The theoretical predictions in the MSSM for Higgs-boson production at a
future e^+e^- Linear Collider and Higgs-boson decay processes are discussed
focusing in particular on recent diagrammatic two-loop results in the MSSM
Higgs sector. The present status of the theoretical predictions is briefly
summarized, and it is emphasized that considerable improvements will be
necessary in order to match the high experimental accuracy achievable at a
future Linear Collider.Comment: 6 pages, 2 figures, to appear in the proceedings of LCWS 200

Heinemeyer, S.

Weiglein, G.

English

arXiv

The theoretical predictions in the MSSM for Higgs-boson production at a future $e^+e^−$ Linear Collider and Higgs-boson decay processes are discussed focusing in particular on recent diagrammatic two-loop results in the MSSM Higgs sector. The present status of the theoretical predictions is briefly summarized, and it is emphasized that considerable improvements will be necessary in order to match the high experimental accuracy achievable at a future Linear Collider

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Higgs production and decay in the MSSM: Status and perspectives

Sven Heinemeyer

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Higgs production and decay in the MSSM: status and perspectives

The theoretical predictions in the MSSM for Higgs-boson production at a future e^+e^- Linear Collider and Higgs-boson decay processes are discussed focusing in particular on recent diagrammatic two-loop results in the MSSM Higgs sector. The present status of the theoretical predictions is briefly summarized, and it is emphasized that considerable improvements will be necessary in order to match the high experimental accuracy achievable at a future Linear Collider.The theoretical predictions in the MSSM for Higgs-boson production at a future e^+e^- Linear Collider and Higgs-boson decay processes are discussed focusing in particular on recent diagrammatic two-loop results in the MSSM Higgs sector. The present status of the theoretical predictions is briefly summarized, and it is emphasized that considerable improvements will be necessary in order to match the high experimental accuracy achievable at a future Linear Collider.The theoretical predictions in the MSSM for Higgs-boson production at a future e^+e^- Linear Collider and Higgs-boson decay processes are discussed focusing in particular on recent diagrammatic two-loop results in the MSSM Higgs sector. The present status of the theoretical predictions is briefly summarized, and it is emphasized that considerable improvements will be necessary in order to match the high experimental accuracy achievable at a future Linear Collider.The theoretical predictions in the MSSM for Higgs-boson production at a future e^+e^- Linear Collider and Higgs-boson decay processes are discussed focusing in particular on recent diagrammatic two-loop results in the MSSM Higgs sector. The present status of the theoretical predictions is briefly summarized, and it is emphasized that considerable improvements will be necessary in order to match the high experimental accuracy achievable at a future Linear Collider.The theoretical predictions in the MSSM for Higgs-boson production at a future e+e− Linear Collider and Higgs-boson decay processes are discussed focusing in particular on recent diagrammatic two-loop results in the MSSM Higgs sector. The present status of the theoretical predictions is briefly summarized, and it is emphasized that considerable improvements will be necessary in order to match the high experimental accuracy achievable at a future Linear Collider

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arXiv:hep-ph/0102117v1  9 Feb 2001BNL–HET–01/5CERN–TH/2001-037hep-ph/0102117Higgs Production and Decay in the MSSM:Status and PerspectivesS. Heinemeyer1 ∗ and G. Weiglein2 †1 HET, Brookhaven Natl. Lab., Upton, New York 11973, USA2 CERN, TH Division, CH-1211 Geneva 23, SwitzerlandAbstract. The theoretical predictions in the MSSM for Higgs-boson production at afuture e+e− Linear Collider and Higgs-boson decay processes are discussed focusingin particular on recent diagrammatic two-loop results in the MSSM Higgs sector. Thepresent status of the theoretical predictions is briefly summarized, and it is empha-sized that considerable improvements will be necessary in order to match the highexperimental accuracy achievable at a future Linear Collider.∗) email: Sven.Heinemeyer@bnl.gov†) email: Georg.Weiglein@cern.chHiggs production and decay in theMSSM: status and perspectivesSven Heinemeyer∗ and Georg Weiglein†∗HET, Brookhaven Natl. Lab., Upton, New York 11973, USA†CERN, TH Division, CH-1211 Geneva 23, SwitzerlandAbstract. The theoretical predictions in the MSSM for Higgs-boson production at afuture e+e− Linear Collider and Higgs-boson decay processes are discussed focusingin particular on recent diagrammatic two-loop results in the MSSM Higgs sector. Thepresent status of the theoretical predictions is briefly summarized, and it is empha-sized that considerable improvements will be necessary in order to match the highexperimental accuracy achievable at a future Linear Collider.I INTRODUCTIONExploring the Higgs sector of the electroweak theory with high precision willbe one of the main goals of a future e+e− Linear Collider (LC). It will allow ahighly sensitive test of the investigated theory and will thus provide a way fordistinguishing between different models.A firm prediction of the Minimal Supersymmetric Standard Model (MSSM) isthe existence of a light neutral Higgs boson. The Higgs sector of the MSSM con-sists of two doublets and besides the gauge couplings is described by two param-eters, conventionally chosen as the ratio of the two vacuum expectation values,tan β = v2/v1, and the mass of the CP-odd Higgs boson, MA. The masses of theother Higgs bosons and the mixing angle in the neutral Higgs sector are predictedin terms of these parameters, giving rise to the well-known result that the massof the lightest CP-even Higgs boson, mh, in the MSSM has to be smaller thanthe Z-boson mass at lowest order. This bound, however, receives large radiativecorrections [1], in particular from the Yukawa sector of the theory, which shift thebound to mh <∼ 135 GeV including two-loop corrections [2].The prospective experimental accuracies at a future Linear Collider in the energyrange 500 GeV – 1 TeV will make it necessary to reduce the theoretical uncertaintiesof the predictions for the Higgs production cross sections and branching ratios belowthe level of 1%. This goal will be very difficult to achieve, owing to the fact thatthere exist several different sources for sizable higher-order corrections and for largetheoretical uncertainties.As mentioned above, large Yukawa corrections affect the predictions for theHiggs-boson masses and the mixing angle α. The leading terms at one- and two-loop order are of O(Gµm4t/M2W) and O(Gµαsm4t/M2W), respectively. Besides thesecorrections, which originate from the t–t˜ sector of the MSSM, for large values oftan β and the Higgs mixing parameter µ also large corrections in the b–b˜ sectorare possible, which in some regions of the parameter space can even invalidate aperturbative treatment. Corrections from the scalar quarks of the third generationcan also be a source for large loop-induced effects in the Higgs sector connected tocomplex phases. Concerning theoretical uncertainties related to large loop correc-tions, in the energy range of a LC genuine vertex and box corrections in general giverise to much bigger effects than at LEP energies, where often the bulk of the weakand QCD corrections originates from universal propagator-type contributions.In the parameter regions where the widths of the MSSM Higgs bosons are large,an accurate treatment of the Higgs-boson production furthermore requires to takeinto account off-shell effects, i.e. to study the full 2 → 4 process including non-resonant contributions.In addition to the above-mentioned effects, a different source of theoretical un-certainties is related to the experimental errors of the input parameters. Owing tothe large corrections from the t–t˜ sector, in particular an accurate measurement ofthe top-quark mass is crucial for precise theoretical predictions in the Higgs sectorof the MSSM.II THE CP-EVEN HIGGS-BOSON MASSES AND αeffThe prediction for the lightest CP-even Higgs-boson mass in the MSSM hasrecently been improved by the inclusion of non-logarithmic genuine two-loop con-tributions obtained via an explicit Feynman-diagrammatic (FD) calculation [2,3].These corrections gave rise to a numerically sizable shift compared to the resultspreviously obtained via a renormalization-group-improved one-loop Effective Po-tential approach (EPA) [4,5]. Recently further sub-leading two-loop electroweakcontributions have been obtained [6].The current theoretical uncertainty in mh from unknown higher-order contri-butions can conservatively be estimated as ∆mtheoh ≈ ±3 GeV. This uncertaintyis smaller than the one induced from the present experimental error on mt, as achange of ∆mt = ±5 GeV leads to a shift in mh of ∆mtheoh ≈ ±5 GeV [7]. Theseuncertainties have to be compared with the prospective accuracies at a future LCof ∆mexph = 0.05 GeV and ∆mexpt = 0.1–0.2 GeV.The theoretical uncertainties in the Higgs propagator corrections affect the pre-dictions for the Higgs production and decay processes via their effects on mh, mH,and on the effective mixing angle αeff in which the bulk of the Higgs propagatorcorrections to the Higgs couplings can be absorbed.The two-loop Higgs propagator corrections evaluated in Refs. [2,3] have recentlybeen incorporated into the diagrammatic one-loop result for the QED and QCDcontributions [8] to the decay processes h → f f¯ [9] and into the complete di-agrammatic one-loop result [10] for the production processes e+e− → hZ ande+e− → hA [11].III HIGGS DECAYS INTO SM FERMIONSThe predictions for the decays h → f f¯ in the MSSM are affected by two mainsources of large corrections which can give rise to large deviations of the MSSMpredictions compared to the SM case. The Higgs propagator corrections affect thecouplings to fermions in particular via large h–H mixing effects. As a consequence,the effective hff¯ coupling can be heavily suppressed in certain regions of the pa-rameter space [9,12,13]. This is shown in the left plot of Fig. 1, where BR(h→ bb¯)is given as a function of MA for MSUSY = Xt = 500 GeV and µ = −1 TeV (MSUSYis the squark mass scale and Xt is the off-diagonal entry in the t˜ mixing matrix, seeRef. [2]). The plot shows that for a given value of MA the theoretical predictionfor BR(h → bb¯) can change drastically if a part of the corrections is neglected.This is illustrated here by neglecting the two-loop contributions or the momentumdependence of the Higgs propagator corrections (the latter corresponds to the αeffapproximation). As a consequence, in these regions of parameter space an accuratetheoretical prediction is very difficult to achieve.100 110 120 130 140 150 160 170 180 190 200MA [GeV]10−210−1100BR( h −>  b b− )one loop, q2 =/ 0one loop, q2 = 0two loop, q2 =/ 0two loop, q2 = 00 200 400 600 800 1000m g ~ [GeV]0.050.100.15BR(h -> τ+τ- )MSUSY = 500 GeV, MA = 600 GeV, tanβ = 40Xt =  600 GeV, µ = -400 GeV, (mh ~ 115 GeV)Xt = -600 GeV, µ =  400 GeV, (mh ~ 115 GeV)SM, mH = 115 GeVFIGURE 1. Effects of large SUSY contributions on BR(h→ bb¯) (left plot) and BR(h→ τ+τ−)(right plot). The error bar at the SM prediction in the right plot indicates the prospectiveexperimental accuracy at a future LC.While the Higgs propagator corrections affect the Higgs couplings to all up-type fermions and to all down-type fermions in a universal way, these couplingscan be shifted relative to each other by large gluino and higgsino loop corrections.Corrections of this kind can occur for large values of tanβ and/or µ. They affect thetree-level relation between the fermion masses (in particular mb and mτ ) and theYukawa couplings [14]. A deviation in the ratio of the hbb¯ and the hτ+τ− couplingsfrom the SM value caused by large gluino corrections to Γ(h → bb¯) can give riseto a sizable shift in BR(h→ τ+τ−). A precise measurement of BR(h→ τ+τ−) ata future LC will thus provide a high sensitivity for a distinction between the SMand the MSSM even for relatively large values of MA, where otherwise the Higgssector behaves mainly SM-like. This is illustrated in the right plot of Fig. 1, whereBR(h → τ+τ−) in the MSSM is shown as a function of the gluino mass, mg˜, incomparison with the SM prediction and the prospective experimental accuracy ata future LC of about 5%.IV HIGGS PRODUCTION IN HIGGS-STRAHLUNGAND ASSOCIATED PRODUCTIONIn Fig. 2 the predictions for the production cross sections e+e− → hZ, hA basedon combining the complete diagrammatic one-loop result in the MSSM [10] withthe dominant two-loop Higgs-propagator corrections (evaluated with the programFeynHiggs [15]) are shown as a function of mh for√s = 500 GeV, MSUSY = 1 TeV,the slepton mass scale Ml˜ = 300 GeV, MA = 200 GeV and Xt/MSUSY = 2, i.e.maximal mixing in the scalar top sector. The result including the two-loop Higgs-propagator corrections is compared with the one-loop result, and the effect of theone-loop box contributions is shown separately. The FD result is furthermorecompared with an improved Born approximation, where only corrections to mhand αeff are taken into account, which are evaluated within the renormalization-group-improved one-loop EPA with the program subhpole (based on Refs. [4,16]).As can be seen in the figure, the inclusion of the two-loop contributions has avery large effect. The deviation between the full result and the improved Bornapproximation based on the renormalization-group-improved one-loop EPA is alsosignificant, exceeding 20% for σAh. The box contributions change the total crosssection by 5–10% at LC collider energies, and in general give even larger correctionsto the differential cross sections. For the prospective experimental accuracies at afuture LC these corrections thus need to be included in the theoretical predictions.REFERENCES1. H. Haber and R. Hempfling, Phys. Rev. Lett. 66 (1991) 1815;Y. Okada, M. Yamaguchi and T. Yanagida, Prog. Theor. Phys. 85 (1991) 1;J. Ellis, G. Ridolfi and F. Zwirner, Phys. Lett. B 257 (1991) 83; Phys. Lett. B 262(1991) 477; R. Barbieri and M. Frigeni, Phys. Lett. B 258 (1991) 395.2. S. Heinemeyer, W. Hollik and G. Weiglein, Eur. Phys. Jour. C 9 (1999) 343.3. S. Heinemeyer, W. Hollik and G. Weiglein, Phys. Rev. D 58 (1998) 091701; Phys.Lett. B 440 (1998) 296; Phys. Lett. B 455 (1999) 179.FIGURE 2. σZh and σAh as a function of mh at√s = 500 GeV for maximal mixing in thescalar top sector. The solid line represents the FD result consisting of the complete one-loopand the two-loop Higgs-propagator corrections. The dot-dashed line indicates the correspondingresult where the box contributions have been omitted, the dashed line shows the one-loop FDresult, and the dotted line represents an improved Born approximation evaluated within therenormalization-group-improved one-loop EPA.4. M. Carena, J. Espinosa, M. Quiro´s and C. Wagner, Phys. Lett. B 355 (1995) 209;M. Carena, M. Quiro´s and C. Wagner, Nucl. Phys. B 461 (1996) 407.5. H. Haber, R. 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Majerotto, Y. Yamada, Phys. Rev. D 62 (2000)055006; M. Carena, D. Garcia, U. Nierste, C. Wagner, Nucl. Phys. B 577 (2000) 88.15. S. Heinemeyer, W. Hollik and G. Weiglein, Comput. Phys. Commun. 124 (2000) 76;CERN-TH/2000-055, hep-ph/0002213.16. M. Carena, H. Haber, S. Heinemeyer, W. Hollik, C. Wagner and G. Weiglein, Nucl.Phys. B 580 (2000) 29.

Higgs Production and Decay in the MSSM: Status and Perspectives

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