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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. Summary. The nineties legacy: a light Higgs.
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Precisepredictionsfor 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
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
The LEP legacy SM Higgs: HZZ coupling = gMZ l with l = 1/cw
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 (c2/d.of. =18.6/13) it will improve if hadronic asymmetries are excluded pushed down, (depend on )
) ( Most sensitive observable , To increase the fitted : (smaller ) Is an heavy Higgs ruled out? NO,but we need new physics of a particular kind that can compensate for the heavy Higgs
SM as an effective theory: linear realization of SU(2)xU(1) Buchmuller, Wyler (86); Hall, Kolda (99); Barbieri, Strumia (99); Han, Skiba (04) dimension 6 that can relax the Higgs bound: The other dimension 6 operators should be suppressed! WHY?
cutoff is (TeV) only if K <0 No Higgs scenario: non linear realization of SU(2)xU(1) Kniehl, Sirlin (99); Bagger, Falk, Swartz (99) Theory is not renormalizable; cutoff It is not easy to find models that give K<0
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. What we learnt from the nineties
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. Å
Higgs sector of the MSSM Two SU(2)xU(1) doublets: Higgs potential: responsible for EWSB
Tree-level mass matrix for the CP-even sector: exploiting the minimization condition for can be expressed in terms of Spectrum: five physical states. neutral CP-even neutral CP-odd charged decoupling limit: ;
Radiative corrections to the MSSM Higgs sector ruled out by LEP! Quantum corrections push above . = effective potential approximation = external momentum contributions solutions of
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 b scenario: Okada, Yamaguchi, Yanagida (91); Ellis, Ridolfi, Zwirner (91); Haber, Hempfling (91); Chankowski et al. (92); Brignole (92)......... completely known
band: 1s error on and . tan b= 50 tan b=1.5 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).... (courtesy of A. Romanino)
same accuracy for the minimization condition Dedes, Slavich (03); Dedes, Slavich, GD (03) Beyond one-loop: MSSM ; Two-loop: mixing can be important. Full calculation is relevant. : dominant contributions known (strong and Yukawa corrections to the one-loop top/bottom term). , , , Heinemeyer, Hollik, Weiglein (98); Espinosa, Zhang (00); Slavich, Zwirner, GD (01) Espinosa, Zhang (00); Brignole, Slavich, Zwirner, GD (02) Dedes, Slavich, GD (03) Brignole, Slavich, Zwirner, GD (02); Heinemeyer, Hollik, Rzehak, Weiglein (05) • Important issues: • scheme-dependence of the input parameters; • , large tan b corrections.
Effect of the two-loop corrections Top Bottom
Bottom corrections should be treated with same care in the OS scheme because of large tan b effects. Same renormalization condition of the top-stop sector gives a counterterm contribution that blows up for large tan b from Heinemeyer, Hollik, Rzehak, Weiglein EPJC 39 (2005) 465
Several public computer codes that include all dominant two-loop corrections. Codes employ input parameters defined in different renormalization scheme (OS, ) • OS • FeynHiggs 2.2 (Heinemeyer, Hollik, Weiglein, Hahn) • 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) DR Scale and scheme dependence estimate of higher order effects Estimate of higher order corrections
Scale dependence in DR fromAllanach et al. JHEP09 (2004) 044 8-10 GeV 1-3 GeV
Scheme dependence fromAllanach et al. JHEP09 (2004) 044
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
from Martin PRD71 (2005) 016012 from Martin PRD67 (2002) 095012 Momentum dependent effects Two-loop electroweak corrections
two-loop electroweak two-loop momentum-dependent leading three-loop corrections Martin’s results are not implemented in the 4 public computer codes.
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 fromAllanach et al. JHEP09 (2004) 044
Light Higgs decays Split SUSY: viable MSSM: residual
gg h largest and best known process Light Higgs production 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)
MSSM: possible negative interference between top and stops Djouadi (98) SUSY-QCD at NLO from Djouadi hep-ph-0503173 Harlander, Steinhauser (04) from Harlander, Steinhauser JHEP09 (2004) 066
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.