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Combination of Standard Model Higgs boson searches and measurements of the properties of the new boson with a mass near 125 GeV

This is a condensed description with plots for the analysis CMS-HIG-12-045

- Combination of Standard Model Higgs boson searches and measurements of the properties of the new boson with a mass near 125 GeV
Abstract
Sensitivities
Exclusion limits on the SM Higgs boson
Significance of the observed excess
Mass of the observed state
- Additional plots
Compatibility of the observed state with the SM Higgs boson hypothesis: signal strengths
- Additional plots
- Numbers
Tests of the Couplings

Abstract

Abstract to be copied

Sensitivities

Plot	Caption
	The median expected 95% CL upper limits on the cross section ratio σ/σ_SM in the absence of a Higgs boson as a function of the SM Higgs boson mass in the range 110–1000 GeV (left) and 110–145 GeV (right), for the five Higgs boson decay channels. Here σ_SM denotes the cross section predicted for the SM Higgs boson. A channel showing values below unity (dotted red line) would be expected to be able to exclude a Higgs boson of that mass at 95% CL. The jagged structure in the limits for some channels results from the different event selection criteria employed in those channels for different Higgs boson mass sub-ranges.
	The median expected p-value for observing an excess at mass m_H in assumption that the SM Higgs boson with this mass exists, as a function of the SM Higgs boson mass in the range 110–1000 GeV (left) and 110–145 GeV (right). Expectations for subcombinations in five Higgs boson decay channels and the overall combination are shown.

Plot

Caption

The median expected 95% CL upper limits on the cross section ratio σ/σ_SM in the absence of a Higgs boson as a function of the SM Higgs boson mass in the range 110–1000 GeV (left) and 110–145 GeV (right), for the five Higgs boson decay channels. Here σ_SM denotes the cross section predicted for the SM Higgs boson. A channel showing values below unity (dotted red line) would be expected to be able to exclude a Higgs boson of that mass at 95% CL. The jagged structure in the limits for some channels results from the different event selection criteria employed in those channels for different Higgs boson mass sub-ranges.

The median expected p-value for observing an excess at mass m_H in assumption that the SM Higgs boson with this mass exists, as a function of the SM Higgs boson mass in the range 110–1000 GeV (left) and 110–145 GeV (right). Expectations for subcombinations in five Higgs boson decay channels and the overall combination are shown.

Exclusion limits on the SM Higgs boson

Plot	Caption
	The CL_s values for the SM Higgs boson hypothesis as a function of the Higgs boson mass. The observed values are shown by the solid line. The dashed line indicates the expected median of results for the background only hypothesis, while the green (dark) and yellow (light) bands indicate the ranges that are expected to contain 68% and 95% of all observed excursions from the median, respectively. The three horizontal lines on the CL_s plot show confidence levels of 90%, 95%, and 99%, defined as (1–CL_s).
	The 95% CL upper limits on the cross section ratio σ/σ_SM for the SM Higgs boson hypothesis as function of the Higgs boson mass. The observed values are shown by the solid line. The dashed line indicates the expected median of results for the background only hypothesis, while the green (dark) and yellow (light) bands indicate the ranges that are expected to contain 68% and 95% of all observed excursions from the median, respectively.

Plot

Caption

The CL_s values for the SM Higgs boson hypothesis as a function of the Higgs boson mass. The observed values are shown by the solid line. The dashed line indicates the expected median of results for the background only hypothesis, while the green (dark) and yellow (light) bands indicate the ranges that are expected to contain 68% and 95% of all observed excursions from the median, respectively. The three horizontal lines on the CL_s plot show confidence levels of 90%, 95%, and 99%, defined as (1–CL_s).

The 95% CL upper limits on the cross section ratio σ/σ_SM for the SM Higgs boson hypothesis as function of the Higgs boson mass. The observed values are shown by the solid line. The dashed line indicates the expected median of results for the background only hypothesis, while the green (dark) and yellow (light) bands indicate the ranges that are expected to contain 68% and 95% of all observed excursions from the median, respectively.

Significance of the observed excess

Plot	Caption
	The observed local p-value p₀ for 7-!TeV, 8-!TeV data, and their combination as a function of the SM Higgs boson mass. The dashed lines show the expected local p-value p₀(m_H), should a Higgs boson with a mass m_H exist.
	The observed local p-value p₀ for five subcombinations by decay mode and the overall combination as a function of the SM Higgs boson mass. The dashed lines show the expected local p-value p₀(m_H), should a Higgs boson with a mass m_H exist.
	The observed local p-value p₀ for γγ, ZZ and their combination as a function of the SM Higgs boson mass. The dashed lines show the expected local p-value p₀(m_H), should a Higgs boson with a mass m_H exist.
	The observed local p-value p₀ for WW, bb, ττ and their combination as a function of the SM Higgs boson mass. The dashed lines show the expected local p-value p₀(m_H), should a Higgs boson with a mass m_H exist.

Mass of the observed state

Plot	Caption
	(Left) 1D test statistics q(m_H) scan vs hypothesized Higgs boson mass m_H for the γγ and 4l final states separately and for their combination. In this combination, three independent signal strengths gg → H → γγ, VBF+VH → H → γγ, and H → ZZ → 4l are proﬁled together with all other nuisance parameters. (Right) 2D 68% CL contours for a hypothesized Higgs boson mass m_H and signal strength σ/σ_SM for the γγ and 4l, and their combination. In this combination, the relative signal strengths for the three final states are constrained by the expectations for the SM Higgs boson.
	1D test statistics q(m_H) scan vs hypothesized Higgs boson mass m_H for the combination of the high resolution channels. 1D-scans of the test statistic q(m_X) versus hypothesized boson mass m_X for the combination of the γ&gamma and 4l final states. The solid line is obtained with all nuisance parameters profiled and, hence, includes both statistical and systematic uncertainties. The dashed line is obtained with all nuisance parameters fixed to their best-fit values and, hence, includes only statistical uncertainties. The crossings with the thick (thin) horizontal lines define the 68\% (95\%) CL interval for the measured mass.

Plot

Caption

(Left) 1D test statistics q(m_H) scan vs hypothesized Higgs boson mass m_H for the γγ and 4l final states separately and for their combination. In this combination, three independent signal strengths gg → H → γγ, VBF+VH → H → γγ, and H → ZZ → 4l are proﬁled together with all other nuisance parameters.
(Right) 2D 68% CL contours for a hypothesized Higgs boson mass m_H and signal strength σ/σ_SM for the γγ and 4l, and their combination. In this combination, the relative signal strengths for the three final states are constrained by the expectations for the SM Higgs boson.

1D test statistics q(m_H) scan vs hypothesized Higgs boson mass m_H for the combination of the high resolution channels. 1D-scans of the test statistic q(m_X) versus hypothesized boson mass m_X for the combination of the γ&gamma and 4l final states. The solid line is obtained with all nuisance parameters profiled and, hence, includes both statistical and systematic uncertainties. The dashed line is obtained with all nuisance parameters fixed to their best-fit values and, hence, includes only statistical uncertainties. The crossings with the thick (thin) horizontal lines define the 68\% (95\%) CL interval for the measured mass.

Additional plots

Plot	Caption
\	*1D test statistics –2 ln Q* vs hypothesized Higgs boson mass m_H for the diphoton final state.** The solid line is obtained with all nuisance parameters profiled and, hence, includes both statistical and systematic uncertainties. The dashed line is obtained with all nuisance parameters fixed to their best-fit values and, hence, includes only statistical uncertainties. The crossings with the thick (thin) horizontal lines define the 68\% (95\%) CL interval for the measured mass.
\	*1D test statistics –2 ln Q* vs hypothesized Higgs boson mass m_H for the four-lepton final state.** The solid line is obtained with all nuisance parameters profiled and, hence, includes both statistical and systematic uncertainties. The dashed line is obtained with all nuisance parameters fixed to their best-fit values and, hence, includes only statistical uncertainties. The crossings with the thick (thin) horizontal lines define the 68\% (95\%) CL interval for the measured mass.
	*2D test statistics –2 ln Q* vs hypothesized Higgs boson mass m_H and signal strength σ/σ_SM for the combination of the high resolution channels.** The cross indicates the best-fit values. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL ranges, respectively. In this combination, the relative signal strengths for the various final states are constrained by the expectations for the SM Higgs boson.
	*2D test statistics –2 ln Q* vs hypothesized Higgs boson mass m_H and signal strength σ/σ_SM for the diphoton final state.** The cross indicates the best-fit values. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL ranges, respectively. In this combination, the relative signal strengths for the various production modes are constrained by the expectations for the SM Higgs boson.
	*2D test statistics –2 ln Q* vs hypothesized Higgs boson mass m_H and signal strength σ/σ_SM for the four-lepton final state.** The cross indicates the best-fit values. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL ranges, respectively.

Compatibility of the observed state with the SM Higgs boson hypothesis: signal strengths

Plot	Caption
	The observed best-fit signal strength μ̂ = σ/σ_SM as a function of the SM Higgs boson mass in the range 110–145 GeV. The bands correspond to the ±1σ uncertainties on the μ̂ values.
	Values of μ̂ = σ/σ_SM for the combination (solid vertical line) and for contributing channels (points). The vertical band shows the overall μ̂ value 0.88 ± 0.21. The horizontal bars indicate the ±1σ uncertainties on the μ̂ values for individual channels; they include both statistical and systematic uncertainties.
	Values of μ̂ = σ/σ_SM for the combination (solid vertical line) and for sub-combinations grouped by decay mode (points). The vertical band shows the overall μ̂ value 0.88 ± 0.21. The horizontal bars indicate the ±1σ uncertainties on the μ̂ values for individual channels; they include both statistical and systematic uncertainties.
	Values of μ̂ = σ/σ_SM for the combination (solid vertical line) and for sub-combinations grouped by a signature enhancing specific production mechanisms (points). The vertical band shows the overall μ̂ value 0.88 ± 0.21. The horizontal bars indicate the ±1σ uncertainties on the μ̂ values for individual channels; they include both statistical and systematic uncertainties.
	(Left plot) The 68% CL (solid lines) and (right plot) 68% CL (solid line) and 95% CL (dashed line) intervals for signal strength in the gluon-gluon-fusion-plus-ttH and in VBF-plus-VH production mechanisms: μ_gg+ttH and μ _VBF+VH, respectively. The different colors show the results obtained by combining data from each of the five analayzed decay modes: γγ (green), WW (blue), ZZ(red), ττ (violet), bb (cyan). The crosses indicate the best-fit values. The diamond at (1,1) indicates the expected values for the SM Higgs boson.

Additional plots

Plot	Caption
	68% CL intervals of μ̂ = σ/σ_SM for the combination (vertical band) and for contributing channels (red lines) computed using the Feldman-Cousins construction.
	The 68% CL (solid lines) intervals for signal strength in the gluon-gluon-fusion-plus-ttH and in VBF-plus-VH production mechanisms: μ_ggH+ttH and μ _VBF+VH, respectively using the Feldman-Cousins construction. The different colors show the results obtained by combining data from each of the five analayzed decay modes: γγ (green), WW (blue), ZZ(red), ττ (violet), bb (cyan). The crosses indicate the best-fit values. The diamond at (1,1) indicates the expected values for the SM Higgs boson.
	Values of μ̂ = σ/σ_SM for the the individual channels. The horizontal bars indicate the ±1σ uncertainties on the μ̂ values for individual channels; they include both statistical and systematic uncertainties. The vertical dashed line indicates the prediction for a SM Higgs boson.
	Values of μ̂ = σ/σ_SM for the sub-combinations by decay mode. The horizontal bars indicate the ±1σ uncertainties on the μ̂ values for individual channels; they include both statistical and systematic uncertainties. The vertical dashed line indicates the prediction for a SM Higgs boson.
	Values of μ̂ = σ/σ_SM for the sub-combinations grouped by a signature enhancing specific production mechanisms. The horizontal bars indicate the ±1σ uncertainties on the μ̂ values for individual channels; they include both statistical and systematic uncertainties. The vertical dashed line indicates the prediction for a SM Higgs boson.

Numbers

The tables below contain the same information that is shown in figures 10a-10c of the HIG-12-045 PAS.

Channel	μ̂ = σ/σ_SM
by decay mode	value	uncertainty
H → bb	+1.075	-0.566/+0.593
H → ττ	+0.875	-0.484/+0.508
H → γγ	+1.564	-0.419/+0.460
H → WW	+0.699	-0.232/+0.245
H → ZZ	+0.807	-0.280/+0.349
by production tag and decay mode	value	uncertainty
H → bb (VH tag)	+1.309	-0.601/+0.654
H → bb (ttH tag)	-0.798	-1.840/+2.100
H → ττ (0/1 jet)	+0.845	-0.657/+0.684
H → ττ (VBF tag)	+0.819	-0.746/+0.824
H → ττ (VH tag)	+0.861	-1.678/+1.924
H → γγ (untagged)	+1.428	-0.457/+0.502
H → γγ (VBF tag)	+2.256	-1.017/+1.286
H → WW (0/1 jet)	+0.774	-0.247/+0.270
H → WW (VBF tag)	-0.046	-0.552/+0.737
H → WW (VH tag)	-0.305	-1.943/+2.223
H → ZZ	+0.807	-0.280/+0.349
by production tag	value	uncertainty
Untagged	+0.891	-0.186/+0.208
VBF tag	+0.915	-0.477/+0.526
VH tag	+1.135	-0.547/+0.597
ttH tag	-0.798	-1.840/+2.100

Tests of the Couplings

Test of Fermion and Vector Boson Couplings

Plot	Caption
	2D test statistics q(κ_V, κ_F) scan.
	2D test statistics q(κ_V, κ_F) scan, including individual channels.
	1D test statistics q(κ_V) scan, profiling κ_F.
	1D test statistics q(κ_F) scan, profiling κ_V.
	1D test statistics q(κ_V) scan, if κ_F is fixed to the SM value.
	1D test statistics q(κ_F) scan, if κ_V is fixed to the SM value.

Test of Custodial Symmetry

Using only untagged WW and ZZ events and assuming SM couplings to fermions

Plot	Caption
	1D test statistics q(λ_WZ) scan vs the coupling modifier ratio λ_WZ, profiling the coupling modifier κ_Z and all other nuisances. The coupling to fermions is taken to be the SM one (κ_F = 1).
	2D test statistics q(λ_WZ, κ_Z) scan, profiling all other nuisances.

Using all channels, and without assumption on the couplings to fermions (except their universality)

Plot	Caption
	1D test statistics q(λ_WZ) scan vs the coupling modifier ratio λ_WZ, profiling the coupling modifiers κ_Z and κ_F and all other nuisances.
	2D test statistics q(λ_WZ, κ_Z) scan, profiling the coupling modifier to fermions κ_F and all other nuisances.
	2D test statistics q(λ_WZ, κ_F) scan, profiling the coupling modifier to the Z boson κ_Z and all other nuisances.
	2D test statistics q(κ_Z, κ_F) scan, profiling the modifier to the ratio of W and Z couplings λ_WZ and all other nuisances.

Test of Fermion Universality

Up-type vs Down-type Fermions

Plot	Caption
	1D test statistics q(λ_du) scan vs the coupling modifier ratio λ_du, profiling the coupling modifiers κ_u and κ_V and all other nuisances. κ_u and κ_V are always taken to be positive.
	2D test statistics q(λ_du, κ_u) scan, profiling the coupling modifier to vector bosons κ_V and all other nuisances. κ_u and κ_V are always taken to be positive.
	2D test statistics q(λ_du, κ_V) scan, profiling the coupling modifier to the up-type fermions κ_u and all other nuisances. κ_u and κ_V are always taken to be positive.
	2D test statistics q(κ_V, κ_u) scan, profiling the modifier to the ratio of up-type and down-type couplings λ_du and all other nuisances.

Leptons vs Quarks

Plot	Caption
	1D test statistics q(λ_lq) scan vs the coupling modifier ratio λ_lq, profiling the coupling modifiers κ_q and κ_V and all other nuisances. κ_q and κ_V are always taken to be positive.
	2D test statistics q(λ_lq, κ_q) scan, profiling the coupling modifier to vector bosons κ_V and all other nuisances. κ_q and κ_V are always taken to be positive.
	2D test statistics q(λ_lq, κ_V) scan, profiling the coupling modifier to the quarks κ_q and all other nuisances. κ_q and κ_V are always taken to be positive.
	2D test statistics q(κ_V, κ_q) scan, profiling the modifier to the ratio of lepton to quark couplings λ_lq and all other nuisances.

Search for Beyond Standard Model Physics in Loops

Plot	Caption
	2D test statistics q(κ_g, κ_γ) scan.
	1D test statistics q(κ_g) scan, profiling the modifier to the effective coupling to photons κ_γ.
	1D test statistics q(κ_γ) scan, profiling the modifier to the effective coupling to gluons κ_g.

Search for Beyond Standard Model Physics in Loops and Decays

Plot	Caption
	1D test statistics q(BR_BSM) scan, profiling the modifier to the effective coupling to photons and gluons κ_γ, κ_g.
	2D test statistics q(κ_g, BR_BSM) scan, profiling the modifier to the effective coupling to photons κ_γ.
	2D test statistics q(κ_g, κ_γ) scan, profiling the branching ratio to BSM decays BR_BSM.

Generic search for deviations in the couplings

The search is performed with six independent coupling modifiers κ_V, κ_b, κ_τ, κ_t, κ_g, κ_γ

Plot	Caption
	1D test statistics q(κ_V) scan, profiling the other five coupling modifiers.
	1D test statistics q(κ_b) scan, profiling the other five coupling modifiers.
	1D test statistics q(κ_τ) scan, profiling the other five coupling modifiers.
	1D test statistics q(κ_t) scan, profiling the other five coupling modifiers.
	1D test statistics q(κ_γ) scan, profiling the other five coupling modifiers.
	1D test statistics q(κ_g) scan, profiling the other five coupling modifiers.
	2D test statistics q(κ_V, κ_γ) scan, profiling the other four coupling modifiers.
	2D test statistics q(κ_g, κ_b) scan, profiling the other four coupling modifiers.
	2D test statistics q(κ_b, κ_τ) scan, profiling the other four coupling modifiers.

Topic revision: r13 - 2012-11-23 - GiovanniPetrucciani

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