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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\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} {~} @@ -1175,6 +1127,18 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{Method of moments} +{~} + \begin{minipage}{\textwidth} +\ARROW See {\color{blue}{\href{http://arxiv.org/abs/1503.04100}{arXiv::1503.04100}}}, F.Beaujean , M.Chrzaszcz, N.Serra, D. van Dyk for details.\\ +\ARROW The idea behind Method of Moments is extremely simple: + + + +\end{minipage} + \vspace*{2.1cm} +\end{frame}