thesis.lof

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\contentsline {figure}{\numberline {\relax 2.1}{\ignorespaces The 95\% confidence upper limits on the ratio of Higgs boson production to the SM prediction as a function of $m_{H}$. The dotted line indicates the median expected exclusion assuming no SM Higgs boson exists while the solid line indicates the observed exclusion obtained from the data. Where this line falls below 1, a SM Higgs boson with that mass is excluded at the 95\% confidence level as indicated by the green bands. The other coloured bands indicate exclusion limits resulting from direct searches for the SM Higgs boson conducted by other Collaborations before June 2012. The figure has been altered from its original source~\cite {tevhiggscombinations}.\relax }}{43}
\contentsline {figure}{\numberline {\relax 2.2}{\ignorespaces Delta chi-squared from global fit to combined data from CDF, D0, SLD and the LEP Collaborations as a function of $m_{H}$~\cite {lepewwgpage}. The solid line is the nominal fit with theoretical uncertainties indicated in blue while the dashed lines indicate alternative theoretical prescriptions. The yellow bands indicate the regions excluded at the 95\% confidence level from direct searches for the SM Higgs boson conducted at LEP and the LHC before March 2012.\relax }}{44}
\contentsline {figure}{\numberline {\relax 2.3}{\ignorespaces Dominant SM Higgs boson production mechanisms: Gluon-gluon fusion (top left), vector-boson fusion (bottom left), associated production with vector boson (top right) and top anti-top quark pair (bottom right).\relax }}{45}
\contentsline {figure}{\numberline {\relax 2.4}{\ignorespaces SM Higgs boson production cross-sections at $\sqrt {s}=7~\mathrm {TeV}$ (top) and 8 TeV (bottom) of the four main production mechanisms, $pp\rightarrow H+X$, along with their theoretical uncertainties as a function of $m_{H}$~\citep {lhcxswg2011,lhcxswg2012}. The coloured bands indicate the theoretical uncertainties.\relax }}{46}
\contentsline {figure}{\numberline {\relax 2.5}{\ignorespaces Left: SM Higgs boson production branching ratios for the dominant decays as a function of $m_{H}$. Right: SM Higgs boson total width, $\Gamma _{H}$, as a function of $m_{H}$~\citep {lhcxswg2011}.\relax }}{47}
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\contentsline {figure}{\numberline {\relax 3.1}{\ignorespaces LHC accelerator ring. The relative locations of the four main experiments are indicated along with their points of access to the beam.\relax }}{50}
\contentsline {figure}{\numberline {\relax 3.2}{\ignorespaces Diagram of the CMS Detector. The arrows indicate the main detector elements. The figure has been altered from its original source~\citep {cmspub}.\relax }}{52}
\contentsline {figure}{\numberline {\relax 3.3}{\ignorespaces Cross-section of the pixel and silicon strip detector components of the CMS tracker~\citep {Weber201159}.\relax }}{53}
\contentsline {figure}{\numberline {\relax 3.4}{\ignorespaces Resolution of vertex $z$-position as a function of the number of tracks associated to the vertex measured in simulation and 2010 data~\citep {TRK-10-005}. The resolution is given for three different average track momenta.\relax }}{54}
\contentsline {figure}{\numberline {\relax 3.5}{\ignorespaces Sub-cluster construction of the Hybrid algorithm used to reconstruct photons and electrons in the ECAL barrel.\relax }}{56}
\contentsline {figure}{\numberline {\relax 3.6}{\ignorespaces Relative ECAL crystal response to blue laser light (440 nm) in bins of pseudo-rapidity, for the 2011 data taking period. The grey bands indicate periods during which there was no beam.\relax }}{57}
\contentsline {figure}{\numberline {\relax 3.7}{\ignorespaces Ratio $E/p$ in electrons reconstructed in the ECAL Barrel from $W\rightarrow e\nu $ events in 2011 data as a function of time before and after applying transparency corrections from the laser monitoring (LM) system. The blue line indicates the correction applied per point averaged over all crystals used in the electron energy measurement.\relax }}{58}
\contentsline {figure}{\numberline {\relax 3.8}{\ignorespaces Shower shape variable $r_{9}$ (left) and $\sigma _{i\eta i\eta }$ (right) distributions for superclusters associated with simulated real and fake photons. The real photon is taken from simulated $H\rightarrow \gamma \gamma $ events while the fake photon is taken from a $\gamma +jet$ sample where the photon candidate is matched to a generated quark leg. In the right hand plot, two distributions can be distinguished. The narrower is from photons in the barrel and the wider from photons in the endcaps. \relax }}{59}
\contentsline {figure}{\numberline {\relax 3.9}{\ignorespaces Response measured from matched generator-L1 jet pairs in MC as a function of the generator jet pseudo-rapidity $|\eta ^{Gen}|$.\relax }}{61}
\contentsline {figure}{\numberline {\relax 3.10}{\ignorespaces Correction function for the $0.348 < |\eta ^{Gen}| < 0.695$. The points represent the average quantities as measured in MC. The blue line is a parametric fit to the points using a chi-squared minimisation. The error bars, estimated from the number of MC events, are too small to be visible in this plot.\relax }}{62}
\contentsline {figure}{\numberline {\relax 3.11}{\ignorespaces Closure tests performed in MC as a function of $E_{T}^{L1}$ (left) and $\eta ^{Gen}$ (right). The test shows that after applying the corrections, the response is within 10\% (dashed lines) of unity. The error bars are too small to be visible in these plots.\relax }}{63}
\contentsline {figure}{\numberline {\relax 3.12}{\ignorespaces Jet energy resolution at L1 as a function of $E_{T}^{L1}$ before and after application of the derived calibrations. The error bars are too small to be visible in these plots.\relax }}{63}
\contentsline {figure}{\numberline {\relax 3.13}{\ignorespaces Energy resolution, $\sigma _{E}$, of L1 jets as a function of transverse energy deposited in the calorimeter, $E_{T}$. The coefficients of the functional form shown are the result of a fit to the points.\relax }}{65}
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\contentsline {figure}{\numberline {\relax 4.1}{\ignorespaces Flow chart of the $H\rightarrow \gamma \gamma $ analysis performed on the 2011 dataset. The blue boxes indicate stages which involve the use of a boosted decision tree (BDT). The red boxes indicate inputs from the common CMS reconstruction and are not detailed in this chapter. The two methods for signal extraction, labelled A and B, are indicated by the green boxes.\relax }}{68}
\contentsline {figure}{\numberline {\relax 4.2}{\ignorespaces Comparison of the diphoton mass peak in Higgs MC with a mass of 120 GeV using different measurements of the photon energy. The black line is from using the raw energy of the supercluster, the blue is from using the analytic fit method (Standard + IC Residual) and the red from using the regression method (Raw + Regression). The quantity $\sigma _{eff}$, the narrowest range in $m_{\gamma \gamma }$ which contains 68\% of the distribution, is given for each peak~\citep {AN-12-048}.\relax }}{73}
\contentsline {figure}{\numberline {\relax 4.3}{\ignorespaces Invariant mass peak in $H\rightarrow \gamma \gamma $ MC with $m_{H}=125$ GeV. The blue histogram is from events in which the generated vertex is within 10mm of the vertex assigned to the diphoton pair. The red histogram is from events in which the incorrect vertex is assigned. Both distributions are normalised to unit area for ease of comparison.\relax }}{75}
\contentsline {figure}{\numberline {\relax 4.4}{\ignorespaces Fraction of simulated gluon-gluon fusion events in which the $z$ position of the selected vertex is within 10mm of the true vertex as a function of Higgs boson $p_{T}$. The red histogram is the average probability to select the correct vertex in each bin estimated from the per-event BDT.\relax }}{76}
\contentsline {figure}{\numberline {\relax 4.5}{\ignorespaces Fraction of $Z\rightarrow \mu ^{+}\mu ^{-}$ events in which the selected vertex is with 10mm of the true vertex in Run 2011A (left) and Run 2011B (right) data and MC as a function of $p_{T}^{Z}$~\citep {AN-12-048}. The BDT selection, labelled MVA, is shown by the open circles where the ranking method, labelled RANK is shown as points.\relax }}{77}
\contentsline {figure}{\numberline {\relax 4.6}{\ignorespaces Kinematic inputs to the diphoton BDT in data and MC. The distributions are for events which pass the full selection including a cut on the diphoton BDT output of 0.05. The expectation from a SM Higgs boson with 125 GeV is shown in red.\relax }}{82}
\contentsline {figure}{\numberline {\relax 4.7}{\ignorespaces Additional input variables to the diphoton BDT in data and MC. The distributions are for events which pass the full selection including a cut on the diphoton BDT output of 0.05. The expectation from a SM Higgs boson with 125 GeV is shown in red.\relax }}{83}
\contentsline {figure}{\numberline {\relax 4.8}{\ignorespaces Diphoton BDT distribution in data and MC. The contribution expected from a SM Higgs boson with mass 125 GeV, scaled by 100, is shown in red. \relax }}{84}
\contentsline {figure}{\numberline {\relax 4.9}{\ignorespaces Invariant mass distribution in data and MC after applying the full event selection in the range 100 to 180 GeV. The contribution expected from a SM Higgs boson with mass 125 GeV, scaled by 10, is shown in red. \relax }}{84}
\contentsline {figure}{\numberline {\relax 4.10}{\ignorespaces Diphoton BDT output distribution in $Z\rightarrow e^{+}e^{-}$ MC and data after the full selection treating the electrons as photons for the purposes of energy reconstruction. The electron veto is inverted to preferentially select electrons. The lower panel show the data/MC ratio.\relax }}{85}
\contentsline {figure}{\numberline {\relax 4.11}{\ignorespaces Per-photon resolution estimator, $\sigma _{E}$, relative to the measured energy in $Z\rightarrow e^{+}e^{-}$ MC and data treating the electrons as photons in the barrel (left) and endcaps (right). The red lines show the $\pm 1\sigma $ systematic error envelope obtained by scaling the value of $\sigma _{E}$ by $\pm 10\%$. The lower panels show the ratios to the nominal MC distributions.\relax }}{86}
\contentsline {figure}{\numberline {\relax 4.12}{\ignorespaces Photon ID BDT output in $Z\rightarrow e^{+}e^{-}$ MC and data treating the electrons as photons in the barrel (left) and endcaps (right). The red lines show the $\pm 1\sigma $ systematic error envelope obtained by shifting the output value by $\pm 0.025\%$. The lower panels show the ratios to the nominal MC distributions.\relax }}{87}
\contentsline {figure}{\numberline {\relax 4.13}{\ignorespaces Separation in $\eta $ between two identified jets in data and MC. The expectation from a SM Higgs boson produced via vector boson fusion ($qqH$), scaled by 100, is shown in red. All cuts other than the one on $\Delta \eta (Jet 1, Jet2)$ are applied to these distributions.\relax }}{88}
\contentsline {figure}{\numberline {\relax 4.14}{\ignorespaces Figure of merit for selection of the signal region cut value, $w$. Each colour shows the evaluation under different Higgs boson mass hypotheses.\relax }}{89}
\contentsline {figure}{\numberline {\relax 4.15}{\ignorespaces Signal to background ratio as a function of diphoton BDT output and $\Delta m/m_{H}$. The red lines indicate the cuts applied before the training and for applying the event selection. Darker shades indicate a regions with a higher signal to background ratio. The seven shades indicate the region contained in each of the seven BDT bins used for the signal extraction at $m_{H}= 123$ GeV.\relax }}{90}
\contentsline {figure}{\numberline {\relax 4.16}{\ignorespaces Signal efficiency vs background rejection curves for three different MVA techniques used to train the signal-background event discriminator. The curves give the (in)efficiencies for signal (background) after applying sequentially tighter cuts on the discriminator output.\relax }}{91}
\contentsline {figure}{\numberline {\relax 4.17}{\ignorespaces Signal and background BDT output distribution with the training sample (points) and testing sample (solid area) superimposed. The comparison is shown using an arbitrary uniform binning (left) and the bins used for extracting the signal (right).\relax }}{92}
\contentsline {figure}{\numberline {\relax 4.18}{\ignorespaces Comparison of the distributions of BDT output at $m_{H}=125$ GeV for data and background MC. The distributions are arbitrarily binned for the purposes of comparison only.\relax }}{93}
\contentsline {figure}{\numberline {\relax 4.19}{\ignorespaces Signal to background ratio as a function of BDT output bin. The red and blue histograms show the distribution after applying step 1 of the binning procedure before and after smoothing respectively. The black vertical lines indicate the boundaries of the final binning choice from the full procedure.\relax }}{95}
\contentsline {figure}{\numberline {\relax 4.20}{\ignorespaces Invariant mass distribution of the full 2011 dataset after selection over the mass range used in the analysis (100 to 180 GeV). The $\pm 2\%$ signal region for $m_{H}=124$ GeV is indicated in red, while the six corresponding sidebands are indicated as blue bands. The blue line is the double power law fit to the data for the background normalisation for this mass hypothesis.\relax }}{96}
\contentsline {figure}{\numberline {\relax 4.21}{\ignorespaces Total error on the background normalisation as a function of $m_{H}$ from different choices of the background shape parameterisation of $m_{\gamma \gamma }$. The total error for the one-parameter exponential and polynomial functions are off the scale of this plot.\relax }}{98}
\contentsline {figure}{\numberline {\relax 4.22}{\ignorespaces Distribution in data from the six sidebands corresponding to $m_{H}=125$ GeV of the two BDT input variables, diphoton BDT (left) and $\Delta m/m_{H}$ (right).\relax }}{99}
\contentsline {figure}{\numberline {\relax 4.23}{\ignorespaces Distribution in data from the six sidebands corresponding to $m_{H}=125$ GeV of the BDT output binned in the 7 BDT output bins used for signal extraction.\relax }}{99}
\contentsline {figure}{\numberline {\relax 4.24}{\ignorespaces Simultaneous fits to the six sidebands in data to determine the background shape for $m_{H}=124$ GeV. There are eight panels showing the result in each of the seven BDT bins plus one for the dijet tagged bin. The six black points in each panel are the fractional populations of the data in each sideband. The blue line represents the linear fit used to determine the fraction of background in each bin.\relax }}{101}
\contentsline {figure}{\numberline {\relax 4.25}{\ignorespaces Covariance matrix from the sideband fit to determine the background shape at $m_{H}=124$ GeV. The covariance matrix includes the additional 20\% systematic attributed to possible second order variations in the BDT output background distribution with mass.\relax }}{102}
\contentsline {figure}{\numberline {\relax 4.26}{\ignorespaces Relative total fit uncertainty on the background model in each bin at $m_{H}=130$ GeV as a function of the number of sidebands used in the fit to determine the shape of the background.\relax }}{103}
\contentsline {figure}{\numberline {\relax 4.27}{\ignorespaces Re-weighting applied to signal MC in which the $z$ position of the selected vertex is within 10mm of the true vertex as a function of $p_{T}^{H}$. The weights are derived from $Z\rightarrow \mu ^{+}\mu ^{-}$ events in data and MC.\relax }}{106}
\contentsline {figure}{\numberline {\relax 4.28}{\ignorespaces Top: Energy scale (left) and resolution (right) uncertainties in the $ggH$ signal model. The effect of $\pm 3\sigma $ variations derived in MC are shown with red dashed lines while the interpolated $\pm 3\sigma $ are shown with blue. Bottom: Variation in bin content at different quantiles (number of standard deviations from the nominal) for the three highest $S/B$ BDT bins. The blue and red markers indicate the yields extracted directly from MC while the black line indicates the quadratic interpolation function used to derive the $\pm 1\sigma $ variations for the signal model.\relax }}{107}
\contentsline {figure}{\numberline {\relax 4.29}{\ignorespaces Efficiency$\times $acceptance for a SM Higgs boson as a function of its mass ($m_{H}$) after applying all of the corrections to the MC. The blue bands indicate the error from each source of systematic uncertainty on the signal model summed in quadrature.\relax }}{108}
\contentsline {figure}{\numberline {\relax 4.30}{\ignorespaces Closure test for signal interpolation to intermediate mass points. The solid grey histogram is the result of a linear interpolation between the efficiency$\times $acceptance in each bin of the blue ($m_{H}=130$ GeV) and red ($m_{H}=140$ GeV) histograms. The efficiency$\times $acceptance from $ggH$ MC generated with mass 135 GeV is shown in black for comparison.\relax }}{110}
\contentsline {figure}{\numberline {\relax 4.31}{\ignorespaces BDT output distribution for $Z\rightarrow e^{+}e^{-}$ events in data and MC (left). Data/MC ratio for the BDT output distribution (right). The variation in MC due to the largest systematic uncertainties included in the signal model are shown for comparison.\relax }}{111}
\contentsline {figure}{\numberline {\relax 4.32}{\ignorespaces Observed number of events in data for each of the seven BDT bins and dijet bin at $m_{H}=125$ GeV. The background model is shown in blue along with the maximal $\pm 1/2\sigma $ variations. The expected contribution from a SM Higgs boson is shown in red~\citep {HIG-12-036}.\relax }}{112}
\contentsline {figure}{\numberline {\relax 4.33}{\ignorespaces Signal to background ratio in each of the seven BDT bins and dijet bin at $m_{H}=125$ GeV. The expected background is taken from the data-driven model described in Section~\ref {sec:backgroundmodel}. The error bars represent the uncertainty in the ratio due to the uncertainties in the background model.\relax }}{112}
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\contentsline {figure}{\numberline {\relax 5.1}{\ignorespaces Distributions of the test statistic $q_{\mu }$ under a background-only hypothesis ($\mu =0$) and signal plus background hypothesis ($\mu =0.6$) for a SM Higgs boson of mass 130 GeV. The distributions are normalised to unit area. The observed value of the test statistic from data is indicated by the black arrow.\relax }}{119}
\contentsline {figure}{\numberline {\relax 5.2}{\ignorespaces Normalised distribution of $q_{0}$ at $m_{H}=124$ GeV under the background-only hypothesis generated from toys (red histogram) and from the analytic form (green line). The observed value, $q_{0}^{obs}$, obtained from the data is indicated by the black arrow.\relax }}{121}
\contentsline {figure}{\numberline {\relax 5.3}{\ignorespaces Exclusion limits on SM Higgs boson production and subsequent decay to two photons in the range $110 < m_{H}< 150$ GeV. The black dashed line indicates the median expected value for the upper limit on $\mu $ given the size of the dataset while the green and yellow bands indicate the 68\% and 95\% quantile ranges respectively. The black solid line shows the observed upper limit extracted from the data at steps in $m_{H}$ of 100 MeV. Where this line falls below the red line at 1, a SM Higgs boson at that mass is excluded at the 95\% confidence level or more.\relax }}{123}
\contentsline {figure}{\numberline {\relax 5.4}{\ignorespaces Local p-value ($p_{0}$) calculated in steps of 100 MeV in the range $110<m_{H}<150$. The observed $p_{0}$ obtained from the data is shown in black while the expected value in the presence of a SM Higgs boson is given by the dashed blue line. The expectation from a Higgs boson with mass 125 GeV is shown as a red dashed line. The right hand scale shows the significance in standard deviations at each $m_{H}$.\relax }}{124}
\contentsline {figure}{\numberline {\relax 5.5}{\ignorespaces Best fit for the signal strength, $\mathaccentV {hat}05E{\mu }$, in steps of 100 MeV in the range $110<m_{H}<150$. The green bands indicate the 68\% uncertainty on $\mathaccentV {hat}05E{\mu }$ for a fixed $m_{H}$. The red line at 1 represents the expectation for a SM Higgs boson.\relax }}{125}
\contentsline {figure}{\numberline {\relax 5.6}{\ignorespaces Relationship between local and global p-values to determine the look-elsewhere effect in the $H\rightarrow \gamma \gamma $ search for the range 110 to 150 GeV. The yellow band indicates the statistical precision of the relationship due to the limited number of toys produced. The red line indicates a fit of an analytic relation between the two and is used to calculate the global p-value for larger local significances.\relax }}{126}
\contentsline {figure}{\numberline {\relax 5.7}{\ignorespaces Observed number of events in the 2012 dataset for each of the seven BDT bins and tight/loose dijet bins for $m_{H}=125$ GeV. The background model is shown in blue along with the maximal $\pm 1/2\sigma $ variations. The expected contribution from a SM Higgs boson is shown in red~\citep {HIG-12-036}.\relax }}{128}
\contentsline {figure}{\numberline {\relax 5.8}{\ignorespaces Exclusion limits on SM Higgs boson production and subsequent decay to two photons (left) and local p-value, $p_{0}$ (right) in the range $110 < m_{H}< 150$ GeV from the combined 2011 (7 TeV) and 2012 (8 TeV) datasets. In the left figure, the black dashed lines indicates the median expected value for the upper limit on $\mu $ given the size of the dataset while the green and yellow bands indicate the 68\% and 95\% quantile ranges respectively. The black solid line shows the observed upper limit. In the right figure, the observed $p_{0}$ obtained from the combined datasets is shown in black while the expected value in the presence of a SM Higgs boson is given by the black dashed line. The observed $p_{0}$ from the 2011 (7 TeV) and 2012 (8 TeV) datasets individually are shown by the blue and red dashed lines respectively. The right hand scale shows the significance in standard deviations at each $m_{H}$~\citep {HIG-12-036}.\relax }}{129}
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\contentsline {figure}{\numberline {\relax 6.1}{\ignorespaces Summary plots for the parameter \texttt {lumi} of the realistic counting experiment. The entries in the histograms are for fits to toys generated under the background-only hypothesis letting $\mu $ float freely. The red histogram includes only toys in which a positive signal strength is fitted. The bottom left panel shows the correlation between the value generated for the pseudo-measurement of the nuisance \texttt {lumi\_In} and the fitted value of the parameter. The bottom right panel shows the shape of the negative log-likelihood (NLL) as a function of the nuisance parameter. The parameters of the fitted Gaussian for each histogram are given as the Mean and Sigma. The value and error of the nuisance parameter are given before fitting to the data (Pre-fit), followed by the best fit value of the parameter under the background-only and signal-plus-background hypotheses.\relax }}{136}
\contentsline {figure}{\numberline {\relax 6.2}{\ignorespaces Median expected 95\% CL upper limits on $\mu =\sigma /\sigma _{SM}$ for the five Higgs boson decay channels and their combination in the absence of a Higgs boson as a function of $m_{H}$. The limits are given in the range 110-600 GeV (left) and 110-145 GeV (right). A channel which falls below 1, indicated by the dashed line, for some range is expected to exclude a Higgs boson in that range at the 95\% CL or more using this dataset~\citep {HIG-12-020}.\relax }}{137}
\contentsline {figure}{\numberline {\relax 6.3}{\ignorespaces Combined 95\% upper limits on the production cross-section of Higgs boson production relative to that of the Standard Model in the $m_{H}$ ranges 110-600 GeV (left) and 110-145 GeV (right)~\citep {HIG-12-020}. The median upper limits expected in the absence of a SM Higgs boson are indicated by the dashed black line and the 68\% and 95\% quantiles by the green and yellow bands respectively. The observed upper limits from the combined ICHEP 2012 dataset is shown by the black solid line. Where the observed limit is lower than 1 (red line), a SM Higgs boson with that $m_{H}$ is excluded at the 95\% confidence level.\relax }}{141}
\contentsline {figure}{\numberline {\relax 6.4}{\ignorespaces The observed local $p$-value, $p_{0}$ for sub-combinations of the low and high resolution channels and the overall combination as a function of $m_{H}$. The dashed line shows the expected $p_{0}$ at each $m_{H}$ should a SM Higgs boson exist with mass $m_{H}$~\citep {HIG-12-020}.\relax }}{142}
\contentsline {figure}{\numberline {\relax 6.5}{\ignorespaces Relationship between the local and global $p_{0}$ in the range 115-130 GeV. The red line indicates the analytic expression (shown) which is fit to the relationship derived from 10,000 pseudo-datasets.\relax }}{143}
\contentsline {figure}{\numberline {\relax 6.6}{\ignorespaces Distributions of the test statistic $q_{\mu }$ for the 0/1 jet bin of the $H\rightarrow \tau \tau $ analysis at the combined best fit mass, $m_{H} = 125.8$ GeV. The green and yellow filled regions indicate the 68\% and 95\% quantiles of the distribution respectively. The left distribution is generated at $\mu =2.28$ which lies outside of the 68\% confidence interval while the right distribution is generated at $\mu =1.34$ which lies inside the 68\% confidence interval. The values of the test statistic obtained from the observed data, $q_{\mu }^{obs}$, are indicated by the solid vertical lines.\relax }}{146}
\contentsline {figure}{\numberline {\relax 6.7}{\ignorespaces Confidence level evaluation curve for the $H\rightarrow \tau \tau $ analysis in the (0/1) jet bin. At each point, pseudo-data are generated with signal injected at the given value of $\mu $ and its confidence level (CL) calculated. Linear interpolation between the generated points is used to determine the 68\% confidence interval; the two values of $\mu $ (horizontal lines) which cross the curve at $1-CL_{s+b}=0.68$ (vertical red line).\relax }}{147}
\contentsline {figure}{\numberline {\relax 6.8}{\ignorespaces Left: One-dimensional scan of $q_{m_{x}}$ for the $H\rightarrow \gamma \gamma $, $H\rightarrow ZZ$ channels and their combination. For the combination, the relative signal strengths between the channels are allowed to float. The 68\% and 95\% confidence intervals for $m_{X}$ are determined as the values at which the curves cross the horizontal red lines. Right: 68\% confidence contours in $m_{X}$ and $\sigma /\sigma _{SM}$ for the $H\rightarrow \gamma \gamma $ and $H\rightarrow ZZ$ channels and their combination. For this combination, the relative signal strengths of the channels are kept fixed to the SM expectation~\citep {HIG-12-045}.\relax }}{148}
\contentsline {figure}{\numberline {\relax 6.9}{\ignorespaces 68\% confidence intervals for $\mu =\sigma /\sigma _{SM}$ for individual channels or combination of sub-channels determined using the Feldman-Cousins procedure (left) and by scanning the likelihood (right). The value of $\sigma /\sigma _{SM}$ denotes the production cross-section times the relevant branching fraction for a given channel, relative to the SM. The green band indicates the 68\% confidence interval on $\sigma /\sigma _{SM}$ for all channels combined. The intervals are determined at the best fit mass, $m_{H}=125.8$ GeV~\citep {HIG-12-045}.\relax }}{149}
\contentsline {figure}{\numberline {\relax 6.10}{\ignorespaces 68\% confidence contours for the production cross-section in $ggH$ and $ttH$ modes ($\mu _{ggH+ttH}$), and $VH$ and $qqH$ modes ($\mu _{VH+qqH}$), relative to the SM determined using the Feldman-Cousins procedure (left) and by scanning the likelihood (right). Each colour indicates the result by combining all sub-channels in a particular decay mode. The crosses indicate the best fit values of the two parameters. The yellow diamond at $(1,1)$ indicates the SM values. The contours are determined at the best fit mass, $m_{H}=125.8$ GeV~\citep {HIG-12-045}.\relax }}{150}
\contentsline {figure}{\numberline {\relax 6.11}{\ignorespaces The 68\% confidence contours extracted from data in the individual decay channels (coloured regions) and the full combination (solid line). The yellow square shows the SM value, while the fermiophobic and background-only scenarios are indicated by the pink dot and red diamond respectively~\citep {HIG-12-045}.\relax }}{152}
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\contentsline {figure}{\numberline {\relax A.1}{\ignorespaces Fitted correction functions for each of the 7 GCT regions covered by the ECAL and HCAL. The points are fit with the function of Equation~\ref {eqn:jecfit} to provide a parameterisation of the corrections to be applied to L1 jets.\relax }}{162}
\contentsline {figure}{\numberline {\relax A.2}{\ignorespaces Fitted correction functions for each of the 4 GCT regions covered by the HF. The points are fit with the function of Equation~\ref {eqn:jecfit} to provide a parameterisation of the corrections to be applied to jets online in the GCT.\relax }}{163}
\contentsline {figure}{\numberline {\relax A.3}{\ignorespaces Part one of the distributions of $E_{T}^{L1}-E_{T}^{Gen}$ in bins of $E_{T}^{L1}$ of the uncorrected MC jets. The fitted Gaussian is used to extract the resolution as a function of $E_{T}^{L1}$.\relax }}{165}
\contentsline {figure}{\numberline {\relax A.4}{\ignorespaces Part two of the distributions of $E_{T}^{L1}-E_{T}^{Gen}$ in bins of $E_{T}^{L1}$ of the uncorrected MC jets. The fitted Gaussian is used to extract the resolution as a function of $E_{T}^{L1}$.\relax }}{166}
\contentsline {figure}{\numberline {\relax A.5}{\ignorespaces Part one of the distributions of $E_{T}^{L1}-E_{T}^{Gen}$ in bins of $E_{T}^{L1}$ of the corrected MC jets. The fitted Gaussian is used to extract the resolution as a function of $E_{T}^{L1}$.\relax }}{167}
\contentsline {figure}{\numberline {\relax A.6}{\ignorespaces Part two of the distributions of $E_{T}^{L1}-E_{T}^{Gen}$ in bins of $E_{T}^{L1}$ of the corrected MC jets. The fitted Gaussian is used to extract the resolution as a function of $E_{T}^{L1}$.\relax }}{168}
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\contentsline {figure}{\numberline {\relax B.1}{\ignorespaces Total number of iterations in the binning optimization scan as a function of the broad step size $P$. The curve is shown for different numbers of final BDT boundaries. The minimum always occurs at the same value of $P$ as indicated by the green vertical line.\relax }}{173}
\contentsline {figure}{\numberline {\relax B.2}{\ignorespaces Increase in expected significance in the presence of a SM Higgs boson as the number of final BDT output bins is increased. The three curves show the improvement for different numbers of initial bins, $B$. The red curve is representative of the result obtained from performing the optimization procedure in the 2011 analysis.\relax }}{173}
\contentsline {figure}{\numberline {\relax B.3}{\ignorespaces Systematic uncertainties on the $ggH$ signal model. The effects of $\pm 3\sigma $ variations derived in MC is shown with red dashed lines while the interpolated $\pm 3\sigma $ are shown with blue.\relax }}{175}
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\contentsline {figure}{\numberline {\relax C.1}{\ignorespaces Per-event delta negative log-likelihood ($\Delta nll$) distributions for the background-only and signal-plus-background hypotheses in the ICHEP 2012 $H\rightarrow \gamma \gamma $ (left) and $H\rightarrow ZZ \rightarrow 4l$ (right) analyses. The distributions for the observed events from each channel are indicated by the black points. The likelihoods are evaluated for $m_{H}=125$ GeV at the best fit values of $\mu $ from the combination of these two channels only.\relax }}{178}
\contentsline {figure}{\numberline {\relax C.2}{\ignorespaces Comparison between 50\% (inner) and 75\% (outer) contours in data from the $H\rightarrow \gamma \gamma $ channel as determined using the Feldman-Cousins and a scan of $q_{{\mathbf {x}}}$ (labelled ``Likelihood Scan''). In the Feldman-Cousins technique, the constraints, $\mu _{ggH+ttH}\ge 0$ and $\mu _{VH+qqH}\ge 0$ are imposed. \relax }}{179}