We analyze the impact of the recent Feynman-diagrammatic (FD) two-loop
results for the mass of the lightest CP-even Higgs boson in the MSSM on the
theoretical upper bound for mh as a function of tan(beta). The results are
compared with previous results obtained by renormalization group (RG) methods.
The incorporation of dominant FD two-loop corrections into the decay width
\Gamma(h -> f \bar f) is also discussed.Comment: 4 pages, 2 figures, presented by G. Weiglein at the ``International
  Europhysics Conference on High Energy Physics'', Tampere, July 199

Heinemeyer, S.

Hollik, W.

Weiglein, G.

English

arXiv

We analyze the impact of the recent Feynman-diagrammatic (FD) two-loop results for the mass of the lightest CP-even Higgs boson in the MSSM on the theoretical upper bound for mh as a function of tan(beta). The results are compared with previous results obtained by renormalization group (RG) methods. The incorporation of dominant FD two-loop corrections into the decay widthWe analyze the impact of the recent Feynman-diagrammatic (FD) two-loop results for the mass of the lightest CP-even Higgs boson in the MSSM on the theoretical upper bound for mh as a function of tan(beta). The results are compared with previous results obtained by renormalization group (RG) methods. The incorporation of dominant FD two-loop corrections into the decay width \Gamma(h -> f \bar f) is also discussed

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arXiv:hep-ph/9912263v1  7 Dec 1999CERN–TH/99–367DESY 99–183KA–TP–23–1999hep-ph/9912263Higher-order results in the Higgs sectorof the MSSM ‡S. Heinemeyer1 §, W. Hollik 2‖and G. Weiglein 3¶1 DESY Theorie, Notkestr. 85, D–22603 Hamburg, Germany2 Institut fu¨r theoretische Physik, Universita¨t Karlsruhe, D–76128 Karlsruhe, Germany3 CERN, TH Division, CH–1211 Geneva 23, SwitzerlandAbstractWe analyze the impact of the recent Feynman-diagrammatic (FD) two-loop results for the mass of thelightest CP-even Higgs boson in the MSSM on the theoretical upper bound for mh as a function of tanβ.The results are compared with previous results obtained by renormalization group (RG) methods. Theincorporation of dominant FD two-loop corrections into the decay width Γ(h→ f f¯) is also discussed.‡ Presented by G. Weiglein at the “International Europhysics Conference on High Energy Physics”, Tampere, July 1999.§ email: Sven.Heinemeyer@desy.de‖ email: Wolfgang.Hollik@physik.uni-karlsruhe.de¶ email: Georg.Weiglein@cern.chHigher-order results in the Higgs sector ofthe MSSMS. Heinemeyer1, W. Hollik2 and G. Weiglein31 DESY Theorie, Notkestr. 85, D–22603 Hamburg, Germany2 Institut fu¨r theoretische Physik, Universita¨t Karlsruhe, D–76128 Karlsruhe, Germany3 CERN, TH Division, CH–1211 Geneva 23, SwitzerlandE-mails: Sven.Heinemeyer@desy.de, Wolfgang.Hollik@physik.uni-karlsruhe.de,Georg.Weiglein@cern.chAbstractWe analyze the impact of the recent Feynman-diagrammatic (FD) two-loop resultsfor the mass of the lightest CP-even Higgs boson in the MSSM on the theoreticalupper bound for mh as a function of tanβ. The results are compared with previousresults obtained by renormalization group (RG) methods. The incorporation ofdominant FD two-loop corrections into the decay width Γ(h→ f f¯) is also discussed.1. IntroductionThe lightest CP-even Higgs boson in the MinimalSupersymmetric Standard Model (MSSM) is ofparticular interest, since it is bounded to be lighterthan the Z boson at the tree level. The one-loopresults [1–3] for its mass, mh, have in the last yearsbeen extended by the leading two-loop corrections,performed in the renormalization group (RG)approach [4], in the effective potential approach [5]and most recently in the Feynman-diagrammatic(FD) approach [6]. These calculations predict anupper bound on mh of about mh <∼ 135 GeV.A precise prediction for the mass of the lightestCP-even Higgs boson as well as for the cross sectionsof its production and decay processes is importantfor the Higgs-boson search at LEP2, the upgradedTevatron and the LHC. If the lightest CP-evenHiggs boson will be found at the present or the nextgeneration of colliders, its mass will be determinedwith a high precision, allowing thus a sensitive testof the model.The dominant radiative corrections to mh arisefrom the top and scalar top sector of the MSSM,with the input parameters mt, MSUSY and Xt. Forsimplicity, the soft SUSY breaking parameters inthe diagonal entries of the scalar top mixing matrixare often assumed to be equal, MSUSY = Mt˜L =Mt˜R . The off-diagonal entry of the mixing matrixin our conventions (see Ref. [6]) reads mtXt =mt(At − µ cotβ).Up to now most phenomenological analyseshave been based on the results obtained withinthe RG approach [4], where the neutral CP-evenHiggs-boson masses are calculated from the effectivecouplings in the Higgs potential. The resultscontain the leading logarithmic contributions at thetwo-loop level.In the FD approach, on the other hand, themasses of the CP-even Higgs bosons are obtainedby evaluating loop corrections to the h, H andhH-mixing propagators and by determining thepoles of the corresponding propagator matrix. InRef. [6] the dominant two-loop contributions to themasses of the CP-even Higgs bosons of O(ααs)have been evaluated in the on-shell renormalizationscheme. They have been combined with thecomplete one-loop on-shell result [3] and the sub-dominant two-loop corrections ofO(G2µm6t ) [4]. Thecorresponding results have been implemented intothe Fortran code FeynHiggs [7].In Ref. [8] the dominant contributions have beenextracted from the full FD result. Taking intoaccount the fact that the FD and the RG resulthave been obtained within different renormalizationschemes and transforming the FD result of Ref. [8]into the MS scheme, it has been shown that theRG and the FD approach agree in the leadinglogarithmic terms at the two-loop level [9]. The FDresult, however, contains further genuine two-loopterms of non-logarithmic nature that go beyond theRG result. These genuine two-loop terms lead toan increase of the maximal value of mh comparedto the RG result of up to 5 GeV [9,10].22. Implications for tanβ exclusion limitsBy combining the theoretical result for the upperbound on mh as a function of tanβ in the MSSMwith the informations from the direct search forthe lightest Higgs boson, it is possible to deriveconstraints on tanβ. Since the predicted value ofmh depends sensitively on the precise numericalvalue of mt, it has become customary to discuss theconstraints on tanβ within a so-called “benchmark”scenario, in which mt is kept fixed at the valuemt = 175 GeV and in which furthermore a largevalue of MSUSY is chosen, MSUSY = 1 TeV, givingrise to large values of mh(tanβ).In Ref. [11] it has recently been analyzed howthe values chosen for the other SUSY parameters inthe benchmark scenario (see Ref. [12] and referencestherein) should be modified in order to obtain themaximal values of mh(tanβ) for given mt andMSUSY. The maximal values for mh as a functionof tanβ within this scenario (mmaxh scenario) arehigher by about 5 GeV than in the usual benchmarkscenario. The constraints on tanβ derived withinthe mmaxh scenario are thus more conservative thanthe ones based on the previous benchmark scenario.The mmaxh scenario is defined as [11, 13]mt = mexpt (= 174.3 GeV), MSUSY = 1 TeVµ = −200 GeV, M2 = 200 GeV, MA ≤ 1000 GeVXt = 2MSUSY (FD calculation)Xt =√6MSUSY (RG calculation)mg˜ = 0.8MSUSY (FD calculation), (1)where the parameters are chosen such that thechargino masses are beyond the reach of LEP2. Ineq. (1) µ is the Higgs mixing parameter,M2 denotesthe soft SUSY breaking parameter in the gauginosector, and MA is the CP-odd Higgs-boson mass.Different values of Xt are specified in eq. (1) forthe results of the FD and the RG calculation, sincewithin the two approaches the maximal values formh are obtained for different values of Xt. Thisfact is partly due to the different renormalizationschemes used in the two approaches, i.e. theparameter Xt in the MS scheme is shifted withrespect to the corresponding parameter in the on-shell scheme [9, 10]. In FeynHiggs the gluino mass,mg˜, can be specified as a free input parameter. Theeffect of varying mg˜ on mh is up to ±2 GeV [6].Within the RG result [4] used so far for the analysisof the benchmark scenario, mg˜ is fixed to mg˜ =MSUSY. The corresponding values of mh are about0.5 GeV lower than the maximal values (obtainedfor mg˜ ≈ 0.8MSUSY).While so far we have only been concerned withthe definition of an appropriate scenario, we now80 90 100 110 120 130mh [GeV]110tanβbenchmark (RG)mhmax (RG)mhmax (FD)MSUSY = 1000 GeV, mt = 174.3 GeVFigure 1. mh is shown as a function of tanβ.The dashed curve displays the RG result within thebenchmark scenario, while the dotted curve shows theRG result for the mmaxh scenario (program subhpole).The solid curve corresponds to the FD result in themmaxh scenario (program FeynHiggs).turn to the impact of the new FD two-loop resultfor mh, which contains previously unknown non-logarithmic two-loop terms. Comparing the FDresult (program FeynHiggs) with the RG result(program subhpole, based on the second and thirdreference of [4]) we find that the maximal value formh within the FD result is higher by up to 4 GeV.In Fig. 1 we show both the effect of modifyingthe previous benchmark scenario to the mmaxhscenario and the impact of the new FD two-loopresult on the prediction for mh. The Higgs-bosonmass is plotted as a function of tanβ. The dashedcurve displays the previous benchmark scenario,while the dotted curve shows the mmaxh scenario.Both curves are based on the RG result (programsubhpole). The full curve corresponds to the FDresult (program FeynHiggs) in the mmaxh scenario.The increase in the maximal value for mh byabout 4 GeV from the new FD result and byfurther 5 GeV if the benchmark scenario is replacedby the mmaxh scenario has a significant effect onexclusion limits for tanβ derived from the Higgs-boson search. Using the FD result for the mmaxhscenario, an excluded tanβ region appears only foran experimental bound on mh of roughly 100 GeV,while in the previous benchmark definition valuesup to tanβ = 2 would already be excluded for aHiggs limit of about 100 GeV.The constraints on tanβ discussed above areof course only valid under the specific assumptionsmade in the considered scenario. In particular,3increasing mt by one or even two standarddeviations above the current experimental centralvalue leads to a significant increase in the maximalvalue ofmh(tanβ); increasingmt by 1 GeV roughlytranslates into an upward shift of mmaxh of 1 GeV.3. O(ααs) Yukawa contributions to the decaywidth Γ(h→ f f¯)As an extension of the FD two-loop results for theneutral CP-even Higgs-boson masses, we considernow the leading two-loop Yukawa corrections ofO(Gµαsm4t/M2W) to the decay width Γ(h → f f¯).These contributions enter the decay amplitudeA(h→ f f¯) in the following way,A(h→ f f¯) =√Zh(Γh + ZhHΓH). (2)Γh, ΓH are the hff¯ and Hff¯ vertex functions, andZh =11 + Σˆ′h(q2)−(Σˆ2hH(q2)q2−m2H,(0)+ΣˆH(q2))′∣∣∣∣∣q2=m2h,ZhH = − ΣˆhH(m2h)m2h −m2H,(0) + ΣˆH(m2h). (3)Here Σˆh(q2), ΣˆhH(q2), ΣˆH(q2) denote the real partsof the renormalized Higgs-boson self-energies andmH,(0) is the tree-level mass of the heavier CP-evenHiggs boson.In Fig. 2 the results for the decay width Γ(h→bb¯) including the two-loop propagator correctionsaccording to eqs. (2)–(3) are compared with thecorresponding one-loop result for the cases of nomixing and maximal mixing in the scalar topsector. In both results the one-loop QED and QCD(gluon and gluino exchange) vertex corrections areincluded. The effect of the two-loop contributionsis seen to be sizable. Since the branching ratioBR(h → bb¯) is in general strongly dominated byΓ(h → bb¯), the correction to a large extent cancelsout in the branching ratio. A comparison of ourFD results with the corresponding results obtainedwithin the RG approach is given in Ref. [14].References[1] H. Haber and R. Hempfling, Phys. Rev. Lett.66 (1991) 1815; J. Ellis, G. Ridolfi andF. Zwirner, Phys. Lett. B 257 (1991) 83; Phys.Lett. B 262 (1991) 477.[2] P. Chankowski, S. Pokorski and J. Rosiek,Nucl. Phys. B 423 (1994) 437; J. Bagger,K. Matchev, D. Pierce and R. Zhang, Nucl.Phys. B 491 (1997) 3.40 50 60 70 80 90 100 110 120 130 140mh [GeV]0.0000.0050.0100.0150.0200.025Γ(h → bb− ) [GeV]MSUSY = 1000 GeV, tanβ = 3one loop, no mixingtwo loop, no mixingone loop, max. mixingtwo loop, max. mixingFigure 2. The results for Γ(h → bb¯) containingthe Higgs propagator corrections at one- and two-looporder are shown as a function of mh. The resultsare given in the no-mixing and maximal-mixing casefor µ = −100 GeV, M2 = MSUSY, mg˜ = 500 GeV,Ab = At.[3] A. Dabelstein, Nucl. Phys. B 456 (1995) 25;Z. Phys. C 67 (1995) 495.[4] J. Casas, J. Espinosa, M. Quiro´s andA. Riotto, Nucl. Phys. B 436 (1995) 3, E: ibid.B 439 (1995) 466; M. Carena, J. Espinosa,M. Quiro´s and C. Wagner, Phys. 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Higher-order results in the Higgs sector of the MSSM

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