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Fitting the MSSM to the Observed Higgs Signal

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Constraining Supersymmetric Models

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Abstract

In order to investigate whether, and if so how much, the MSSM can improve the theoretical description of the experimental data compared to the SM, we fit the experimentally measured Higgs decay rates, the Higgs mass and low-energy observables under the hypothesis that the light or the heavy CP-even Higgs of the MSSM is the observed state at 126 GeV. The fit quality in the MSSM, for both Higgs interpretations, is compared to the SM. We determine the regions of the MSSM parameter space which are favoured by the experimental data, and we demonstrate some features of the best-fit point.

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Notes

  1. 1.

    The reader should keep in mind here (and in the following) that the point density has no statistical meaning.

  2. 2.

    This HiggsBounds version contains besides the results in the last publicly available version (version 4.1.0) the CMS result from the search for neutral Higgs bosons decaying into \(\tau \) pairs [7].

  3. 3.

    The measured rates, which are taken into account, can be seen in Figs. 7.1 and 7.3 where we present the results, see discussion below.

  4. 4.

    We note that the Belle Collaboration has reported a new (lower) measurement of \(\mathrm{BR}(B_u \rightarrow \tau \nu _\tau )\) that is in better agreement with the SM (and also with models with two Higgs doublets, like the MSSM) [41]. While we do not take this new result into account in our overall fit results, in the following we do comment briefly on its possible effects. The measurement of \(\mathrm{BR}(B_s \rightarrow \mu ^- \mu ^+)\) [42, 43] became public shortly after this analysis was conducted. Therefore here only an upper limit on \(\mathrm{BR}(B_s\rightarrow \mu ^+\mu ^-)\) is included. Both of these results are included in the updated analysis. We do not include the BaBar result on \(\bar{B} \rightarrow D^{(*)}\tau ^-\bar{\nu }_\tau \) [44], which shows (combining the D and \(D^{(*)}\) measurements) a \(3.4\,\sigma \) deviation from the SM prediction, which can not be explained in the MSSM either.

  5. 5.

    The Mathematica code is too slow to be included in a scan with \(\mathcal{O}(10^7)\) points.

  6. 6.

    The contributions from light sleptons can even be significantly larger (up to \({\sim }60\) MeV) when all sleptons have masses just above the LEP limit as we have shown in Chap. 5, which requires \(M_{\tilde{E}}=M_{\tilde{L}} \sim 100\) GeV together with a small mixing in the slepton sector (the mixing has to be quite small to keep \(m_{\tilde{\tau }_1}\) above the LEP limit). Such parameter points are not present here, since we choose \(M_{\tilde{l}_3} > 200\) GeV and \(M_{\tilde{E}_{1,2}}=M_{\tilde{L}_{1,2}} = 300\) GeV (\(M_{\tilde{E}_{1,2}}=M_{\tilde{L}_{1,2}} = M_{\tilde{l}_3}\)) in the original (updated) analysis. A similar argument holds for the chargino/neutralino contributions, since we choose \(M_2>200\) GeV.

  7. 7.

    The measured rates, which are taken into account, can be seen in Fig. 7.2 where we present the results, which will be discussed below.

  8. 8.

    The SM \(M_W\) value is slightly different from the one in Table 7.2, due to small changes in the input values for SM parameters. We set the SM parameters here to the FeynHiggs default values. While here the \(M_W\) prediction in the MSSM is obtained from FeynHiggs, we plan to use the Fortran code presented in Chap. 5 in a future update of this analysis.

  9. 9.

    We did not update the analysis for the heavy Higgs case yet.

  10. 10.

    The p-value provides information about the goodness of a fit, by quantifying the discrepancy between the observed data and what one would expect from a certain hypothesis (e.g. a certain model: SM, MSSM light Higgs case,...). To be more precise it gives the probability that a test statistic is in equal or worse agreement with the expectation from the hypothesis than the actual data. Thus large p-values show a good agreement of the expectation from the hypothesis with the data, whereas small p-values correspond to a poor agreement. More details can be found e.g. in the “Statistics” review in Ref. [25] .

  11. 11.

    The pull values are defined as (predicted value - observed value)/(uncertainty).

  12. 12.

    In the updated fit, points with large \(\tan \beta \) values that have a small \(\chi ^2_{(g-2)_{\mu }}\) have typically \(M_{\tilde{E}_{1,2}}=M_{\tilde{L}_{1,2}} \gtrsim 400\) GeV.

  13. 13.

    In Fig. 7.15 we extended the plotted range to large \(m_{\tilde{t}_1}\) values, to include the best-fit point in the plot. The edges for large \(m_{\tilde{t}_1}\) indicate the upper scan limits. The same feature would be visible in Fig. 7.14 if the plotting range were extended to larger \(m_{\tilde{t}_1}\) masses.

  14. 14.

    The dominant contributions to \(\Delta _b\) beyond one-loop order are the QCD corrections, given in [83]. Those two-loop contributions are not included in our analysis.

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    Lisa Zeune

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Zeune, L. (2016). Fitting the MSSM to the Observed Higgs Signal. In: Constraining Supersymmetric Models . Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-22228-8_7

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