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# Statistical combination of several important Standard Model Higgs boson searches

**This page contains approved plots and results in the order as they appear in the CSC note. Only the CSC note contains all the relevant information and should thus be consulted if one of the plots is used.**

**Figure 1:** Illustration of the determination of the p-value of a hypothesized value of μ. The left-hand curve indicates the pdf of q_{μ} for data generated with the same value of μ as was used to define the statistic q_{μ} ; this is used to determine the p-value of μ, shown as the shaded region. The right-hand curve indicates the pdf of q_{μ} for data generated with a different value of the strength parameter, μ'.

**Figure 2:** Illustration of the correspondence between the significance Z and a p-value.

**Figure 3:** Scatterplot of μ^ versus -2 ln λ(μ ); (b) the distribution of μ^ (see text).

**Figure 4:** (a) Scatterplot of μ^ versus q_{μ} from a Monte Carlo study with μ = 0; (b) the distribution of q0 (see text).

**Figure 5:** Distributions of -2 ln λ (μ ) for (a) μ^ > μ and (b) μ^ <= μ. The superimposed curves are chi-square distributions for one degree of freedom normalized to half the number of entries in the original distribution (see Fig. 3(a)).

**Figure 6:** The distribution of the test statistic q0 (for H -> γγ ), under the null background only hypothesis, for m

_{H} = 120

GeV with an integrated luminosity of 2 (a) and 10 (b) fb

^{-1}. A ½ χ

_{1}^{2} distribution is superimposed.

**Figure 7:** The distribution of the test statistic q1 for μ^ <= 1 under the s + b hypothesis (for H -> γγ ), for m

_{H} = 120

GeV with an integrated luminosity of (a) 2 fb

^{-1} and (b) 10 fb

^{-1}. A ½ χ

_{1}^{2} distribution is superimposed.

**Figure 8:** The distribution of the test statistic q0 for H + 0 j -> WW + 0 j, under the background-only hypothesis, with the same fixed QCD WW shape parameters used at both the generator and the fit level, for m

_{H} = 150

GeV and for an integrated luminosity of 10 fb

^{-1} (a) with the same shape parameters for event generation and fitting; (b) with altered shape parameters. A ½ χ

_{1}^{2} distribution is superimposed.

**Figure 9:** The distribution of the test statistic q1 for μ^ <= 1 under the s + b hypothesis for H + 0 j -> WW + 0 j, for m

_{H} = 150

GeV with an integrated luminosity of (a) 2 fb

^{-1} and (b) 10 fb

^{-1}. A χ

_{1}^{2} distribution is superimposed.

**Figure 10:** The distribution of the test statistic q0 (for H + 2 j -> WW + 2 j), under the null background only hypothesis, for m

_{H} = 150

GeV and for an integrated luminosity of 2 (a) and 10 (b) f b

^{-1}. A ½ χ

_{1}^{2} distribution is superimposed.

**Figure 11:** The distribution of the test statistic q1 for μ^ <= 1 under the s + b (μ = 1) hypothesis (for H + 2 j -> WW + 2 j), for m

_{H} = 150

GeV with an integrated luminosity of (a) 2 fb

^{-1} and (b) 10 fb

^{-1}. A χ

_{1}^{2} distribution is superimposed.

**Figure 12:** The distribution of the test statistic q0 for H -> τ τ under the null background-only hypothesis, for m

_{H} = 130

GeV with an integrated luminosity of 2 (a) and 10 (b) fb

^{-1}. A ½ χ

_{1}^{2} distribution is superimposed. Figures (c) and (d) show 1 - F(q

_{0} ) where F(q

_{0} ) is the corresponding cumulative distribution. The small excess of events at high q

_{0} is statistically compatible with the expected curves, as can be seen by comparison with the dotted histograms that show the 68.3% central confidence intervals for p = 1 - F(q

_{0} |0). The lower dotted line at 2.87×10

^{-7} shows the 5σ discovery threshold.

**Figure 13:** The distribution of the test statistic q1 for μ^ <= 1 under the s + b hypothesis for H -> τ

^{+} τ

^{-} , for m

_{H} = 130

GeV with an integrated luminosity of (a) 2 fb

^{-1} (b) and 10 fb

^{-1}. A χ

_{1}^{2} distribution is superimposed.

**Figure 14:** The distribution of the test statistic q

_{0} (for H -> 4l), under the null background only hypothesis, for m

_{H} = 200

GeV with an integrated luminosity of 2 (a) and 10 (b) fb

^{-1}. A ½ χ

_{1}^{2} distribution is superimposed. Figures (c) and (d) show 1 - F(q

_{0} ) where F(q

_{0} ) is the corresponding cumulative distribution. The small excess of events at high q

_{0} is statistically compatible with the expected curves, as can be seen by comparison with the dotted histograms showing the 68.3% central confidence intervals for p = 1 - F(q

_{0} |0). The lower dotted line at 2.87×10

^{-7} shows the 5σ discovery threshold.

**Figure 15:** The distribution of the test statistic q

_{1} for μ^ <= 1 under the s + b hypothesis (for H -> 4l), for m

_{H}=200

GeV with an integrated luminosity of (a) 2 fb

^{-1} and (b) 10 fb

^{-1}. A χ

_{1}^{2} distribution is superimposed.

**Figure 16:** The median discovery significance for the various channels and the combination with an integrated luminosity of 10 fb

^{-1} for (a) the lower mass range (b) for masses up to 600

GeV.

**Figure 17:** Significance contours for different Standard Model Higgs masses and integrated luminosities. The thick curve represents the 5σ discovery contour. The median significance is shown with a colour according to the legend. The hatched area below 2 fb^{-1} indicates the region where the approximations used in the combination are not accurate, although they are expected to be conservative.

**Figure 18:** The median p-value obtained for excluding a Standard Model Higgs Boson for the various channels as well as the combination for (a) the lower mass range (b) for masses up to 600

GeV.

**Figure 19:** The expected luminosity required to exclude a Higgs boson with a mass m_{H} at a confidence level given by the corresponding colour. The hatched area below 2 fb^{-1} indicates the region where the approximations used in the combination are not accurate, although they are expected to be conservative.

**Major updates**:

--

WolfgangMader - 27 Jan 2009

Responsible: CalebLampen

Last reviewed by: **Never reviewed**