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......@@ -5,8 +5,8 @@
% Abstract Header:
\begin{center}
{\large Observation of a Standard Model Higgs boson and
a search for additional scalar in the \llll final state with the ATLAS detector}
{\large Observation of the Standard Model Higgs boson and
search for an additional scalar in the \llll final state with the ATLAS detector}
\vspace{0.5cm}
{\large Xiangyang Ju\\}
......@@ -24,16 +24,26 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Abstract Text:
This thesis presents the observation of a Standard Model Higgs boson and a
search for heavy resonances decaying into a pair of Z bosons that decays subsequently
to \llll.
The observation of a Standard Model Higgs boson uses the proton--proton
collision data at a center-of-mass energies of 7 and 8 TeV collected with ATLAS detector
during 2011 and 2012 at the Large Hadron Collider, while
the search for an additional scalar uses proton--proton collision data
at a center-of-mass energy of 13 \tev\ corresponding to an integrated luminosity of \lumiTot\
collected with the ATLAS detector during 2015 and 2016. The mass range of the hypothesized additional scalar
considered is from 200 \gev to 1.2 \tev. The results are interpreted as
upper limits on the production cross section of an additional scalar and are translated
to the exclusion contour in the content of Type-I and Type-II
two-Higgs-doublet models.
\ No newline at end of file
This thesis presents the observation of a Standard Model Higgs boson ($h$) and a
search for an additional scalar ($H$) in the $h/H \to \zz\to \llll$ channel (four-lepton channel),
where $\ell$ stands for either an electron or a muon.
The observation of a Standard Model Higgs boson in the four-lepton channel
uses the proton--proton collision data collected with the ATLAS detector
during 2011 and 2012 at center-of-mass energies of 7 and 8~\tev.
An excess with a local significance of 8.1 standard deviation is observed
in the four-lepton invariant mass spectrum around 125~\gev.
The mass of the excess measured in \llll channel is $125.51 \pm 0.52$~\gev.
Further measurements on the production cross section times branching ratio of the excess
agree well with the Standard Model predictions within the experimental uncertainties.
The search for an additional scalar uses an integrated luminosity of \lumiTot\
proton--proton collision data at a center-of-mass energy of 13 \tev\
collected with the ATLAS detector during 2015 and 2016.
The results of the search are interpreted as upper limits on the
production cross section of a spin-0 resonance.
The mass range of the hypothesized additional scalar
considered is between 200 \gev and 1.2 \tev.
The upper limits for the spin-0 resonance are translated to
exclusion contours in the content of Type-I and Type-II two-Higgs-doublet models.
This analysis is combined with
the same search in the $H\to ZZ\to \llvv$ channel to enhance the search sensitivities in the high mass region.
......@@ -6,4 +6,93 @@
\vspace{0.5cm}
Thanks.
First and foremost, I want to express my deepest sincere gratitude to my advisor,
Prof.~Sau Lan Wu,
for her patience, dedication and immense knowledge.
It has been a great honor to join her prestigious group in particle physics.
I am deeply grateful for all her contributions of time, ideas
and funding that make my particle physics endeavor successful.
Besides my advisor, I would like to thank the rest of my thesis
committee: Prof.~Lisa Everett, Prof.~Marshall Onellion,
Prof.~Kimberly Palladino and Prof.~Wesle Smith,
for their insightful comments and encourangement,
but also for the hard questions which incented me
to widen my research from various perspectives.
I give my sincere deep thanks to Dr.~Kamal Benslama, for
educating me with the fundamental knowledge of particle physics,
which, in turn, enables me to perform simple researches.
I enjoyed the days and nights we spent in searching for the first
candidate of $W$, $Z$ boson and top-pairs using the ATLAS detector.
I was very fortunate to take courses from the outstanding Wisconsin
professors, including Prof.~Robert Joynt, Prof.~Lisa Everett, Prof.~Aki Hashimoto
and Prof.~Michael Winokur and many others.
They equipped me with the knowledge needed for future research,
for which I really owe them a great thank you.
Distinguished members of the Wisconsin Group have influenced me
immensely in my particle physics endeavor.
I want to express my special thanks to Prof.~Luis Roberto Flores Castillo,
for supervising me on the search for the Standard Model Higgs boson
in the $H\to \zz\to \llll$ final state.
I thank Haoshuang Ji and Haichen Wang for teaching me
how to interpret research results using the statistical tools.
At different stages of my Ph.D program, I have been worked
closely with Laser Kaplan, Lashkar Kashif, Fuquan Wang, Andrew Hard and Hongtao Yang
on various topics.
I value the pleasant time working with them,
and I thank them for all the support and understanding they gave.
I thank Neng Xu, Wen Guan, Shaojun Sun for their timely and continuous support on computing.
I also thank other group members including Lianliang Ma, Swagato Banerjee, Yaquan Fang, Fangzhou Zhang,
Yang Heng, Yao Ming, Chen Zhou and Alex Wang for their friendship.
I enjoyed my six years in the ATLAS HSG2 (or HZZ) working group, working with
many talented scientists from all overall the world.
In the observation of the Standard Model Higgs analysis,
I give my special thanks to Konstantinos Nikolopoulos and
Christos Anastopoulos for their guidance and other helps.
The time working with them, along with Fabien Tarrade,
Eleni Mountricha, Meng Xiao, Valerio Ippolito and Luis, during the Higgs discovery time
was a precious period in my life.
I also thank Marumi Kado and Eilam Gross for their coordination of the Higgs working group.
I thank the group conveners including Stefano Rosati, Rosy Nikolaidou,
Robert Harrington for their coordination of the analyses and support to me on various aspects.
In the search for additional scalars effort, I would like to
give my sincere gratitude to Roberto Di Nardo, Arthur Schaffer and Giacomo Artoni
for their insights and guidance.
The analysis would not finish so swiftly and successfully,
without the help I received from other analysis team members.
I thank Denys Denysiuk, Graham Cree, Pavel Podberezko, Syed Haider Abidi,
Daniela Paredes Hernandez,
Marc Cano Bret and Prof. Haijun Yang, for their important contributions.
I also would like to thank the ATLAS editorial board
chaired by Patricia Ward for ensuring the quality of the publication with admirable amount of effort.
%I am deeply grateful to have supports from
% Bing Zhou, Fabio Cerutti, Arthur Schaffer, Marumi Kado and Konstantinos Nikolopoulos,
% when I apply for post-doctoral positions.
I want to thank Maurice Garcia-Sciveres and Ian Hinchliffe for
arranging me to visit LBNL and work with Maurice on Phase 2 Pixel upgrade.
I sincerely thank the LBNL engineer Cory Lee for his support
in making different metal parts that I needed.
I am also grateful for the direct helps from Karol Krizka and Timon Heim in solving
software issues.
During my short stay in LBNL, I appreciate the friendship of Berkeley colleagues.
Thank you to my friends from all over the world, particularly, Haiyun Teng,
Guoming Liu, Cuihong Huang, Jie Yu, Jin Wang,
Liang Sun, Huasheng Shao, Jie Zhang, Mingming Jiang, Xuan Zhao,
Haidong Liang, Chuanzhou Yi, Weidong Zhou, Jiecheng Ding and Mengyi Xu.
Life can be lonely, but I was fortunate to have you.
Finally, I would like to thank my family for
supporting me throughout my pursuing particle physics researches,
even though that means less time I can spend with them.
I owe them a debt, which I can never pay back.
This thesis is dedicated to them.
......@@ -73,8 +73,8 @@
\newcommand{\mfl}{\ensuremath{m_{4\ell}}\xspace}
\newcommand{\mll}{\ensuremath{m_{\ell\ell}}\xspace}
\newcommand{\mzz}{\ensuremath{m_{\text{\zz}}}\xspace}
\newcommand{\ttH}{t\={t}H\xspace}
\newcommand{\bbH}{b\={b}H\xspace}
\newcommand{\ttH}{\ensuremath{t\bar{t}H}\xspace}
\newcommand{\bbH}{\ensuremath{b\bar{b}H}\xspace}
% variables for mT
\newcommand{\mt}{\ensuremath{m_\text{T}}\xspace}
......
......@@ -4,5 +4,5 @@
\vspace*{6.0cm}
\begin{center}
{\large \textit{Dedication}} \\
{\large \textit{To my family}} \\
\end{center}
......@@ -220,6 +220,22 @@ T.~W.~B. Kibble, {\em {Symmetry breaking in nonAbelian gauge theories}\/},
\href{http://dx.doi.org/10.5170/CERN-2012-002}{CERN-2012-002 (2012) },
\href{http://arxiv.org/abs/1201.3084}{{\tt arXiv:1201.3084 [hep-ph]}}.
\bibitem{Heinemeyer:2013tqa}
{LHC Higgs Cross Section Working Group}, S.~Heinemeyer, C.~Mariotti,
G.~Passarino, and R.~Tanaka~(Eds.), {\em {Handbook of LHC Higgs Cross
Sections: 3. Higgs Properties}\/},
\href{http://dx.doi.org/10.5170/CERN-2013-004}{CERN-2013-004 (CERN, Geneva,
2013) },
\href{http://arxiv.org/abs/1307.1347}{{\tt arXiv:1307.1347 [hep-ph]}}.
%%CITATION = ARXIV:1307.1347;%%.
\bibitem{Heinemeyer:2016YR4}
{LHC Higgs Cross Section Working Group}, S.~Heinemeyer, C.~Mariotti,
G.~Passarino, and R.~Tanaka~(Eds.), {\em {Handbook of LHC Higgs Cross
Sections: 4. Deciphering the Nature of the Higgs Sector}\/},
\href{http://arxiv.org/abs/1610.07922}{{\tt arXiv:1610.07922 [hep-ph]}}.
%%CITATION = ARXIV:1610.07922;%%.
\bibitem{Georgi:1977gs}
H.~M. Georgi, S.~L. Glashow, M.~E. Machacek, and D.~V. Nanopoulos, {\em {Higgs
Bosons from Two Gluon Annihilation in Proton Proton Collisions}\/},
......
......@@ -89,23 +89,23 @@
\pagenumbering{roman}
% COMMENT OUT DEDICATION AND ACKNOWLEDGMENTS UNTIL FINAL:
% \include{Dedication} % *.tex file for dedication
% \include{Acknowledgments} % *.tex file for acknowledgments
\include{Dedication} % *.tex file for dedication
\include{Acknowledgments} % *.tex file for acknowledgments
\tableofcontents % *.toc file with table of contents
% COMMENT OUT LIST OF TABLES AND FIGURES UNTIL FINAL
%\addcontentsline{toc}{chapter}{LIST OF TABLES}
%\listoftables % *.lot file with list of tables
%
%\addcontentsline{toc}{chapter}{LIST OF FIGURES}
%\listoffigures % *.lof file with list of figures
%\pagebreak % Enforce the start of a new page
\addcontentsline{toc}{chapter}{LIST OF TABLES}
\listoftables % *.lot file with list of tables
\addcontentsline{toc}{chapter}{LIST OF FIGURES}
\listoffigures % *.lof file with list of figures
\pagebreak % Enforce the start of a new page
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Abstract %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\addcontentsline{toc}{chapter}{ABSTRACT}
%%\include{Abstract}
\addcontentsline{toc}{chapter}{ABSTRACT}
\include{Abstract}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Main Text %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
......
......@@ -5,7 +5,7 @@
\begin{center}
{\large Observation of the Standard Model Higgs boson and
search for additional scalars in the \llll final state with the ATLAS detector} \\
search for an additional scalar in the \llll final state with the ATLAS detector} \\
by \\
{\large Xiangyang Ju} \\
\vspace{2.0cm}
......@@ -36,7 +36,7 @@
\indent Marshall F Onellion, Professor, Physics \\
\indent Kimberly J. Palladino, Assistant Professor, Physics \\
\indent Wesley H Smith, Professor, Physics \\
\indent Sau Lau Wu, Professor, Physics \\
\indent Sau Lau Wu, Professor, Physics
\vfill\eject % End this page
......@@ -4,8 +4,8 @@
\subsection{Overview}
The non-resonant SM \zz continuum process,
whose cross section is about 10 times larger than
that of $H\to \zz$, is called \textit{irreducible background},
as it possesses the same final state as the \hzztollll does.
that of $H\to \zz$, is called the \textit{irreducible background},
as it possesses the same final state as the \hzztollll process.
The irreducible background is modeled by Monte Carlo (MC)
simulation with next-to-next-to-leading order QCD corrections
and next-to-leading order electroweak
......@@ -17,10 +17,10 @@ enter the four-lepton signal region via fake leptons,
which are reduced by imposing identification requirements.
The reducible backgrounds are important for the observation of the SM Higgs boson
but much less important for the search for additional scalars,
as they populate mainly in the low mass region.
as they populate mainly the low mass region.
The rate of these reducible backgrounds entering the signal region
is very low, requiring many simulated events in order to have small statistical uncertainties.
To cope with that, data-driven methods are employed to estimate the reducible backgrounds.
To cope with this, data-driven methods are employed to estimate the reducible backgrounds.
Minor contamination from tri-bosons and leptonic decay channels of \ttbar$+$Z is
modeled by MC simulation.
......@@ -32,7 +32,7 @@ via data-driven methods that follow a general procedure:
by relaxing or inverting isolation/impact parameter significance criteria and/or lepton
identification requirements;
\item study background compositions and shapes in these CRs,
\item measure fake rates for each background source in these CRs or
\item measure efficiencies for each background source in these CRs or
in additional other control regions.
\item extract background events in the signal region from the
CRs via transfer factors, which are calculated from MC simulation with corrections
......
......@@ -2,11 +2,10 @@
\section{Combination of the results from \llll and \llvv}
\label{ch:comb}
The \llll final state is featured by excellent mass resolution
while the \llvv benefits from the larger branching ratio.
The \llll and \llvv analyses compensate each other
when they are combined, leading to
to better search sensitivities over the whole mass range.
The \llll final state features excellent mass resolution
while the \llvv benefits from a larger branching ratio.
The \llll and \llvv analyses compliment each other
when they are combined, leading to better search sensitivities over the whole mass range.
Section~\ref{sec:llvv} provides an overview of the search
for heavy resonances in the \llvv final state.
Section~\ref{sec:correlation} describes the correlation schemes used in the combination,
......@@ -29,9 +28,9 @@ due to the same sources are fully correlated between/within the two analyses.
The uncertainties on QCD scale are uncorrelated for
the ggF/VBF signal productions and the \zz continuum backgrounds,
as the three processes are evaluated in different QCD scales;
but the uncertainties are correlated for \qqZZ and \ggZZ background.
The uncertainties on parton distribution functions are
fully correlated for ggF signal production and the \ggZZ background
but the uncertainties are correlated for the \qqZZ and the \ggZZ background.
The uncertainties on the parton distribution functions are
fully correlated for the ggF signal production and the \ggZZ background
as well as for VBF signal production and the \qqZZ background.
The uncertainties resulting from data-driven methods are uncorrelated.
A given correlated uncertainty is modeled in the fit by using a
......@@ -68,7 +67,7 @@ is excluded at 95\% confidence level by the \llvv search,
which is more sensitive in this mass range.
The excess at 240~\gev\ is not covered by the \llvv search,
the sensitivity of which starts from 300~\gev.
When combing the results from the two final states, the largest
When combining the results from the two final states, the largest
deviation with respect to the background expectation
is observed around 700~\gev\ with a global significance of
less than 1~$\sigma$ and a local significance of about 2~$\sigma$.
......
......@@ -4,7 +4,7 @@
The observation of the SM Higgs boson in the
decay channel \hzztollll is presented.
It uses $pp$ collision data corresponding to
integrated luminosity of 4.5~\ifb and 20.3~\ifb
integrated luminosities of 4.5~\ifb and 20.3~\ifb
at \sqs = 7~\tev\ and \sqs = 8~\tev, respectively,
recorded with the ATLAS detector at the LHC.
In the mass range 120 --- 130~\gev,
......@@ -40,7 +40,7 @@ during 2015 and 2016 at the Large Hadron
Collider at a centre-of-mass energy of 13~\tev\
corresponding to an integrated luminosity of \lumiTot.
The results of the search are interpreted as
upper limits on the production cross section of a spin-0 or spin-2 resonance. The mass range
upper limits on the production cross section of a spin-0 resonance. The mass range
of the hypothetical resonances considered
is between 200~\gev\ and 2000~\gev\ depending on the final state, and the model considered.
The spin-0 resonance is assumed to be a heavy scalar,
......
......@@ -7,13 +7,13 @@ The observation of the SM Higgs boson does not exclude the possibility
that it may be a part of an extended Higgs sector,
as predicted by several beyond the SM models~\cite{Hill:1987ea, Branco:2011iw}.
The search for additional heavy scalars in
the \llll final states uses an integrated luminosity of 36.1~\ifb\ $pp$ collision data at
the \llll final state uses an integrated luminosity of 36.1~\ifb\ $pp$ collision data at
\sqs = 13~\tev\ collected by ATLAS
during 2015 and 2016 to look for a peak structure
on top of a continuous background spectrum in the four-lepton invariant mass distribution.
The signal and background modeling is described in Section~\ref{ch:modeling},
followed by the evaluation of systematic uncertainties in Section~\ref{ch:sys}.
The results in the \llll final state is presented in Section~\ref{ch:results}.
The results in the \llll final state are presented in Section~\ref{ch:results}.
In order to improve the sensitivity of searching for a heavy scalar
in the high mass range, results from the \llll
and \llvv final states are combined.
......
......@@ -12,7 +12,7 @@
\multirow{2}{*}{Mass} & \multirow{2}{*}{Production mode} & \multicolumn{2}{c}{ggF-enriched categories} & \multirow{2}{*}{VBF-enriched category} \\
& & \mm channel & \ee channel & \\
\midrule
\multirow{2}{*}{300~\gev} & ggF & 6\% & 5\% & <0.05\% \\
\multirow{2}{*}{300~\gev} & ggF & 6\% & 5\% & $<0.05$\% \\
& VBF & 2.6\% & 2.4\% & 0.7\% \\
\midrule
\multirow{2}{*}{600~\gev} & ggF & 44\% & 44\% & 1\% \\
......
......@@ -2,13 +2,13 @@
% ATLAS detector
%\clearpage
\clearpage
\chapter{The Large Hadron Collider and the ATLAS detector}
\chapter{The LHC and ATLAS detector}
\label{ch:atlas}
%\section{The ATLAS detector}
%https://twiki.cern.ch/twiki/bin/view/AtlasPublic/AtlasTechnicalPaperListOfFigures
%\label{sec:atlas}
\section{The Large Hadron Collider}
\section{The LHC}
\label{ch:lhc}
The Large Hadron Collider (LHC) at the European Organization for Nuclear Physics (CERN)
is the world's largest and most powerful particle accelerator.
......
%% description of llvv analysis.
\subsection{Search for heavy resonances in the \llvv final state}
\label{sec:llvv}
The search for heavy resonances in the \llvv final state
is to select the events that contain two oppositely charged
isolated leptons that are originated from a on-shell $Z$ boson
The search for heavy resonances in the \llvv final state selects the events that contain two oppositely charged
isolated leptons originating from an on-shell $Z$ boson
along with a large missing transverse momentum (\met).
Different assumptions of the origin of the \met lead to
Different assumptions of the origin of \met lead to
different signal models, therefore
the \llvv final state is sensitive to different signal models.
For example, it is sensitive to the Higgs boson decays
to invisible particles when the \met is assumed to come from
to invisible particles when \met is assumed to come from
the invisible decay of the Higgs boson,
and sensitive to the dark matter production rate when the \met
is assumed to come from dark particles that are form dark matters.
and sensitive to the dark matter production rate when \met
is assumed to come from dark particles that form dark matter.
The two results are reported in Ref.~\cite{Aaboud:2017bja},
using 36.1~\ifb\ $pp$ collision data at \sqs = 13~\tev\ collected by ATLAS.
However, in this thesis, the \met is
presumably from the neutrinos that are decayed from the $Z$ boson.
However, in this thesis, \met is
presumably from the neutrinos that have decayed from the $Z$ boson.
For two on-shell $Z$ bosons, the branching ratio of $ZZ\to \llvv$
is 4.044\% and that of $ZZ\to \llll$ is 0.452\%, where $\ell$ stands for $e$ or $\mu$.
......@@ -43,15 +42,15 @@ are used depending on the instantaneous luminosity of the LHC.
The trigger efficiency for signal events passing the final
selection is about 99\%.
Selected events must have exactly two opposite-charge leptons of
the same flavor and the ``medium'' identification, with
the same flavor and ``medium'' identification, with
the more energetic lepton having $\pt > 30~\gev$\ and the other one
having $\pt > 20~\gev$.
The same impact parameter significance criteria as defined in Chapter~\ref{ch:sel}
are applied to the selected leptons.
Track- and calorimeter-based isolation criteria as defined in Chapter~\ref{ch:sel}
are also applied to the leptons, but in this analysis
the criteria are optimized such that by adjusting the isolation threshold
the selection efficiency of the isolation criteria is 99\% for
the criteria are optimized by adjusting the isolation threshold
so that the selection efficiency of the isolation criteria is 99\% for
signal leptons.
If an additional lepton with $\pt > 7~\gev$\ and ``loose''
identification is found then the event is rejected, to reduce the
......@@ -69,7 +68,7 @@ amount of \Zjets background. In signal events with no initial-
or final-state radiation the Z boson is expected to be produced
back-to-back with respect to the missing transverse momentum,
and this characteristic is used to further suppress the \Zjets background.
The azimuthal angle between dilepton system and the missing
The azimuthal angle between the dilepton system and the missing
transverse momentum ($\Delta\Phi(\ell\ell, \vecmet)$) is thus required to
be greater than 2.7 and the fractional \pt difference, defined as
$|p_\text{T}^{\text{miss,jet}} - \ptll|/\ptll$, to be less than 20\%,
......@@ -104,14 +103,14 @@ Table~\ref{tab:H2l2vacc}, for the ggF and VBF production modes as well as for
different resonance masses.
\input{texfiles/hllvv_acceptance}
The \llvv search starts only from 300~\gev because this is where it
The \llvv search starts only from 300~\gev\ because this is where it
begins to improve the combined sensitivity as the acceptance increases
due to a kinematic threshold coming from the \met selection criteria,
also seen from Table~\ref{tab:H2l2vacc}.
\paragraph{Background Estimation}
\label{sec:sigbkgllvv}
The dominant and irreduciable background for this search is the
The dominant and irreducible background for this search is the
non-resonant \ZZ production which accounts for about 60\% of the expected
background events.
The second largest background comes from the \WZ production ($\sim$30\%)
......@@ -132,7 +131,7 @@ for its normalization is extracted as the ratio of data events to
the simulated events in a \WZ-enriched control region, after subtracting
from data the non-\WZ background contribution.
The \WZ-enriched control region, called the $3\ell$ control region,
is built by selection $Z\to \ell\ell$ candidates with an additional
is built by selecting $Z\to \ell\ell$ candidates with an additional
electron or muon. This additional lepton is required to pass all
selection criteria used for the other two leptons, with the only
difference that its transverse momentum is required to be greater than
......@@ -163,7 +162,7 @@ leptons and \met. It is estimated by using a control sample of
events with lepton pairs of different flavour ($\emu$), passing
all analysis selection criteria.
Figure~\ref{fig:llvv_crs_sub2} shows the missing transverse momentum
distribution for \emu evens in data and simulation after applying
distribution for \emu events in data and simulation after applying
the dilepton invariant mass selection but before applying the
other selection requirements.
The non-resonant background in the \ee and \mm channels is estimated
......
......@@ -2,9 +2,9 @@
\clearpage
\subsection{\llee background}
\label{sec:bkg_zee}
The \llee reducible background originates mainly from the light-flavor jets ($f$),
The \llee reducible background originates mainly from light-flavor jets ($f$),
converted photons ($\gamma$) and heavy-flavor semileptonic decays ($q$).
A control region that enriches in events associated with each of these sources are
A control region enriched in events associated with each of these sources is
defined, namely the $3\ell+X$ control region,
allowing data-driven classification of reconstructed events into matching sources.
The efficiencies needed to extrapolate the different background
......@@ -14,17 +14,17 @@ in \pt and $\eta$ bins from simulation.
These simulation-based efficiencies are corrected to the ones measured in data
using another control region, denoted as $Z+X$.
The $Z+X$ control region has a leading lepton pair compatible with the decay
of a $Z$ boson, passing the full event selection;
and the additional object ($X$) satisfies the relaxed requirements as for the
of a $Z$ boson, passing the full event selection.
And the additional object ($X$) satisfies the relaxed requirements as for the
$X$ in the $3\ell+X$ control region.
Candidates in the $3\ell+X$ control region are selected by following the
standard analysis selections, but requiring relaxed selections on the lowest-\et electron:
only a track with minimum number of silicon hits which matches
only a track with a minimum number of silicon hits which matches
a cluster is required.
For the \RunOne analysis, the electron identification and isolation/impact
parameter significance selection criteria are not applied,
while for the \RunTwo analysis, the vertex and impact parameter significance
The electron identification and isolation/impact
parameter significance selection criteria are not applied.
For the \RunTwo analysis, the vertex and impact parameter significance
requirements are applied to reject the $q$ background source, which
is then estimated from MC simulation.
In addition, the subleading electron pair is required to have the
......@@ -37,7 +37,7 @@ The yields of different background sources are extracted from a template fit.
For the \RunOne analysis, two observables are used in the fit:
the number of hits in the innermost layer of the pixel detector ($\nBL$)
and the ratio of the number of high-threshold to low-threshold TRT hits ($\rTRT$),
allowing separations of $f$, $\gamma$ and $q$ components,
allowing separation of the $f$, $\gamma$ and $q$ components,
since most photons convert after the innermost pixel layer,
and hadrons faking electrons have a lower \rTRT compared to conversions and
heavy-flavor electrons.
......@@ -49,18 +49,19 @@ defined as the number of IBL hits, or the number of hits
on the next-to-innermost pixel layer when such hits are expected due to a dead area of the IBL.
The fitted results are shown in Figure~\ref{fig:8TeV_llee} for the \RunOne data sets
and in Figure~\ref{fig:13TeV_llee} for the \RunTwo data sets.
The \emph{sPlot} method~\cite{Pivk2005356} is used to unfold the contribution
The \emph{sPlot} method~\cite{Pivk2005356} is used to unfold the contributions
from the different background sources as a function of electron \pt.
To extrapolate the $f$, $\gamma$ and $q$ components (only for the \RunOne analysis)
To extrapolate the $f$, $\gamma$ and $q$ components
(the $q$ component is only presented in the \RunOne analysis)
from the $3\ell+X$ control region to the signal region, the efficiency for
the different components to satisfy all selection criteria is obtained from the
$Z+X$ simulation, and adjusted to match the measured efficiency in data.
The systematic uncertainty is dominated by the simulation efficiency corrections,
corresponding to 30\%, 20\%, 25\% uncertainties for $f$, $\gamma$, $q$, respectively,
corresponding to 30\%, 20\%, 25\% uncertainties for the $f$, $\gamma$, $q$, respectively,
for the \RunOne analysis,
and about 23\% uncertainties for $f$ and $\gamma$ for the \RunTwo analysis.
The final results for $2\mu2e$ and $4e$ reducible backgrounds are given
and about 23\% uncertainties for the $f$ and $\gamma$ for the \RunTwo analysis.
The final results for treducible backgrounds in the $2\mu2e$ and $4e$ channels are given
in Table~\ref{tab:llee_yields} for the Higgs analysis and the high-mass analysis.
\begin{figure}[!htbp]
......@@ -92,8 +93,8 @@ for background sources in the $3\ell+X$ control region.
together in the present plots.
The data are represented by the filled circles.
The sources of background electrons are denoted as light-flavor jets faking an electron
($f$, green dashed histogram), photon conversion ($\gamma$, yellow filled histogram).
Electrons from heavy-flavor quark semileptonic decays are negligibly small.
($f$, green dashed histogram) and photon conversion ($\gamma$, yellow filled histogram).
The number of electrons from semileptonic decays of heavy-flavor quarks are negligibly small.
The total background is given by the solid red histogram.
\label{fig:13TeV_llee}}
\end{figure}
......@@ -102,11 +103,14 @@ for background sources in the $3\ell+X$ control region.
\caption{
The fit results for the $3\ell+X$ control region, the extrapolation factors and the signal
region yields for the reducible \llee background.
The sources of background electrons are denoted as light-flavor jets faking an electron
($f$), photon conversion ($\gamma$)
and electrons from heavy-flavor quark semileptonic decays ($q$).
The second column gives the fit yield of each component in the $3\ell+X$ control region.
The corresponding extrapolation efficiency and signal region yield are in the next two
columns.
The background values represent the sum of the $2\mu2e$ and $4e$ channels.
The uncertainties are the combination of the statistical and systematic uncertainties.
The uncertainties are a combination of the statistical and systematic uncertainties.
\label{tab:llee_yields}}
\centering
......
......@@ -3,12 +3,12 @@
\label{sec:bkg_zmm}
The \llmm reducible background arises mainly from three components:
the semileptonic decays of $Z+$heavy-flavor (HF) jets,
the in-flight decays of $Z+$light-flavor (LF) jets and
the in-flight decays of $Z+$light-flavor (LF) jets, and
the decays of \ttbar process.
A reference control region that are enriched in the three components
with a good statistic is defined
by applying the analysis event selection except for the isolation and impact parameter
requirements to the two muons in the subleading dilepton pair.
A reference control region that is enriched in the three components
with good statistics is defined
by applying the analysis event selections, except for the isolation and impact parameter
requirements that are applied on the two muons in the subleading dilepton pair.
The number of events for each background component
in the reference control region is estimated from an unbinned
maximum likelihood fit, performed simultaneously to four orthogonal
......@@ -143,7 +143,7 @@ The systematic uncertainty in these transfer factors stems mostly
from the size of the simulated MC samples.
It is 6\% for $Z+$heavy-flavor jets,
60\% for $Z+$light-flavor jets and 16\% for \ttbar for the \RunOne analysis;
It is 12\% for $Z+$heavy-flavor jets, 70\% for $Z+$light-flavor jets, and 10\% for \ttbar
and it is 12\% for $Z+$heavy-flavor jets, 70\% for $Z+$light-flavor jets, and 10\% for \ttbar
for the \RunTwo analysis.
Furthermore, these simulation-based transfer factors
are validated with data using muons accompanying $Z\to \ell\ell$
......@@ -157,10 +157,10 @@ For the \RunTwo analysis, the mismodeling of the efficiency of isolation for
a light-flavor jet in simulation is observed, resulting in a
conservative 100\% systematic uncertainty for the $Z+$light-flavor jets.
The reducible background estimates in the signal region in full \mfl mass range are
The reducible background estimates in the signal region in the full \mfl mass range are
given in Table~\ref{tab:SR_llmm},
separately for the \sqs = 7~\tev, 8~\tev\ and 13~\tev\ data.
The uncertainties are separately into statistical and systematic contributions,
The uncertainties are separate into statistical and systematic contributions,
where in the latter the transfer factor uncertainty and the fit systematic uncertainty
are included.
......@@ -172,7 +172,7 @@ for the \sqs = 7~\tev, 8~\tev\ and 13~\tev\ data.
The $Z+$jets and \ttbar background estimates are data-driven and the $WZ$
contribution is from simulation.
The statistical and systematic uncertainties are presented in a sequential order.
Statistical uncertainty for $WZ$ contribution is negligible.
The statistical uncertainty for the $WZ$ contribution is negligible.
\label{tab:SR_llmm}
}
\begin{tabular}{ccc}
......
......@@ -61,7 +61,7 @@ The significance of the two excesses evaluated from maximum likelihood is presen
\caption{
Distribution of the four-lepton invariant mass $m_{4\ell}$ in the \llll final state for (a) the ggF-enriched category
(b) the VBF-enriched category. The last bin includes the overflow.
The simulated \mH = 600~\gev signal is normalized to a cross section corresponding
The simulated \mH = 600~\gev\ signal is normalized to a cross section corresponding
to five times the observed limit given in Section 8.5.4.
The error bars on the data points indicate the statistical uncertainty,
while the systematic uncertainty in the prediction is shown by the hatched band.
......@@ -98,15 +98,15 @@ each with a local significance of 3.6~$\sigma$ estimated
under the asymptotic approximation,
assuming the signal comes only from the ggF production.
The local $p_0$ has non-trival dependence on the signal hypothesis. It is checked that in the case of
signal models with LWA, the local significance is lower than the one under NWA,
signal models with the LWA, the local significance is lower than the one under the NWA,
indicating the two excesses are with narrow widths.
The global significance, taking into account the \textit{look-elsewhere-else} effect,
is evaluated from pseudo-data in the range of
$200~\gev < \mH < 1200~\gev$ assuming the signal comes only from the ggF production.
Each pseduo-data is generated from the background-only model by
Each pseudo-data is generated from the background-only model by
randomizing the global observables and the
expected yields, and then it is performed in the same way as for data to find the largest local
significance for each pseduo-data.
significance for each pseudo-data.
Figure~\ref{fig:pdf_localP} shows the distribution of the maximum local significance of each
pseudo-experiment. Therefore given the search region it is expected to have a local excess with
a significance of about 2.4~$\sigma$.
......@@ -142,9 +142,9 @@ are obtained as a function of \mH with the $CL_{s}$ procedure in the asymptotic
\refF{fig:NWAlimits_ggF} presents the expected and observed limits, at 95\%
confidence level, on the cross section time branching ratio of the heavy Higgs
decaying to \llll final state in steps of comparable to the detector resolution.
Without a specfic model, the ratio of the ggF cross section and VBF cross section
Without a specfic model, the ratio of the ggF cross section to the VBF cross section
is unknown, therefore, when setting limits on the ggF production the VBF cross section
is profiled, and vise versa.
is profiled, and vice versa.
This result is valid for models in which the width is less than 0.5\% of \mH.
\begin{figure}[!htbp]
......@@ -168,8 +168,8 @@ explained in Section~\ref{sec:h4l_interf_model}.
The total signal yields are parameterized as:
\[S = \mu \times S_{\text{H-only}} + \sqrt{\mu} \times (I_{H-B} + I _{H-h}) \]
where $\mu$ is the signal strength modifier,
the $S_{\text{H-only}}$ is the expected number of events for heavy scalar signal only,
$I_{H-B}$ and $I_{H-h}$ are the yields of the corresponding interference terms.
$S_{\text{H-only}}$ is the expected number of events for heavy scalar signal only,
and $I_{H-B}$ and $I_{H-h}$ are the yields of the corresponding interference terms.
Figure~\ref{fig:LWAlimits} shows the limits for widths of 1\%, 5\% and 10\% of \mH, respectively.
The limits are set for masses of \mH higher than 400~\gev.
......@@ -188,16 +188,16 @@ The limits are set for masses of \mH higher than 400~\gev.
\end{figure}
\subsection{2HDM interpretation}
A search in the context of a CP-conserving 2HDM, decribed in Section~\ref{sec:2hdm},
A search in the context of a CP-conserving 2HDM, described in Section~\ref{sec:2hdm},
is also presented.
Figure~\ref{fig:2HDM_tanb_cba_mH200} shows the exclusion limits in the \cosba versus \tanb plane
for Type-I and Type-II 2HDMs, for a heavy Higgs boson with mass of 200~\gev.
for Type-I and Type-II 2HDMs, for a heavy Higgs boson with a mass of 200~\gev.
This mass value is chosen so that the assumption of a narrow-width Higgs boson is valid over most
of the parameter space, and the experimental sensitivity is maximal.
The range of \cosba and \tanb presented is limited to the region where both the assumption of a
heavy narrow-width Higgs boson and the purtabativity
in calculating the cross section are valid.
The upper limits at a given value of \cosba and \tanb is re-calculated by using the predicted
The upper limits at a given value of \cosba and \tanb are re-calculated by using the predicted
ratio of ggF production rate over VBF.
\begin{figure}[!htbp]
\centering
......@@ -213,7 +213,7 @@ Figure~\ref{fig:2HDM_tanb_mH} shows the exclusion limits in the \cosba
versus \mH plane for $\cosba = -0.1$.
The valid range of \cosba is constrained by the measurement of the
coupling of the SM Higgs boson with the
Z-boson ($\kappa_h$), which is proportional to the $\sin(\beta - \alpha)$.
Z-boson ($\kappa_h$), which is proportional to $\sin(\beta - \alpha)$.
From the combined measurement of Higgs couplings at LHC~\cite{LHCcoupling2016},
the measured $\kappa_h$
is consistent with the SM prediction within the uncertainty of about 7\%, therefore the chosen
......@@ -242,12 +242,14 @@ is consistent with the SM prediction within the uncertainty of about 7\%, theref
\centering
\subfigure[]{\includegraphics[width=0.47\textwidth]{figures/Limits/exclusion-tanb-mH-cba01-typeI} \label{fig:2HDM_tanb_mH_1}}
\subfigure[]{\includegraphics[width=0.47\textwidth]{figures/Limits/exclusion-tanb-mH-cba01-typeII} \label{fig:2HDM_tanb_mH_2}}
\caption{The exclusion limits as function of \tanb and \mH with
\caption{The exclusion limits as a function of \tanb and \mH with
$\cos(\beta-\alpha) = -0.1$ for Type-I~\subref{fig:2HDM_tanb_mH_1} and Type-II~\subref{fig:2HDM_tanb_mH_2} 2HDM\@.
The green and yellow bands represent the $\pm1\sigma$ and $\pm2\sigma$ uncertainties
on the expected limits. The hatched area shows the observed exclusion.
\label{fig:2HDM_tanb_mH}}
\end{figure}
%
%\begin{figure}[!htbp]
% \centering
% \includegraphics[width=0.49\textwidth]{figures/fig_mH_br_1}
......@@ -267,5 +269,5 @@ on the expected limits. The hatched area shows the observed exclusion.
%\end{figure}
The hatched red area in this exclusion plots is the excluded parameter space.
Compared with the results prestented in Run 1~\cite{HIGG-2013-20},
Compared with the results presented in Run 1~\cite{HIGG-2013-20},
the exclusion limits presented here is almost twice more stringent.
\ No newline at end of file
This diff is collapsed.
......@@ -6,23 +6,23 @@ first reported in Ref.~\cite{HIGG-2011-05} in September 2011,
using an integrated luminosity of 2.1~\ifb\
$pp$ collision data at \sqs = 7~\tev.
The SM Higgs boson was excluded at 95\% confidence level (CL) in the
mass range 191--197, 199--200 and 214--224~\gev.
Five months later (Febrary 2012), this search was updated in Ref.~\cite{HIGG-2012-01} with
mass ranges 191--197, 199--200 and 214--224~\gev.
Five months later (February 2012), this search was updated in Ref.~\cite{HIGG-2012-01} with
an integrated luminosity of 4.8~\ifb\ $pp$ collision data at \sqs = 7~\tev.
The SM Higgs boson was excluded at 95\% CL in the mass
range 134--156, 182--233, 256--265~\gev.
ranges 134--156, 182--233 and 256--265~\gev.
In the same paper, three excesses were reported with local significances of 2.1, 2.2 and 2.1
standard deviations at 125~\gev, 244~\gev\ and 500~\gev, respectively.
Another five months later (July 2012), ATLAS reported the
observation of a new particle in the combined searches for the SM Higgs boson, where
the four-lepton analysis was the most sensitive channel for a 125~\gev\ SM Higgs boson with
an expected significance of 2.7 standard deviation~\cite{HIGG-2012-27}.
an expected significance of 2.7 standard deviations~\cite{HIGG-2012-27}.
Although the SM Higgs boson was discovered by the combination of different decay channels,
it is of great interest to discover the Higgs boson independently in the four-lepton final state alone.
After the discovery of a new particle, the four-lepton analysis was fully optimized to search for,
After the discovery of a new particle, the four-lepton analysis was fully optimized to search for
and measure a SM Higgs boson with a mass of about 125~\gev.
Section~\ref{sm_higgs_categorization} describes the categorization strategies that are designed
to prob different Higgs production modes, thus enhancing the overall sensitivities.
to probe different Higgs production modes, thus enhancing the overall sensitivities.
Background estimates are presented in Section~\ref{sec:smH_bkg}.
Since the mass of the Higgs boson was known~\cite{HIGG-2012-27, HIGG-2013-12}
and other properties could be simulated,
......@@ -30,19 +30,15 @@ the \RunOne Higgs analysis employed multivariate techniques in most categories t
either signal from \zz background or one production mode from others,
as presented in Section~\ref{sec:smH_mva}.
Furthermore, this analysis conducted two-dimensional fits in some categories
to reduce the statistic uncertainties.
%These improvement reduced the overall uncertainty dramatically
%despite being dependent on the Higgs modeling.
%The two-dimensional fit in the VBF-enriched category reduces the expected uncertainty
%on the signal strength of the VBF and VH production modes $\mu_{\text{VBF+VH}}$ by about 25\%.
to reduce the statistical uncertainties.
Section~\ref{sm_higgs_modeling} discusses the signal and background modeling
in each category, followed by the systematic uncertainties in Section~\ref{sm_higgs_sys}.
Final results based on the LHC \RunOne data sets are then presented in Section~\ref{sm_higgs_res}.
\section{Event categorization}
\label{sm_higgs_categorization}
The four-lepton candidates that are passed the selections described in Chapter~\ref{ch:sel}
are classified into one of these categories: VBF enriched, VH-hadronic enriched, VH-leptonica
The four-lepton candidates passing the selections described in Chapter~\ref{ch:sel}
are classified into one of these categories: VBF enriched, VH-hadronic enriched, VH-leptonic
enriched or ggF enriched.
A schematic view of the event categorization strategy is shown in Fig.~\ref{fig:sm_categories}.
\begin{figure}
......@@ -117,7 +113,7 @@ For the reducible backgrounds, the fraction of background
in each category is evaluated using simulation.
Applying these fractions to the background yields
of \llmm described in Section~\ref{sec:bkg_zmm} and
that of \llee in Section~\ref{sec:bkg_zee},
that of \llee in Section~\ref{sec:bkg_zee}
gives the reducible background estimates per category shown in
Table~\ref{tab:smH_reducible_bkg}.
......@@ -146,11 +142,11 @@ Channel & ggF enriched & VBF enriched & VH-hadronic enriched & VH-leptonic e
The analysis sensitivity is improved by employing three
multivariate discriminants to distinguish between
different classes of four-lepton events: one to separate the Higgs boson signal
from the \zz background in the include analysis,
from the \zz background in the inclusive analysis,
and two to separate the VBF- and VH-produced Higgs
boson signal from the ggF-produced Higgs boson signal
in the VBF enriched and VH-hadronic enriched categories.
These discriminants are based on boosted decision tree (BDT)~\cite{Speckmayer:2010zz}.
These discriminants are based on boosted decision trees (BDTs)~\cite{Speckmayer:2010zz}.
\paragraph{BDT for \zz background rejection}
The differences in the kinematics of the $H\to \zz\to \llll$
......@@ -188,6 +184,11 @@ The separation between a SM Higgs signal and the \zz background can be seen in F
As discussed in Sec.~\ref{sm_higgs_modeling}, the \bdtzz output is exploited
in the two-dimensional model built to measure the Higgs boson mass, the inclusive signal
strength and the signal strength in the ggF enriched category.
The signal strength $\mu$ is defined as the ratio of the measured Higgs boson production
cross section times the branching ratio
over that predicted by the SM\@.
Therefore, by definition, the SM predicted value of the signal strength
for the SM Higgs boson signla is 1 and for the SM background is 0.
\begin{figure}[!htb]
\subfigure[]{\includegraphics[width=0.45\textwidth]{SMHiggs/dzz} \label{fig:dzz}}
\subfigure[]{\includegraphics[width=0.45\textwidth]{SMHiggs/pt4l} \label{fig:pt4l}}
......@@ -278,7 +279,7 @@ and background (ggF events, blue) events.
\section{Signal and background modeling}
\label{sm_higgs_modeling}
To enhance analysis sensitivities different discriminants are used in different categories.
In \textbf{ggF-enriched category}, a two-dimensional (2D) fit to \mfl and the \bdtzz
In the \textbf{ggF-enriched category}, a two-dimensional (2D) fit to \mfl and the \bdtzz
output (\obdtzz) is used, because it provides the smallest expected uncertainties for
the inclusive signal strength measurements and the largest expected significance over
a background hypothesis.
......@@ -305,13 +306,13 @@ For the \zz and reducible \llmm backgrounds, the 2D probability density
distributions are derived from simulation, where \llmm simulation was shown to
agree well with data in the control region.
For the \llee background model, the two dimensional probability density can
only be obtained from data, which is done using the $3\ell + X$ data control regin
only be obtained from data, which is done using the $3\ell + X$ data control region
weighted with the transfer factor to match the kinematics of the signal region.
Figure~\ref{fig:m4l_vs_bdtZZ} shows the probability density in the $\obdtzz$--\mfl
plane, for the signal with \mH = 125~\gev, the \zz background from simulation
and the reducible background from the data control region.
With respect to a 1D approach, there is an expected reduction of the statistical
uncertainty for hte inclusive signal strength measurements, which
uncertainty for the inclusive signal strength measurements, which
is estimated from simulation to be approximately 8\% for both measurements.
Both the 1D and the 2D models are built using \mfl after applying
a Z-mass constraint to $m_{12}$ during the fit, as described in Chapter~\ref{ch:sel}.
......@@ -332,7 +333,7 @@ on \mfl for both signal and background.
The \bdtvbf output dependence on the Higgs boson mass is negligible and is neglected
in the probability density.
Adding the \bdtvbf in the VBF enriched category reduces the expected uncertainty on
signal strength of the VBF and VH production mechanisms $\mu_{\text{VBF+VH}}$ by about 25\%.
the signal strength of the VBF and VH production mechanisms $\mu_{\text{VBF+VH}}$ by about 25\%.
The improvement in the expected uncertainty on $\mu_{\text{VBF+VH}}$ reaches approximately
35\% after adding the leptonic and hadronic VH categories to the model.
......@@ -376,7 +377,7 @@ The impact is presented for the individual final states and for all channels com
The level of agreement between data and simulation for the efficiency of the isolation
and impact parameter requirements of the analysis is studied using a tag-and-probe
method. As a result, a small additional uncertainty on the isolaiton and
method. As a result, a small additional uncertainty on the isolation and
impact parameter selection efficiency is applied for electrons with \et below 15~\gev.
The effect of the isolation and impact parameter uncertainties on the signal strength
is given in Table~\ref{tab:smH_sys}.
......@@ -389,13 +390,13 @@ and their impact on the signal strength is given in Table~\ref{tab:smH_sys}.
Uncertainties on the predicted Higgs boson \pt spectrum due to those on the PDFs
and higher-order corrections are estimated to affect the signal strength by less than $\pm 1\%$.
The systematic uncertainty of the \zz background rate is around $\pm 4\%$ for \mfl = 125~\gev\
and increase for higher mass, averaging to around $\pm 6\%$ for the \zz production above 110~\gev.
and increases for higher mass, averaging to around $\pm 6\%$ for the \zz production above 110~\gev.
The main experimental uncertainty relating to categorization strategies is
related to the jet energy scale determination, including the uncertainties associated with
the modeling of the absolute and relative $in situ$ jet calibrations, as well as
the jet energy scale determination, including the uncertainties associated with
the modeling of the absolute and relative \textit{in situ} jet calibrations, as well as
the flavor composition of the jet sample.
The impact on the jets of the various categories is anticorrelated because
The impact of the jet uncertainties on the various categories is anticorrelated because
a variation of the jet energy scale results primarily in the migration of events
among the categories. The impact of the jet energy scale uncertainty
results in an uncertainty of about $\pm 10\%$ for the VBF enriched category,
......@@ -433,13 +434,13 @@ The number of observed candidate events for each of the four decay channels
in a mass window of 120--130~\gev\ and
the signal and background expectations are presented in Table~\ref{tab:smH_yields}.
Three events in the mass range $120 < \mfl < 130~\gev$ are corrected for FSR: one
$4\mu$ event and one $2\mu2e$ are corrected for nocollinear FSR,
$4\mu$ event and one $2\mu2e$ are corrected for non-collinear FSR,
and one $2\mu2e$ event is corrected for collinear FSR. In
the full mass spectrum, there are 8 (2) events corrected for collinear (noncollinear) FSR,
in good agreement with the expected number of 11 events.
\begin{table}[!htb]
\caption{
The number of events expected and observed for a \mH = 125~\gev hypothesis
The number of events expected and observed for a \mH = 125~\gev\ hypothesis
for the four-lepton
final states in a window of $120 < \mfl < 130~\gev$.
The second column shows the number of expected signal events for the full mass range,
......@@ -503,11 +504,12 @@ represented by the hatched areas.
The local $p_0$-value of the observed signal, representing the significance of the excess
relative to the background-only hypothesis, is obtained with the asymptotic approximation~\cite{Cowan2011}
using the 2D fit without any selection on \bdtzz output and is shown as a
fuction of \mH in Figure~\ref{fig:sm_localp0}.
The local $p_0$-value at the measured mass for this channel, 124.51~\gev, is 8.2 standard deviations.
function of \mH in Figure~\ref{fig:sm_localp0}.
The local significance of the excess observed at the measured mass for this channel,
124.51~\gev, is 8.2 standard deviations.
At the value of the Higgs boson mass, \mH = 125.36~\gev, obtained from the combination
of the $H\to\zz\to\llll$ and $H\to\gamma\gamma$ mass measurement~\cite{HIGG-2013-12},
the local $p_0$-value decreases to 8.1 standard deviations.
the local significance decreases to 8.1 standard deviations.
The expected significance at these two masses is 5.8 and 6.2 standard deviations, respectively.
\begin{figure}[!htb]
\centering
......@@ -519,12 +521,12 @@ as red and blue solid lines, respectively. The dashed curves show the expected
median of the local $p_0$-value for the signal hypothesis with a signal strength $\mu = 1$,
when evaluated at the corresponding \mH.
The horizontal dot-dashed lines indicate the $p_0$-values corresponding to local
significances of 1--8$\sigma$.
significances of 1--8~$\sigma$.
\label{fig:sm_localp0}}
\end{figure}
The measured Higgs boson mass obtained with the 2D method is
$\mH = 125.51 \pm 0.52~\gev$.
$\mH = 124.51 \pm 0.52~\gev$.
The signal strength at this value of \mH is
$\mu = 1.66_{-0.34}^{+0.398}\text{(stat)} _{-0.14}^{+0.21}\text{(syst)}$.
The production mechanisms are grouped into the ``fermionic'' and the ``bosonic'' ones.
......
\clearpage
\section{Statistical methodology}
\label{ch:stats}
%For purposes of discovering a new signal process,
%a null hypothesis, $H_0$, which includes only the known background processes,
%is defined to be tested against an alternative hypothesis, $H_1$,
%which includes both background and the sought after signal.
%When setting limits, the model with signal and background is treated as
%$H_0$, which is then tested against the background-only hypothesis, $H_1$.
The statistical interpretation of an analysis can be summarized by either a \textit{$p$-value}
for discovery purposes or
an \textit{upper limit} on one or more parameters of the signal model under test
for excluding any values of the parameter(s) that is/are above the upper limit.
an \textit{upper limit} on one or more parameters of the signal model under test.
The $p$-value is defined as the probability, under an assumption, of finding
data of equal or greater incompatibility with the predictions of the assumption.
The measure of incompatibility is based on a \textit{test statistics},
The measure of incompatibility is based on a \textit{test statistic},
such as the number of events in the signal region.
When the look-elsewhere-else effect~\cite{Gross:2010qma}
is taken into account in calculating a $p$-value,
......@@ -47,12 +39,12 @@ of $\mu$ and $\vect{\theta}$, respectively,
and the $\hat{\hat{\vect{\theta}}}(\mu)$ refers to the best fitted
values of $\vect{\theta}$ when
the parameters of interest are set to $\mu$ as constant values.
Neyman-Pearson lemma~\cite{10.2307/91247} indicated that the
test statistic of likelihood offers a good separation power for any types of hypotheses.
The Neyman-Pearson lemma~\cite{10.2307/91247} indicates that the
test statistic of likelihood offers good separation power for any type of hypotheses.
The final likelihood $\mathcal{L}$ is a multiplication of
The final likelihood $\mathcal{L}$ is a product of
the likelihood for each category $\mathcal{L}_i$,
each $\mathcal{L}_i$ consisting a Poisson term, likelihood functions and Gaussian
each $\mathcal{L}_i$ consisting of a Poisson term, likelihood functions and Gaussian
constraint terms:
\begin{equation}
\label{eq:likelihood}
......@@ -65,7 +57,7 @@ constraint terms:
\end{split}
\end{equation}
where $S^i$ and $B^i$ are the expected number of signal and background events in category $i$.
The $f_X(\vect{x}; \vect{\theta})$, the probability density function
$f_X(\vect{x}; \vect{\theta})$, the probability density function
of the observable $\vect{x}$,
usually depends on some systematic uncertainties $\vect{\theta}$,
such as lepton energy/momentum scale uncertainties.
......@@ -98,16 +90,17 @@ $\mu$ is the signal strength,
$\sigma$ is the total cross section;
$A\times C$ is the acceptance times efficiency;
$\int\mathcal{L}$ is the integrated luminosity of the dataset;
the $\brp$ is the branching ratio of $H\to\zz$
and the $\brd$ is that of $\zz\to \llll$.
$\brp$ is the branching ratio of $H\to\zz$
and $\brd$ is that of $\zz\to \llll$.
The advantage of factorizing the two branching ratios
is that for the search for additional scalars,
the \brp depends on the nature of the additional scalars
but the \brd is known from the SM
when both $ZZ$ are on-shell, $\brd(ZZ\to \llll) = 0.00452$, where $\ell$
\brp depends on the nature of the additional scalars
but \brd is known from the SM
when both $ZZ$ are on-shell.
$\brd(ZZ\to \llll) = 0.00452$, where $\ell$
stands for a $e$ or $\mu$,
allowing for setting upper limits on the $\sigma \times \brp$.
The term of $\epsilon(\vect{\theta})$ represents
allowing for setting upper limits on $\sigma \times \brp$.
The term $\epsilon(\vect{\theta})$ represents
the relative impact of systematic uncertainties $\vect{\theta}$.
%These parameters implicitly have dependence on the mass \mH and width
%\widthH of the hypothetical resonance.
......@@ -149,22 +142,22 @@ Ref.~\cite{Cowan2011} finds the probability distribution function of the profile
% \end{split}
%\end{equation}
likelihood ratio can be approximated by a $\chi^2$ function with
the same degree of freedoms as the one in the parameters of the interest.
the same number of degrees of freedom as the one in the parameters of the interest.
Consequently, the significance of the deviation of data from background-only
expectations can be obtained simply by $Z_\mu = \Phi^{-1}(1 - p_\mu) = \sqrt{q_\mu}$.
The limits setting is based on the $CL_s$ prescription~\cite{Read:2002hq},
The limit setting is based on the $CL_s$ prescription~\cite{Read:2002hq},
which protects from excluding the regions that the analysis is not sensitive to.
The confidence level of $CL_s$ is defined as
The confidence level $CL_s$ is defined as
$CL_s = \frac{p_{s+b}}{1 - p_b}$,
where $p_{s+b}$ is the $p$-value of signal plus
background asimov data~\footnote{
background Asimov data~\footnote{
a single representative data set of the ensemble of simulated data sets.},
and $p_b$ is the $p$-value of background-only asimov data.
and $p_b$ is the $p$-value of background-only Asimov data.
In general, the probability distribution function of $\qmu$ for
signal plus background and background-only asimov data follows the
asymptotic assumption~\cite{Cowan2011}, but the assumption would fail
if the expected background events are too small, for example less than one.
asymptotic assumption~\cite{Cowan2011}, but the assumption fails
if the number of expected background events is too small, for example less than one.
Therefore, the probability distribution functions constructed from pseudo experiments
are used as a cross check.
......
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