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of the $\PBzero \to \PKstar \Pmuon \APmuon$, Selection} -{~} - \begin{minipage}{\textwidth} -\begin{columns} - -\column{0.5\textwidth} -\begin{itemize} -\item PID, kinematics and isolation variables used in a Boosted Decision Tree (BDT) to discriminate signal and background. -\item Reject the regions of $\PJpsi$ and $\Ppsi(2S)$. -\item Specific vetos for backgrounds: $\PLambdab \to \Pproton \PK \Pmu \Pmu$, $\PBs \to \Pphi \Pmu \Pmu$, etc. -\item Using k-Fold technique and signal proxy $\PB \to \PJpsi \PKstar$ for training the BDT. -\item Improved selection allowed for finer binning than the $1\invfb$ analysis. -\end{itemize} - - -\column{0.5\textwidth} - -\includegraphics[width=0.88\textwidth]{images/Fig1.pdf} \\ -\includegraphics[width=0.88\textwidth]{images/fold.png} - -\end{columns} - - - -\end{minipage} - \vspace*{2.1cm} -\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{LHCbs $\PBzero \to \PKstar \Pmuon \APmuon$, Selection} @@ -896,79 +868,119 @@ \vspace*{2.1cm} \end{frame} -\begin{frame}{Multivariate classification} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{Multivariate simulation} {~} \begin{minipage}{\textwidth} +\begin{columns} + +\column{0.5\textwidth} +\begin{itemize} +\begin{footnotesize} +\item PID, kinematics and isolation variables used in a Boosted Decision Tree (BDT) to discriminate signal and background. +\item BDT with k-Folding technique. +\item Completely data drive. +\end{footnotesize} +\end{itemize} +\begin{center} +\includegraphics[width=0.70\textwidth]{images/Chopping_Distrib.pdf} +\end{center} + +\column{0.5\textwidth} + +\includegraphics[angle=-90,width=0.82\textwidth]{images/Fig1.pdf} \\ +\includegraphics[width=0.88\textwidth]{images/fold.png} + +\end{columns} + + + +\end{minipage} + \vspace*{2.1cm} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{Multivariate simulation, efficiency} +{~} + + \begin{minipage}{\textwidth} \begin{footnotesize} -\begin{columns} -\column{0.2in} -{~} -\column{2in} -\ARROW Nature provided us with an excellent proxy channel:\\$\PBd \to \PKstar \PJpsi(\to \mu \mu)$.\\ -\ARROW Using the {\it{Splot}} technique one can train a MVA in purely data driven fashion.\\ -\ARROW The variables used in the classifier were selected primary on the basis of the MC modelling.\\ -\ARROW Additionally we have choose the variables that are uncorrelated in the helicity angles.\\ -\ARROW In order to increase the training performance a k-folding technique was used. - -\column{3in} +\ARROW BDT was also check in order not to bias our angular distribution: \begin{center} -\only<1>{ -\includegraphics[angle=-90,width=0.95\textwidth]{{images/FitJpsiKstar_1}.pdf} -} - - +\includegraphics[angle=-90,width=0.8\textwidth]{images/BDT_Eff_Comp.pdf} \end{center} +\ARROW The BDT has small impact on our angular observables. We will correct for this effects later on. -\end{columns} - - - \end{footnotesize} +\end{footnotesize} \end{minipage} \vspace*{2.1cm} \end{frame} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}{LHCb update of the $\PBzero \to \PKstar \Pmuon \APmuon$, Selection} + + +\begin{frame}{Mass modelling} {~} \begin{minipage}{\textwidth} - -\begin{itemize} -\item Signal modelled by a sum of two Crystal-Ball functions. -\item Shape is defined using $\PB \to \PJpsi \PKstar$ and corrected for $q^2$ dependency. -\item Combinatorial background modelled by exponent. -\end{itemize} - +\begin{tiny} \begin{columns} -\column{0.5\textwidth} -\begin{itemize} -\item $\PK \Ppi$ system: -\begin{itemize} -\item Rel. Breit Wigner for P-wave -\item Lass model for the S-wave. -\item Linear model for background. -\end{itemize} -\end{itemize} +\column{0.1in} +{~} +\column{2.5in} +\ARROW The signal is modelled by a sum of two Crystal-Ball function with common mean.\\ +\ARROW The background is a single exponent\\ +\ARROW The base parameters is performed in the proxy channel: $\PBd \to \PJpsi (\mu\mu) \PKstar$.\\ +\ARROW All the parameters are fixed in the signal pdf.\\ +\ARROW Scaling factors for resolution are determined from MC.\\ +\ARROW In fitting the rare mode only the signal, background yield and the slope of the exponential is left floating.\\ +\begin{center} +\includegraphics[angle=-90,width=0.9\textwidth]{images/msignal.pdf}\\ -\column{0.5\textwidth} - -\includegraphics[width=0.88\textwidth]{images/pbkg} - +\end{center} +\ARROW We got $624\pm30$ candidates in the most interesting $\left[1.1,6.0\right]~\GeV^2/c^4$ region \\ and $2398 \pm 57$ in the full range $\left[ 1.1, 19.\right]~\GeV^2/c^4$. +\column{2.5in} +\includegraphics[angle=-90,width=0.95\textwidth]{{images/FitJpsiKstar_withBDT_withoutPartially}.pdf}\\ +\includegraphics[angle=-90,width=0.95\textwidth]{{images/Scaling_factor}.pdf}\\ +\ARROW The S-wave fraction is extracted using a \texttt{LASS} model. \end{columns} -\begin{large} -\begin{itemize} -\item In total we found $2398\pm57$ candidates in the $(0.1,19)~\GeV^2$ $q^2$ region. -\item $624 \pm 30$ candidates in the theoretically the most interesting $(1.1-6.0)~\GeV^2$ region. -\end{itemize} -\end{large} - - - - +\end{tiny} \end{minipage} \vspace*{2.1cm} \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{Monte Carlo corrections} +{~} + \begin{minipage}{\textwidth} +\begin{footnotesize} +\ARROW No Monte Carlo simulation is perfect! One needs to correct for remaining differences.\\ +\ARROW We reweighed our $\PBd \to \PKstar \mu \mu$ Monte Carlo accordingly to differences between the $\PBd \to \PKstar \PJpsi$ in data (Splot) and Monte Carlo. +\only<1>{ +\begin{center} +\includegraphics[angle=-90,width=0.38\textwidth]{images/pt.pdf} +\includegraphics[angle=-90,width=0.38\textwidth]{images/vertex.pdf}\\ +\includegraphics[angle=-90,width=0.38\textwidth]{images/nTracks.pdf} +\end{center} +} +\only<2>{ +\begin{center} +\includegraphics[angle=-90,width=0.38\textwidth]{images/eta_logy.pdf} +\includegraphics[angle=-90,width=0.38\textwidth]{images/B0_p.pdf} \\ +\includegraphics[angle=-90,width=0.38\textwidth]{{images/bdt_data_mc_nominalMkpi}.pdf} +\end{center} +} + +\end{footnotesize} +\end{minipage} + \vspace*{2.1cm} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + @@ -977,6 +989,8 @@ \begin{frame}{Detector acceptance} {~} \begin{minipage}{\textwidth} +\begin{footnotesize} + \begin{columns} \column{0.6\textwidth} @@ -989,20 +1003,32 @@ \end{align*} where $P_i$ is the Legendre polynomial of order $i$. \item We use up to $4^{th}, 5^{th}, 6^{th}, 5^{th}$ order for the $\cos \thetal, \cos \thetak, \phi, q^2$. +\item The coefficients were determined using Method of Moments, with a huge simulation sample. +\item The simulation was done assuming a flat phase space and reweighing the $q^2$ distribution to make is flat. +\item To make this work the $q^2$ distribution needs to be reweighed to be flat. \end{itemize} - +%\includegraphics[width=0.75\textwidth]{images/q2PHSP.png} \column{0.4\textwidth} +\only<1>{ +\includegraphics[width=0.99\textwidth]{images/q2PHSP.png}\\ +\includegraphics[width=0.99\textwidth]{images/q2PHSPw.png} +} + +\only<2>{ \includegraphics[width=0.99\textwidth]{images/det.png} +} \end{columns} +\end{footnotesize} \end{minipage} \vspace*{2.1cm} \end{frame} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -1038,6 +1064,144 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{The columns of New Physics} +{~} + \begin{minipage}{\textwidth} +\includegraphics[width=0.95\textwidth]{images/columns.png} + + +\end{minipage} + \vspace*{2.1cm} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{The columns of New Physics} +{~} + \begin{minipage}{\textwidth} +\begin{enumerate} +\item Maximum likelihood fit: +\begin{itemize} +\item The most standard way of obtaining the parameters. +\item Suffers from convergence problems, under coverages, etc. in low statistics. +\end{itemize} +\item Method of moments: +\begin{itemize} +\item Less precise then the likelihood estimator ($10-15\%$ larger uncertainties). +\item Does not suffer from the problems of likelihood fit. +\end{itemize} +\item Amplitude fit: +\begin{itemize} +\item Incorporates all the physical symmetries inside the amplitudes! The most precise estimator. +\item Has theoretical assumptions inside! +\end{itemize} +\end{enumerate} + +\end{minipage} + \vspace*{2.1cm} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{The columns of New Physics} +{~} + \begin{minipage}{\textwidth} +\begin{enumerate} +\item Maximum likelihood fit: +\begin{itemize} +\item The most standard way of obtaining the parameters. +\item Suffers from convergence problems, under coverages, etc. in low statistics. +\end{itemize} +\item Method of moments: +\begin{itemize} +\item Less precise then the likelihood estimator ($10-15\%$ larger uncertainties). +\item Does not suffer from the problems of likelihood fit. +\end{itemize} +\item Amplitude fit: +\begin{itemize} +\item Incorporates all the physical symmetries inside the amplitudes! The most precise estimator. +\item Has theoretical assumptions inside! +\end{itemize} +\end{enumerate} + +\end{minipage} + \vspace*{2.1cm} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{Maximum likelihood fit} +{~} + \begin{minipage}{\textwidth} +\ARROW In the maximum likelihood fit one could weight the events accordingly to the $\dfrac{1}{\varepsilon(\cos \thetal, \cos \thetak, \phi, q^2)}$\\ +\ARROW Better alternative is to put the efficiency into the maximum likelihood fit itself: +\begin{align*} +\mathcal{L}=\prod_{i=1}^N \epsilon_i(\Omega_i, q_i^2) \mathcal{P}(\Omega_i, q_i^2) / \int \epsilon(\Omega, q^2) \mathcal{P}(\Omega, q^2) d\Omega dq^2 +\end{align*} +\ARROW Only the relative weights matters!\\ +\ARROW The Procedure was commissioned with TOY MC study.\\ +\ARROW Background is modelled with $2^{\rm nd }$ order Chebyshev polynomials, which was tested on the sidebands. + + + +\end{minipage} + \vspace*{2.1cm} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{Maximum likelihood fit} +{~} + \begin{minipage}{\textwidth} +\ARROW In the maximum likelihood fit one could weight the events accordingly to the $\dfrac{1}{\varepsilon(\cos \thetal, \cos \thetak, \phi, q^2)}$\\ +\ARROW Better alternative is to put the efficiency into the maximum likelihood fit itself: +\begin{align*} +\mathcal{L}=\prod_{i=1}^N \epsilon_i(\Omega_i, q_i^2) \mathcal{P}(\Omega_i, q_i^2) / \int \epsilon(\Omega, q^2) \mathcal{P}(\Omega, q^2) d\Omega dq^2 +\end{align*} +\ARROW Only the relative weights matters!\\ +\ARROW The Procedure was commissioned with TOY MC study.\\ +\ARROW Angular background component is modelled with $2^{\rm nd }$ order Chebyshev polynomials, which was tested on the side-bands. + + + +\end{minipage} + \vspace*{2.1cm} +\end{frame} + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{Results in $\PB \to \PKstar \Pmu \Pmu$} \begin{minipage}{\textwidth} \begin{center}