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\author{Marcin Chrzaszcz (CERN)}
\institute{UZH}
\title[FlavBit update]{FlavBit update}
\begin{document}
\tikzstyle{every picture}+=[remember picture]
{
\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}}
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\begin{center}
\begin{center}
\begin{columns}
\begin{column}{0.15\textwidth}
{~}
\end{column}
\begin{column}{0.02\textwidth}
{~}
\end{column}
\begin{column}{0.73\textwidth}
\bfseries \Huge {FlavBit update}
\end{column}
\begin{column}{0.02\textwidth}
{~}
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\end{center}
\quad
\vspace{3em}
\begin{columns}
\begin{column}{0.44\textwidth}
\flushright \vspace{-2.8em} {Florian Bernlochner\\ Jihyun Bhom\\ Marcin Chrzaszcz\\ Nazila Mahmoudi\\ Pat Scott}
%\flushright \vspace{-2.8em} { Marcin Chrzaszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
\end{column}
\begin{column}{0.53\textwidth}
\hspace{2.0cm}
\includegraphics[height=1.6cm]{cern}{~}
\includegraphics[height=1.6cm]{ifj.png} \\{~}{~}{~}
\includegraphics[height=0.8cm]{imperial.png}
\end{column}
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\vspace{1em}
\vspace{1.4cm}
\textcolor{normal text.fg!50!Comment}{Gambit collaboration meeting, June 6, 2019}
\end{center}
\end{frame}
}
\begin{frame}\frametitle{FlavBit: the past}
\begin{center}
\begin{columns}
\column{0.5\textwidth}
\ARROW Theory predictions calculated via SuperIso v2.3.\\
\ARROW Theoretical errors hard-coded and scaled if needed.\\
\column{0.5\textwidth}
\ARROW Experimental results are stored in YAML files and read by \texttt{Flav\_reader}.\\
\ARROW The class also store theoretical errors.\\
\ARROW Errors were symmetrized and other nasty assumptions were made.
\end{columns}
\begin{exampleblock}{Future}
Each of the elements of the code is there and we just need to put them together inside Gambit.
\end{exampleblock}
\end{center}
\end{frame}
\begin{frame}\frametitle{FlavBit: present and future}
\begin{center}
\begin{columns}
\column{0.5\textwidth}
\ARROW Theory predictions calculated via SuperIso v3+.\\
\ARROW Program can calculate theoretical errors for each scanning point.\\
\column{0.5\textwidth}
\ARROW Experimental results are stored in YAML files and read by external program called \texttt{HEPLike}.\\
\ARROW Very nice features included.
\end{columns}
\end{center}
\end{frame}
\iffalse
\begin{frame}\frametitle{HEP results}
\ARROW How do we publish results?
\begin{columns}
\column{0.35\textwidth}
\includegraphics[width=0.95\textwidth]{images/arxiv.png}\\
\pause
\begin{align*}
R_K=0.846^{+0.060 +0.016}_{-0.054 - 0.014}
\end{align*}
\pause
\column{0.65\textwidth}
\begin{center}
\includegraphics[angle=-90,width=0.5\textwidth]{images/FigS8.pdf}\\
\pause
\includegraphics[width=0.75\textwidth]{images/hepdata.png}
\end{center}
\end{columns}
\end{frame}
\begin{frame}\frametitle{HEP results}
\ARROW How are the results used?
\begin{columns}
\column{0.5\textwidth}
\ARROWR Correlations are neglected
\includegraphics[width=0.75\textwidth]{{images/Table_12}.pdf}
\ARROWR Non Linear effects are forgotten
\includegraphics[angle=-90,width=0.75\textwidth]{{images/example}.pdf}
\column{0.5\textwidth}
\ARROWR Errors are being symmetrized
\includegraphics[angle=-90,width=0.75\textwidth]{{images/Fig62aS}.pdf}
{~}\\{~}\\
\end{columns}
\end{frame}
\begin{frame}\frametitle{HEP results}
\ARROW How are the results used?\\{~}\\
\ARROWR Interpreting Upper limits [HLFAV, 90\% UL]:
\begin{align*}
\mathcal{B} (\tau \to \mu \mu e) < 9.9 \times 10^{-9}
\end{align*}
\ARROW People interpret this assuming it's a gaussian centered around $0$ and width $\frac{9.9\times 10^{-9}}{1.64} $.\\
\ARROW Usually a full p-value scan is published:
\begin{columns}
\column{0.5\textwidth}
\includegraphics[width=0.75\textwidth]{{images/180}.png}
\column{0.5\textwidth}
\includegraphics[width=0.75\textwidth]{{images/dupa}.png}
\end{columns}
\ARROW The examples go on and on...
\end{frame}
\begin{frame}\frametitle{The idea}
\ARROW The theory and experimental community need to work together about proper interpretation.
\pause
\begin{center}
\includegraphics[width=0.95\textwidth]{{images/kim}.jpg}
\end{center}
\end{frame}
\fi
\begin{frame}\frametitle{HEPLike}
\ARROW High Energy Physics Likelihood (HEPLike).
\begin{itemize}
\item Open source software.
\item With separate database of measurements.
\item Statistics library.
\item Can be interfaced with existing codes.
\end{itemize}
\ARROW It constructs the experimental likelihoods for you!\\
\ARROW Does work with both the $\chi^2$ and (log-)likelihood fits.\\
\ARROW Useful utilities for creating citations and database search.
\end{frame}
\begin{frame}\frametitle{HEPLike}
\ARROW The are couple of measurement types:
\begin{itemize}
\item Upper limits,
\item Single measurement with symmetric uncertainty,
\item Single measurement with asymmetric uncertainty,
\item Multiple measurements with symmetric uncertainty,
\item Multiple measurements with asymmetric uncertainty,
\item One dimensional likelihood function,
\item n-dimensional likelihood function.
\end{itemize}
\begin{alertblock}{Bonus}
In addition we provide a way for the future that the experiments can publish the dataset.
\end{alertblock}
\end{frame}
\begin{frame}\frametitle{HEPLike - code structure}
\begin{center}
\includegraphics[width=0.99\textwidth]{images/diagram.png}
\end{center}
\end{frame}
\begin{frame}\frametitle{Measurement encoding, \texttt{Hl\_Data}}
\ARROW Measurements are stored in \texttt{YAML} file:
\includegraphics[width=0.9\textwidth]{images/yaml.png} \\
\includegraphics[width=0.9\textwidth]{images/yaml2.png}
\end{frame}
\begin{frame}\frametitle{Upper limits, \texttt{HL\_Limit}}
\ARROW Example of published p-value scans:\\
\begin{columns}
\column{0.4\textwidth}
\includegraphics[angle=-90,width=0.95\textwidth]{images/Bs2tautau.pdf}
\column{0.6\textwidth}
\ARROW Information coded as:
\includegraphics[width=0.95\textwidth]{images/yaml3.png}
\end{columns}
\end{frame}
\begin{frame}\frametitle{Upper limits, \texttt{HL\_Limit}}
\begin{equation}
pdf(x) = \frac{1}{2^{1/2} \Gamma(1/2)} x^{1/2 -1} e ^{-x/2},
\end{equation}
which had the cumulative distribution function defined as:
\begin{equation}
cdf(x)=\frac{1}{\Gamma(1/2) } \gamma(1/2,x/2).
\end{equation}
In the above equations the $\Gamma(x)$ and $\gamma(k,x)$ correspond to Gamma and incomplete gamma functions.
By revering the $cdf(x)$ one can obtain the $\chi^2$ value:
\begin{equation}
\chi^2=cdf^{-1}(1-p),
\end{equation}
and if needed the log-likelihood:
\begin{equation}
-\log(\mathcal{L})= \frac{1}{2}\chi^2, \label{eq:wilks}
\end{equation}
\end{frame}
\begin{frame}\frametitle{Single measurement, symmetric error, \texttt{HL\_Gaussian}}
\ARROW Well this is as simple as:
\begin{center}
\includegraphics[width=0.6\textwidth]{images/yaml4.png}
\end{center}
\ARROW The $\chi^2$ is simple:
\begin{equation}
\chi^2 = \frac{(x_{obs}-x)^{2}}{ \sigma_{stat}^{2}+ \sigma_{syst}^{2} },
\end{equation}
\ARROW Wilks theorem can be used to translate to (log-)likelihood.
\end{frame}
\begin{frame}\frametitle{Single measurement, symmetric error, \texttt{HL\_Gaussian}}
\ARROW Well this is as simple as:
\begin{center}
\includegraphics[width=0.6\textwidth]{images/yaml4.png}
\end{center}
\ARROW The $\chi^2$ is simple:
\begin{equation}
\chi^2 = \frac{(x_{obs}-x)^{2}}{ \sigma_{stat}^{2}+ \sigma_{syst}^{2} },
\end{equation}
\ARROW Wilks theorem can be used to translate to (log-)likelihood.
\end{frame}
\begin{frame}\frametitle{Multiple measurement, symmetric error, \texttt{HL\_nDimGaussian}}
\ARROW You need to pass two arguments:
\begin{center}
\includegraphics[width=0.6\textwidth]{images/yaml5.png}
\end{center}
\ARROW From this one constructs the covariance matrix, and evaluates the $\chi^2$:
\begin{align}
\chi^2 = V^{T} {\rm Cov}^{-1} V,\label{eq:chi2ndim}
\end{align}
\end{frame}
\begin{frame}\frametitle{Measurement, asymmetric error, \texttt{HL\_BifurGaussian}, \texttt{HL\_ndimBifurGaussian}}
\ARROW You need to pass two arguments:
\begin{center}
\includegraphics[width=0.6\textwidth]{images/yaml6.png}
\end{center}
\ARROW We choose to interpret this as Bifurcated Gaussian:
\begin{align}
{\rm Cov}_{i,j}=
\begin{cases}
{\rm Corr}_{i,j}~\sigma^{i}_+ \sigma^{j}_+, & \text{if } x^i \geq x^i_{obs} \text{ and } x^j \geq x^j_{obs} \\
{\rm Corr}_{i,j}~\sigma^{i}_+ \sigma^{j}_-, & \text{if } x^i \geq x^i_{obs} \text{ and } x^j < x^j_{obs} \\
{\rm Corr}_{i,j}~\sigma^{i}_- \sigma^{j}_+, & \text{if } x^i < x^i_{obs} \text{ and } x^j \geq x^j_{obs} \\
{\rm Corr}_{i,j}~\sigma^{i}_- \sigma^{j}_-, & \text{if } x^i < x^i_{obs} \text{ and } x^j < x^j_{obs} \\
\end{cases}
\end{align}
\end{frame}
\begin{frame}\frametitle{Likelihoods, \texttt{HL\_ProfLikelihood}, \texttt{HL\_nDimLikelihood}}
\ARROW Here we add just the location of \texttt{ROOT} object.\\
\begin{columns}
\column{0.7\textwidth}
\begin{center}
\includegraphics[width=0.9\textwidth]{images/yaml7.png}\\
\includegraphics[width=0.9\textwidth]{images/yaml8.png}
\end{center}
\ARROW This is the best way to publish results!!!\\
\ARROW The problem is in what way one should publish the higher dim likelihoods?
\column{0.3\textwidth}
\includegraphics[angle=-90,width=0.95\textwidth]{images/Fig2-S.pdf}\\
\includegraphics[angle=-90,width=0.95\textwidth]{images/Fig21.pdf}
\end{columns}
\end{frame}
\begin{frame}\frametitle{Publishing data \texttt{HL\_ExpData}}
\ARROW The \texttt{YAML} entry:
\includegraphics[width=0.5\textwidth]{images/yaml9.png}\\
\ARROW Set the PDF you want to fit:\\ \texttt{double (*fun)(vector<double> par , vector<double> point)}\\
\ARROW The program will evaluate the (log-)likelihood on the whole dataset for given parameters.\\
\ARROW You only need a scanning tools and you are done.
\end{frame}
\begin{frame}\frametitle{Useful functions}
\ARROW Search for measurement you need:
\begin{center}
\includegraphics[width=0.9\textwidth]{images/example.png}
\end{center}
\ARROW Create citation file:
\begin{center}
\includegraphics[width=0.9\textwidth]{images/example2.png}
\end{center}
\end{frame}
\begin{frame}\frametitle{Other things in the pipeline, a bit lost but need to reactivated}
\ARROW Backending \texttt{flavio}.\\
\ARROW Backending \texttt{EOS}.\\
\end{frame}
\iffalse
\begin{frame}\frametitle{Check it out}
\ARROW The HEPLike code:\\
\url{https://github.com/mchrzasz/HEPLike}
\ARROW The HEPLike database:\\
\url{https://github.com/mchrzasz/HEPLikeData}
\begin{alertblock}{}
Don't be shy! Give it a spin. Feedback is welcomed.
\end{alertblock}
\pause
\begin{exampleblock}{}
\begin{center}
Thank you for your attention
\end{center}
\end{exampleblock}
\end{frame}
\fi
\backupbegin
\begin{frame}\frametitle{Backup}
\topline
\end{frame}
\backupend
\end{document}
Marcin Chrzaszcz