As examples of new physics models that would be probed with precision Higgs measurements at TLEP, supersymmetric models that are compatible with current measurements, including the non-observation of supersymmetric particles at the LHC, are considered. These models are simplified, in that they assume universal supersymmetry-breaking masses for squarks and sleptons, and for gauginos, at a high scale. In the case of the CMSSM, this assumption is extended to include the supersymmetric Higgs bosons, but this assumption is relaxed in the NUHM1 model \cite{Isidori_Marrouche_et_al__2012}. A global frequentist analysis of the present data found two CMSSM fits that yield very similar values of the global \(\chi^{2}\) function, with lower and higher sparticle masses respectively, whilst the best NUHM1 fit is qualitatively similar to the low-mass CMSSM fit. These fits have not been excluded by the 2012 LHC run at 8 TeV, but lie within the potential reach of the forthcoming LHC 13/14 TeV run. On the other hand, the high-mass CMSSM point is likely to lie beyond the reach of the LHC. Thus, these models represent different potential challenges for the TLEP precision physics programme: verify predictions of new physics models at the quantum level, or find indirect evidence for new physics beyond the reach of the LHC.

Figure \ref{fig:SUSYbenchmarks} displays the deviations from the Standard Model predictions for some principal Higgs decay branching ratios, calculated in these CMSSM and NUHM1 models. Also shown are the potential measurement uncertainties attainable with the LHC programme that is currently approved, with HL-LHC, with the ILC and with TLEP. Only TLEP has measurement errors that are expected to be significantly smaller than the deviations of the supersymmetric model predictions from the central values of the Standard Model predictions, thereby offering the possibilities of a check of the predictions of the low-mass models at the quantum level, and of indirect evidence for the high-mass CMSSM.

It can also be noted from Fig. \ref{fig:SUSYbenchmarks}, however, that the uncertainties in the Standard Model predictions for the Higgs decay branching ratios stated by the LHC Higgs cross section Working Group \cite{1307.1347} are considerably larger than the deviations of the supersymmetric models from the Standard Model predictions, and also larger than the projected experimental errors. This means that the TLEP programme of high-precision Higgs measurements must be accompanied by a substantial theoretical effort to reduce the uncertainties in the theoretical calculations of Higgs properties.