanagida (91) ; Carena et al. (95-96, SubHPole).... band: 1  error on and. tan  = 50 tan  =1.5 (courtesy of A. Romanino)

16. Beyond one-loop: MSSM : dominant contributions known (strong and Yukawa corrections to the one-loop top/bottom term). Two-loop: mixing can be important. Full calculation is relevant. ; Dedes, Slavich, GD (03) same accuracy for the minimization condition Dedes, Slavich (03); Dedes, Slavich, GD (03) Important issues: scheme-dependence of the input parameters;, large tan  corrections.,,, Heinemeyer, Hollik, Weiglein (98); Espinosa, Zhang (00); Slavich, Zwirner, GD (01) Espinosa, Zhang (00); Brignole, Slavich, Zwirner, GD (02) Brignole, Slavich, Zwirner, GD (02); Heinemeyer, Hollik, Rzehak, Weiglein (05)

17. Effect of the two-loop corrections Top Bottom

18. Bottom corrections should be treated with same care in the OS scheme because of large tan  effects. Same renormalization condition of the top-stop sector gives a counterterm contribution that blows up for large tan  from Heinemeyer, Hollik, Rzehak, Weiglein EPJC 39 (2005) 465

19. Several public computer codes that include all dominant two-loop corrections. Codes employ input parameters defined in different renormalization scheme (OS, ) DR Estimate of higher order corrections OS FeynHiggs 2.2 DR (possibility of input parameters via RG evolution from a set of high-energy boundary conditions) SoftSusy 1.9 (Allanach) SPheno 2.2 (Porod) Suspect 2.3 (Djoudi, Kneur, Moultaka) (Heinemeyer, Hollik, Weiglein, Hahn) Scale and scheme dependence estimate of higher order effects

20. Scale dependence in DR 8-10 GeV 1-3 GeV from Allanach et al. JHEP09 (2004) 044

21. Scheme dependence from Allanach et al. JHEP09 (2004) 044

22. Towards a complete two-loop calculation The presently available public codes do not include: electroweak contributions in Recent progress: (S.P. Martin (02-05)) complete two-loop (Landau gauge, DR scheme) complete two-loop Strong and Yukawa corrections in

23. Two-loop electroweak corrections from Martin PRD67 (2002) 095012 from Martin PRD71 (2005) 016012 Momentum dependent effects

24. Martin’s results are not implemented in the 4 public computer codes. two-loop electroweak two-loop momentum-dependent leading three-loop corrections

25. Bound on Bound depends on and on the chosen range of the SUSY parameter. Fix assuming relations among the parameters dictated by an underline theory of SUSY breaking (mSUGRA, GMSB, AMSB) scanning in a “reasonable” region of the parameter space from Allanach et al. JHEP09 (2004) 044

26. Light Higgs decays Split SUSY: viable MSSM: residual

27. Light Higgs production gg h largest and best known process SM: QCD at NNLO Djouadi, Graudens, Spiras, Zerwas (91-95); Harlander, Kilgore (01-02); Catani, de Florian, M. Grazzini (01) Anastasiou, Melnikov (02); Ravindran, Smith, van Neerven (03) EW at NLO Aglietti, Bonciani,Vicini, GD (04) Maltoni, GD (04)

28. MSSM: possible negative interference between top and stops Djouadi (98) from Djouadi hep-ph-0503173 SUSY-QCD at NLO from Harlander, Steinhauser JHEP09 (2004) 066 Harlander, Steinhauser (04)

29. Conclusions New value of the top mass strengthens the indication for a light Higgs (but a heavy Higgs is not ruled out, although it needs some “conspiracy” to survive) The determination of the mass of the light neutral Higgs in the MSSM has become very precise A Split SUSY Higgs can be detected via h W W* The gluon fusion production cross-section is now available at the NLO in the SUSY contribution.