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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Drell-Yan measurement]{Drell-Yan measurement} +\author{Marcin Chrz\k{a}szcz$^{1}$} +\institute{$^1$~University of Zurich} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz{~}} +\institute{(UZH)} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame}\frametitle{Outlook} +\begin{itemize} +\item Nicola performed this analysis for PhD. +\item Bringing the analysis towards publication. +\item Cross checking and trying to improve. +\item Nicola gave all the code with documentation. +\item I am old fashioned and rewrote the code from scratch. +\end{itemize} + + + +\end{frame} + +\begin{frame}\frametitle{Preselection} +\begin{itemize} +\item No Changes here. +\item Trigger lines: + +\begin{itemize} +\item \texttt{L0DiMuonDecision\_TOS}, \texttt{Hlt1DiMuonHighMassDecision\_TOS}, \texttt{Hlt2DiMuonDY(2,3,4)Decision\_TOS} +\end{itemize} +\item Selection: +\begin{itemize} +%\item a +\item \texttt{muminus\_TrEta>2.0}, \texttt{ muminus\_TrEta<4.5}, \texttt{muplus\_TrEta>2.0}, \texttt{ muplus\_TrEta<4.5}, \texttt{ min(muminus\_TrPChi2,muplus\_TrPChi2)>0.001}, \texttt{min(muminus\_P , muplus\_P)>10000}, \texttt{ min(muminus\_PT , muplus\_PT)>3000} +\end{itemize} +\end{itemize} + + +\end{frame} + +\begin{frame}\frametitle{Muon isolation} +\begin{itemize} +\item We define an isolation for a single track: +\end{itemize} +\includegraphics[width=0.95\textwidth]{images/iso1.png} +\begin{itemize} +\item And for 2 tracks: +\end{itemize} +\includegraphics[width=0.95\textwidth]{images/iso2.png} +\begin{itemize} +\item No changes here. +\end{itemize} +\end{frame} + + +\begin{frame}\frametitle{Background Templates} +\begin{itemize} +\item Now I started playing around :) +\item We have two sources of background: MissID and Heavy Flavour decays. +\item For now I take MissID for same sign data, and Heavy Flavour decays from selecting muons with Vertex $\chi > 50$. This cut is much larger what it was before. +\item For cross check I have 2 different sources of templates: MinBias(muon free), and IP cut(also tighter) instead of vertex. +\end{itemize} + + + + +\end{frame} +\begin{frame}\frametitle{Signal Templates -Nicola approach} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.95\textwidth]{images/Z0.png} +\begin{itemize} +\item $\PZzero$ is background free, take range of $80,100$ and we have a data $\mu\mu_{iso}$ for the $\PZzero$. +\item Determine the scale factor to minimalize the $\chi^2$ in MC. +\end{itemize} +\column{2.5in} +\includegraphics[width=0.95\textwidth]{images/scale.png}\\ +\includegraphics[width=0.85\textwidth]{images/chi2.png} +\end{columns} + + +\end{frame} + +\begin{frame}\frametitle{Signal Templates - My idea} +\begin{itemize} +\item Instead of extrapolating from $\PZzero$, let's try interpolating :) +\item \texttt{Splot}ed Both $\PZzero$ and $\PUpsilon(1S)$. +\end{itemize} +\begin{columns} +\column{1.6in} +\includegraphics[width=0.95\textwidth]{images/result_upsilon.png} +\column{1.6in} +\includegraphics[width=0.95\textwidth]{images/result_Z0.png} +\column{1.6in} +\includegraphics[width=0.95\textwidth]{images/result_1CB.png} +\end{columns} +\begin{itemize} +\item For $\PZzero$ we need to to use double CB. +\end{itemize} + +\end{frame} +\begin{frame}\frametitle{Signal Templates - My idea} +\only<1>{ +\begin{itemize} +\item Ok form \texttt{Splot} we have the $\mu\mu_{iso}$ for two mass points: $M_Z$ and $M_{\PUpsilon}$ +\item Ad hoc anzats to get the signal template for $M_X$: +\end{itemize} +\begin{equation} +\mu\mu_{iso, M_X} =\dfrac{M_X-M_{\PUpsilon}}{M_Z-M_{\PUpsilon}} \times T_Z + (1-\dfrac{M_X-M_{\PUpsilon}}{M_Z-M_{\PUpsilon}}) \times T_{\PUpsilon} +\end{equation} +} + +\only<2> +{ +\begin{center} +\begin{Large} +Attention, from this slide work has been done on jet lag, during confernece talks, in airplane, or all above. +\end{Large} +\end{center} + + +} + +\end{frame} +\begin{frame}\frametitle{Signal Templates - My idea, results} +\begin{itemize} +\item Some $M_{\mu\mu}, y$ bins don't converge. +\item But the ones that do look awesome (to be checked): +\end{itemize} +\includegraphics[width=0.95\textwidth]{images/dupa.png} + +\end{frame} + + \begin{frame}\frametitle{Todo} +\begin{itemize} +\item Those are just preliminary results! Don't bite my head off. +\item Want to compare the two method of obtaining signal templates. +\item Try different ''mixing'' functions. +\item See why some bins do not converge. +\item Lots of fun ahead. +\end{itemize} + +\end{frame} + + + +\end{document} diff --git a/Kstmumu/08_05_2015/mchrzasz.toc b/Kstmumu/08_05_2015/mchrzasz.toc new file mode 100644 index 0000000..ab3aa12 --- /dev/null +++ b/Kstmumu/08_05_2015/mchrzasz.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.24pt} +\select@language {english} diff --git a/Kstmumu/08_05_2015/mchrzasz_kstarmumu.aux b/Kstmumu/08_05_2015/mchrzasz_kstarmumu.aux new file mode 100644 index 0000000..e7da26e --- /dev/null +++ b/Kstmumu/08_05_2015/mchrzasz_kstarmumu.aux @@ -0,0 +1,41 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline 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+%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[$\PBzero \to \PKstar \mu\mu$ update]{$\PBzero \to \PKstar \mu\mu$ update} +\author{Marcin Chrz\k{a}szcz$^{1}$} +\institute{$^1$~University of Zurich} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz{~}} +\institute{(UZH)} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame}\frametitle{Reminder} +\begin{itemize} +\item Last time I show you how to get the $P_x$ distributions by simulating the bifurcated Gaussian. +\item Now how to get the mean and error on this distribution. +\end{itemize} + + + +\end{frame} + +\begin{frame}\frametitle{Basics} +\begin{itemize} +\item We cannot just take the expected $S_x$ and expected $F_l$ and calculate: $P_x =\dfrac{S_x}{\sqrt{F_l(1-F_l)}}$ to get expected $P_x$. +\item This will work only for Gaussian distributions(but not for bifurcated). +\item Proposal: Fit a parabola in range $[-0.5 \rm{RMS}, 0.5\rm{RMS}]$ +\item Get the most probable value. +\end{itemize} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.95\textwidth]{images/P1.pdf} +\column{2.5in} +\includegraphics[width=0.95\textwidth]{images/P5.pdf} + +\end{columns} + + + + +\end{frame} + + \begin{frame}\frametitle{Confidence interval} + \begin{small} + + +\begin{itemize} +\item Now just need to find the $68.27\%$ interval. +\item Draw a horizontal line $y=y_{max} \times 0.9$ +\item Iterate among all bins and select bins with events that have $y_{i~bin}>y$. +\item Find $y_{68}$ for which $68.27\%$ have the property$\sum y_{i~bin>y_{68}}=0.6827 $ +\item Find the two spots where the $y_{68}$ line crosses the distribution. +\item With current statistics I have $\mathcal{O}(10^{-4})$ error on the input $S_x$ and $\mathcal{O}(10^{-3})$ on output $P_x$. +\end{itemize} + \end{small} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.95\textwidth]{images/P1.pdf} +\column{2.5in} +\includegraphics[width=0.95\textwidth]{images/P5.pdf} + +\end{columns} + + +\end{frame} + + \begin{frame}\frametitle{Systematics} + \begin{small} + + +\begin{itemize} +\item To access systematics due to unfolding procedure we use the higher($+2$) order acceptance correction function on high statistics MC. +\item I noticed that some of the weights ($1/eff$) are super large ($>100$) or even negative which fucks up our distributions and creates larger systematics then it should be. +\item Repeated this study rejecting this events. +\end{itemize} + \end{small} +\begin{tiny} +\begin{tabular}{|c|c|c|c|c|c|c|c|c|} +$q^2$ & $F_l$ & $S_3$ & $S_4$ & $S_5$ & $S_6$ & $S_7$ & $S_8$ & $S_9$ \\ \hline +0 & 0.0022 & 0.005 & 0.0003 & 0.0077 & 0.0066 & 0.0080 & 0.0002 & 0.0032 \\ +1 & 0.0048 & 0.001 & 0.0014 & 0.0051 & 0.0088 & 0.0036 & 0.0048 & 0.0003 \\ +2 & 0.0004 & 0.0001 & 0.00013 & 0.0056 & 0.0046 & 0.0014 & 0.0003 & 0.0022 \\ +3 & 0.0002 & 0.0012 & 0.0007 & 0.0017 & 0.0001 & 0.0016 & 0.0011 & 0.0021 \\ +4 & 0.002 & 0.0004 & 0.0005 & 0.0015 & 0.0003 & 0.0009 & 0.0002 & 0.0010 \\ +5 & 0.006 & 0.0011 & 0.0007 & 0.0026 & 0.0014 & 0.0016 & 0.0015 & 0.0004 \\ +6 & 0.008 & 0.0019 & 0.0008 & 0.0024 & 0.0029 & 0.0033 & 0.0019 & 0.0000 \\ +7 & 0.0062 & 0.0015 & 0.0002 & 0.0011 & 0.0036 & 0.0028 & 0.0016 & 0.0005 \\ +8 & 0.0035 & 0.0037 & 0.0017 & 0.0046 & 0.0037 & 0.0005 & 0.0040 & 0.0040 \\ +9 & 0.005 & 0.0001 & 0.0004 & 0.0010 & 0.0009 & 0.0050 & 0.0043 & 0.0033 \\ +10 & 0.0011 & 0.0044 & 0.002 & 0.0060 & 0.0059 & 0.0101 & 0.0000 & 0.0012 \\ +11 & 0.0021 & 0.0018 & 0.0001 & 0.0020 & 0.0004 & 0.0052 & 0.0082 & 0.0059 \\ + +\end{tabular} +\end{tiny} + + +\end{frame} + + + + \begin{frame}\frametitle{The end} +\begin{itemize} +\item If we all agree with thouse procedure would like to put them in the note +\item Keep on working on other systematics. +\end{itemize} + +\end{frame} + + + + +\end{document} diff --git a/Kstmumu/08_05_2015/mchrzasz_kstarmumu.toc b/Kstmumu/08_05_2015/mchrzasz_kstarmumu.toc new file mode 100644 index 0000000..ab3aa12 --- /dev/null +++ b/Kstmumu/08_05_2015/mchrzasz_kstarmumu.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.24pt} +\select@language {english} diff --git a/Kstmumu/Edinburgh/beamerthemeSybila.sty b/Kstmumu/Edinburgh/beamerthemeSybila.sty new file mode 100644 index 0000000..b7d5cc7 --- /dev/null +++ b/Kstmumu/Edinburgh/beamerthemeSybila.sty @@ -0,0 +1,165 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + 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+\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + +%% Shortcuts %% +\newcommand{\aver}[1]{\langle #1 \rangle} +\newcommand{\dual}[1]{\tilde{#1}} +\newcommand{\est}[1]{\widehat{#1}} +\newcommand{\ie}{\textit{i.e.}} +\newcommand{\nuvec}{\vec{\nu}} +\newcommand{\order}[1]{\mathcal{O}\left({#1}\right)} +\newcommand{\refapp}[1]{app.~(\ref{app:#1})} +\newcommand{\refeq}[1]{eq.~(\ref{eq:#1})} +\newcommand{\reffig}[1]{fig.~(\ref{fig:#1})} +\newcommand{\refsec}[1]{sec.~(\ref{sec:#1})} +\newcommand{\reftab}[1]{tab.~(\ref{tab:#1})} +\newcommand{\rmdx}[1]{\mbox{d} #1 \,} % differential +\newcommand{\subd}{_{\text{d}}} +\newcommand{\subt}{_{\text{t}}} +\newcommand{\thvec}{\vec{\vartheta}} +\let\oldtheta\theta +\renewcommand{\theta}{\vartheta} +\let\eps\varepsilon +\newcommand{\vecest}[1]{\widehat{\vec{#1}}} +\newcommand{\wwhat}[1]{\widehat{\widehat{#1}}} +\newcommand{\xd}{x\subd} +\newcommand{\xt}{x\subt} +\newcommand{\Ekernel}{E(\xd|\xt)} +\newcommand{\pdf}{p.d.f.{~}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Extracting angular observables with Method of Moments]{Extracting angular observables\\ with Method of Moments} +\author{Marcin Chrz\k{a}szcz$^{1}$ \\in collaboration with \\Frederik Beaujean, Nicola Serra and Danny van Dyk,\\{~}\\ based on \href{http://arxiv.org/abs/1503.04100}{\textit{arXiv:1503.04100}} } +\institute{$^1$~University of Zurich} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz{~}} +\institute{(UZH)} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\tableofcontents + +\placelogotrue +\section{Motivation} +\begin{frame}\frametitle{Motivation} + +Likelihood(LL) fits even though widely used suffer from couple of draw backs: +\begin{enumerate} +\item In case of small number events LL fits suffer from convergence problems. This behaviour is well known and was observed several times in toys when we done $\PB \to \PKstar \Pmu \Pmu$. +\item LL can exhibit a bias when underlying physics model is not well known, incomplete or mismodeled. +\item The LL have problems converging when parameters of the \pdf are close to their physical boundaries, so-called ''boundary problem'' +\item Accessing uncertainty in LL in some cases requires application of computationally expensive Feldman-Cousins method. +\end{enumerate} + + + +\end{frame} + + + +\begin{frame}\frametitle{Method of Moments} +\begin{columns} +\column{0.05in}{~} +\column{2.2in} +\begin{center} MoM solves the above problems:\end{center} + +\column{2.in} +\only<3>{ +\begin{center} Drawback:\end{center} +} +\end{columns} + + + +\begin{columns} +\column{0.05in}{~} +\column{2.2in} +\only<1>{ +%\begin{center} MoM solves the above problems:\end{center} +\begin{exampleblock}{Advantages of MoM} + \begin{itemize} + \item Probability distribution function rapidity converges towards the Gaussian distribution. + \item MoM gives an unbias result even with small data sample. + \item Insensitive to large class of remodelling of physics models. + \item Is completely insensitive to boundary problems. + \end{itemize} +\end{exampleblock} +} +\only<2,3>{ +%\begin{center} MoM solves the above problems:\end{center} +\begin{exampleblock}{Advantages of MoM} + \begin{itemize} + \item Each observable can be determined separately from other. + \item Uncertainly follows perfectly $1/\sqrt{N}$ scaling. + \end{itemize} +\end{exampleblock} +} +\column{2.in} +\only<3>{ + +%\begin{center} Drawback:\end{center} +\begin{alertblock}{Advantages of MoM} + \begin{itemize} + \item Estimated uncertainty in MoM is larger then the ones from LL. + \end{itemize} +\end{alertblock} +} + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Method of Moments} +\begin{frame}\frametitle{Introduction to MoM} +Let us a define a probability density function \pdf of a decay: +\begin{align} +P(\nuvec, \thvec) \equiv \sum_i S_i(\nuvec) \times f_i(\thvec) +\end{align} +Let's assume further that there exist a dual basis: $\lbrace f_i(\thvec) \rbrace$, $\{\dual{f}_i(\thvec)\}$ that the orthogonality relation is valid: +\begin{equation} + \label{eq:def-ortho-rel} + \int_\Omega \rmdx{\vec{\theta}} \dual{f}_i(\thvec) f_j(\thvec) = \delta_{ij} +\end{equation} +Since we want to use MoM to extract angular observables it's normal to work with Legendre polynomials. In this case we can find self-dual basis: +\begin{equation} +\forall_i \dual{f}_i = f_i~, +\end{equation} + +just by applying the ansatz: $\dual{f}_i=\sum_i a_{ij} f_j$. + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}\frametitle{Determination of angular observables} +Thanks to the orthonormality relation Eq.~\ref{eq:def-ortho-rel} one can calculate the $S_i(\nuvec)$ just by doing the integration: +\begin{align} +S_i(\nuvec)=\int_\Omega d \thvec P(\nuvec, \thvec) \dual{f}_i(\thvec) +\end{align} +\pause +We also need to integrate out the $\nuvec$ dependence: +\begin{align}\label{eq:canonical} +\langle S_i \rangle= \int_\Theta d \nuvec \int_\Omega d \thvec P(\nuvec, \thvec) \dual{f}_i(\thvec) +\end{align} +\pause +MoM is basically performing integration in~Eq.~\ref{eq:canonical} using MC method: +\begin{align*} +E[S_i] \to \widehat{E[S_i]}=\dfrac{1}{N}\sum_{k=1}^{N} \dual{f}(x_k) +\end{align*} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}\frametitle{Uncertainty estimation} +MoM provides also a very fast and easy way of estimating the statistical uncertainty: +\begin{align} +\sigma (S_i)= \sqrt{\dfrac{1}{N-1}\sum_{k=1}^N ( \dual{f}_i(x_k) - \widehat{S_i} )^2 } +\end{align} +and the covariance: +\begin{equation} +\mathrm{Cov} [S_i, S_j]=\dfrac{1}{N-1} \sum_{k=1}^N [ \widehat{S_i} - \dual{f}_i(x_k) ][ \widehat{S_j} - \dual{f}_j(x_k) ] +\end{equation} +\pause +Thanks to the CLT both equations are satisfied. + + + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Systematic uncertainties} +\begin{frame}\frametitle{Partial Waves mismodeling} + + +\end{frame} + + +\begin{frame}\frametitle{Detector effects} + + + +\end{frame} + + + + + + + + +\end{document} diff --git a/Kstmumu/Edinburgh/mchrzasz.toc b/Kstmumu/Edinburgh/mchrzasz.toc new file mode 100644 index 0000000..d473083 --- /dev/null +++ b/Kstmumu/Edinburgh/mchrzasz.toc @@ -0,0 +1,5 @@ +\beamer@endinputifotherversion {3.24pt} +\select@language {english} +\beamer@sectionintoc {1}{Motivation}{2}{0}{1} +\beamer@sectionintoc {2}{Method of Moments}{7}{0}{2} +\beamer@sectionintoc {3}{Systematic uncertainties}{13}{0}{3}