High-Precision Tests of the MSSM with GigaZ
aa r X i v : . [ h e p - ph ] N ov High-Precision Tests of the MSSM with GigaZ
S. Heinemeyer , W. Hollik , A.M. Weber and G. Weiglein ∗
1- Instituto de Fisica de Cantabria (CSIC-UC), Santander, Spain2- Max-Planck-Institut f¨ur Physik, F¨ohringer Ring 6, D–80805 Munich, Germany3- IPPP, University of Durham, Durham DH1 3LE, UKWe review the physics potential of the GigaZ option of the International Linear Col-lider (ILC) for probing the Minimal Supersymmetric Standard Model (MSSM) via thesensitivity of the electroweak precision observables measured at the ILC to quantumcorrections [1]. A particular focus is put on the effective leptonic weak mixing angle,sin θ eff . The MSSM predictions take into account the complete one-loop results in-cluding the full complex phase dependence, all available MSSM two-loop correctionsas well as the full Standard Model (SM) results. We find that the anticipated experi-mental accuracy at the ILC with GigaZ option may resolve the virtual effects of SUSYparticles even in scenarios where the SUSY particles are so heavy that they escapedirect detection at the LHC and the first phase of the ILC. Electroweak precision observables (EWPO) are very powerful for testing the Standard Model(SM) and extensions of it. A particularly attractive extension is the Minimal Supersym-metric Standard Model (MSSM), see Ref. [2] for a review of electroweak precision physicsin the MSSM. In this context the Z -pole observables (and also the relation between the W -and Z -boson masses obtained from muon decay) play an important role. They comprisein particular the effective leptonic weak mixing angle, sin θ eff , the total Z -boson width,Γ Z , the ratio of the hadronic to leptonic decay width of the Z , R l , the ratio of the partialdecay width for Z → b ¯ b to the hadronic width, R b , and the hadronic peak cross section, σ . Performing fits in constrained SUSY models a certain preference for not too heavySUSY particles has been found [3–7]. The prospective improvements in the experimentalaccuracies, in particular at the ILC with GigaZ option, will provide a high sensitivity todeviations both from the SM and the MSSM. In Tab. 1 we summarize the current experi-mental results [8–10] together with the anticipated improvements at the LHC and the ILCwith GigaZ option, see Refs. [2, 11–13] for details.In order to confront the predictions of supersymmetry (SUSY) with the electroweakprecision data and to derive constraints on the supersymmetric parameters, it is desirable toachieve the same level of accuracy for the SUSY predictions as for the SM. In Refs. [14, 15]an new evaluation of M W and the Z -pole observables in the MSSM has been presented. Itincludes the full one-loop result (for the first time with the full complex phase dependence),all available MSSM two-loop corrections (entering via the ρ parameter [16–18]), as well as thefull SM results, see Refs. [14, 15] for details. The Higgs-boson sector has been implementedincluding higher-order corrections (as evaluated with FeynHiggs [19–21]). These corrections,being formally of higher-order, can give sizable contributions to the EWPO. The remainingtheory uncertainties have been estimated to be δM theo W < ∼
10 MeV [14] and δ sin θ theoeff < ∼ × − [15]. It has furthermore been shown in Ref. [15] that M W , sin θ eff and Γ Z show ∗ email: [email protected] LCWS/ILC 2007 bservable central exp. value σ ≡ σ today σ LHC σ ILC / GigaZ M W [GeV] 80 .
398 0 .
025 0 .
015 0 . θ eff . . . . . Z [GeV] 2 . . R l .
767 0 .
025 — 0.01 R b . . σ .
540 0 .
037 — 0 . m t [GeV] 170 . . . . σ ≡ σ today [8–10]. Alsoshown are the anticipated experimental accuracies at the LHC, σ LHC , and the ILC (includingthe GigaZ option), σ ILC . Each number represents the combined results of all detectors andchannels at a given collider, taking into account correlated systematic uncertainties, seeRefs. [2, 11–13] for details. Non-existing analyses are referred to as “—”.a pronounced sensitivity to the SUSY parameters, while the other EWPO exhibit only asmall variation over the MSSM parameter space. In view of the extraordinary anticipatedaccuracy of δ sin θ ILC / GigaZeff = 1 . × − [13], the effective leptonic weak mixing angle willbe a highly sensitive probe of electroweak physics. θ eff in a global MSSM scan We first analyse the sensitivity of sin θ eff to higher-order effects in the MSSM by scanningover a broad range of the SUSY parameter space. The following SUSY parameters are variedindependently of each other in a random parameter scan within the given range:sleptons : M ˜ F , ˜ F ′ = 100 . . . , light squarks : M ˜ F , ˜ F ′ up/down = 100 . . . , ˜ t/ ˜ b doublet : M ˜ F , ˜ F ′ up/down = 100 . . . , A τ,t,b = − . . . , gauginos : M , = 100 . . . , m ˜ g = 195 . . . ,µ = − . . . , Higgs : M A = 90 . . . , tan β = 1 . . . . . (1)Here M ˜ F, ˜ F ′ are the diagonal soft SUSY-breaking parameters in the sfermion sector, A f denote the trilinear couplings, M , are the soft SUSY-breaking parameters in the charginoand neutralino sectors, m ˜ g is the gluino mass, µ the Higgs mixing parameter, M A the CP -odd Higgs boson mass, and tan β is the ratio of the two vacuum expectation values. Onlythe constraints on the MSSM parameter space from the LEP Higgs searches [22, 23] andthe lower bounds on the SUSY particle masses from direct searches as given in Ref. [24]were taken into account. Apart from these constraints no other restrictions on the MSSMparameter space were made.In Fig. 1 we compare the SM and the MSSM predictions for sin θ eff as a function of m t as obtained from the scatter data. The predictions within the two models give rise to LCWS/ILC 2007
60 165 170 175 180 185 m t [GeV] s i n θ e ff SMMSSM M H = G e V M H = G e V hea vy sc a l a r s li gh t sc a l a r s m t ~ ,b ~ / m t ~ ,b ~ > 2.5 SMMSSMboth models Heinemeyer, Hollik,Weber, Weiglein ’07 experimental errors 68% CL:LEP2/Tevatron (today)Tevatron/LHCILC/GigaZ
Figure 1: MSSM parameter scan for sin θ eff as a function of m t over the ranges given ineq. (1). Todays 68% C.L. ellipses as well as future precisions, drawn around todays centralvalue, are indicated in the plot.two bands in the m t –sin θ eff plane with only a relatively small overlap region (indicatedby a dark-shaded (blue) area). The allowed parameter region in the SM (the medium-shaded (red) and dark-shaded (blue) bands) arises from varying the only free parameter ofthe model, the mass of the SM Higgs boson, from M SM H = 114 GeV, the LEP exclusionbound [23] (lower edge of the dark-shaded (blue) area), to 400 GeV (upper edge of themedium-shaded (red) area). The very light-shaded (green), the light shaded (green) andthe dark-shaded (blue) areas indicate allowed regions for the unconstrained MSSM. In thevery light-shaded region at least one of the ratios m ˜ t /m ˜ t or m ˜ b /m ˜ b exceeds 2.5 (withthe convention that m ˜ f ≤ m ˜ f ), while the decoupling limit with SUSY masses of O (2 TeV)yields the upper edge of the dark-shaded (blue) area. Thus, the overlap region betweenthe predictions of the two models corresponds in the SM to the region where the Higgsboson is light, i.e., in the MSSM allowed region ( M h < ∼
130 GeV [19, 20]). In the MSSMit corresponds to the case where all superpartners are heavy, i.e., the decoupling region ofthe MSSM. The 68% C.L. experimental results for m t and sin θ eff are indicated in the plot.As can be seen from Fig. 1, the current experimental 68% C.L. region for m t and sin θ eff is in good agreement with both models and does not indicate a preference for one of thetwo models. The prospective accuracies for the Tevatron/LHC and the ILC with GigaZoption, see Tab. 1, are also shown in the plot (using the current central values). Especiallythe ILC/GigaZ precision indicates the strong potential for a significant improvement of thesensitivity of the electroweak precision tests [12]. A comparison of the MSSM parameterspace preferred by sin θ eff and the directly measured values will constitute a highly sensitivetest of the model. LCWS/ILC 2007
Scenario where no SUSY particles are observed at the LHC
It is interesting to investigate whether the high accuracy achievable at the GigaZ option ofthe ILC would provide sensitivity to indirect effects of SUSY particles even in a scenariowhere the (strongly interacting) superpartners are so heavy that they escape detection atthe LHC.
100 200 300 400 500 600 700 800 900 1000 m χ ± ~ [GeV] s i n θ e ff SM (M H SM = M h MSSM ) ± σ para-ILC (sin θ eff ) exp = today ± σ ILC squarks & gluinos: M
Q,U,D =6 (M
Q,U,D ) SPS ; A u,d =6 (A u,d ) SPS ; m g =6 (m g ) SPS~~ sleptons, neutralinos & charginos: M
L,E =scale (M
L,E ) SPS ; A τ =scale (A τ ) SPS ; M =scale (M ) SPS superpotential: µ = scale ( µ ) SPS scale = (SUSY mass scale varied)
SPS1a’ ± σ para-ILC Figure 2: Theoretical prediction for sin θ eff in the SM and the MSSM (including prospectiveparametric theoretical uncertainties) compared to the experimental precision at the ILCwith GigaZ option. An SPS1a ′ inspired scenario is used, where the squark and gluino massparameters are fixed to 6 times their SPS 1a ′ values. The other mass parameters are variedwith a common scalefactor.We consider in this context a scenario with very heavy squarks and a very heavy gluino.It is based on the values of the SPS 1a ′ benchmark scenario [25], but the squark and gluinomass parameters are fixed to 6 times their SPS 1a ′ values. The other masses are scaledwith a common scale factor except M A which we keep fixed at its SPS 1a ′ value. In thisscenario the strongly interacting particles are too heavy to be detected at the LHC, while,depending on the scale-factor, some colour-neutral particles may be in the ILC reach. InFig. 2 we show the prediction for sin θ eff in this SPS 1a ′ inspired scenario as a function of thelighter chargino mass, m ˜ χ ± . The prediction includes the parametric uncertainty, σ para − ILC ,induced by the ILC measurement of m t , δm t = 100 MeV [26], and the numerically morerelevant prospective future uncertainty on ∆ α (5)had , δ (∆ α (5)had ) = 5 × − [27]. The MSSMprediction for sin θ eff is compared with the experimental resolution with GigaZ precision, σ ILC = 0 . M SM H = M MSSM h ) is also shown, applying again the parametric uncertainty σ para − ILC . LCWS/ILC 2007 espite the fact that no coloured SUSY particles would be observed at the LHC in thisscenario, the ILC with its high-precision measurement of sin θ eff in the GigaZ mode couldresolve indirect effects of SUSY up to m ˜ χ ± < ∼
500 GeV. This means that the high-precisionmeasurements at the ILC with GigaZ option could be sensitive to indirect effects of SUSYeven in a scenario where SUSY particles have neither been directly detected at the LHCnor the first phase of the ILC with a centre of mass energy of up to 500 GeV.
EWPO provide a very powerful test of the SM and the MSSM. We have reviewed resultsfor M W and Z boson observables such as sin θ eff , Γ Z , R l , R b , σ . Within the MSSM newresults for the EWPO containing the complete one-loop results with complex parametersand all available higher-order corrections in the SM and the MSSM have recently becomeavailable. The sensitivity to higher-order effects will drastically improve with the ILC pre-cision (including the GigaZ option) on the EWPO and m t . This has been illustrated in twoexamples. A general scan over the MSSM parameter space for sin θ eff and m t currently doesnot prefer the SM or the MSSM over the other. However, the anticipated GigaZ precisionindicates the high potential for a significant improvement of the sensitivity of the electroweakprecision tests. In a second example we have assumed a scenario with very heavy SUSYparticles, outside the reach of the LHC and the first stage of the ILC with √ s = 500 GeV.It has been shown that even in such a scenario the GigaZ precision on sin θ eff may resolvevirtual effects of SUSY particles, providing a possible hint to the existence of new physics. Acknowledgements
We thank G. Moortgat-Pick for interesting discussions concerning Sect. 3. Work supportedin part by the European Community’s Marie-Curie Research Training Network under con-tract MRTN-CT-2006-035505 ‘Tools and Precision Calculations for Physics Discoveries atColliders’ (HEPTOOLS).
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