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Presentations / Zurich_group / 25_03_2014 / group_meeting.tex
@mchrzasz mchrzasz on 31 Mar 2014 11 KB update
  1. % This program can be redistributed and/or modified under the terms
  2. % of the GNU Public License, version 3.
  3. %
  4. % Seth Brown, Ph.D.
  5. % sethbrown@drbunsen.org
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  144. % see the macros.tex file for definitions
  145. \include{macros }
  146.  
  147. % title slide definition
  148. \title{Updates on activities.}
  149. %\subtitle{a bias report}
  150. \author{ Marcin Chrz\k{a}szcz$^{1,2}$ , Nicola Serra$^{1}$ }
  151. \institute[UTH, IFJ]
  152. {
  153. %\begin{tiny}
  154. $ ^1$ University of Zurich , $ ^2$ Institute of Nuclear Physics, Krakow,
  155. %\end{tiny}smallsmall
  156. }
  157.  
  158. \date{ \today }
  159. %--------------------------------------------------------------------
  160. % Introduction
  161. %--------------------------------------------------------------------
  162.  
  163. \begin{document}
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  191.  
  192. %--------------------------------------------------------------------
  193. % OUTLINE
  194. %--------------------------------------------------------------------
  195.  
  196.  
  197.  
  198.  
  199. \section[Outline]{}
  200. \begin{frame}
  201. \tableofcontents
  202. \end{frame}
  203.  
  204.  
  205.  
  206.  
  207. %-------------------------------------------------------------------
  208. % Introduction
  209. %-------------------------------------------------------------------
  210. %
  211. % Set the background for the rest of the slides.
  212. % Insert infoline
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  214. {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}}
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  216.  
  217. \title{Update on analysis}
  218.  
  219.  
  220. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  221. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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  226. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%2>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  227.  
  228. \section{$\Ptau \to 3\mu$ many solutions}
  229. \begin{frame}\frametitle{$\PDs \to \eta(\mu\mu\gamma)\mu \nu$}
  230. \only<1>
  231. {
  232. \begin{itemize}
  233. \item Last time I showed you the fits with $\eta$ background.
  234. \item Now the fits are updated with the $\eta$ calibrated $\PDs \to \eta(\mu\mu\gamma)\mu \nu$ yield.
  235. \item Still everything looks fine.
  236. \end{itemize}
  237. \includegraphics[scale=0.15]{eta/eta_bck.png} \\
  238. }
  239.  
  240.  
  241. \textref {M.Chrz\k{a}szcz, N.Serra 2014}
  242. \end{frame}
  243.  
  244. \begin{frame}\frametitle{$\PDs \to \eta(\mu\mu\gamma)\mu \nu$}
  245. \begin{columns}
  246. \column{1.25in}
  247. \includegraphics[scale=0.09]{figs/exp_with_eta_2011/pid_0p8_1p0001geo0p45_0p61.png} \\
  248. \column{1.25in}
  249. \includegraphics[scale=0.15]{figs/exp_with_eta_2011/pid_0p45_0p54geo0p28_0p32.png} \\
  250. \column{1.25in}
  251. \includegraphics[scale=0.15]{figs/exp_with_eta_2011/pid_0p45_0p54geo0p54_0p65.png} \\
  252. \end{columns}
  253. \begin{columns}
  254. \column{1.25in}
  255. \includegraphics[scale=0.15]{figs/exp_with_eta_2011/pid_0p54_0p63geo0p65_0p8.png} \\
  256. \column{1.25in}
  257. \includegraphics[scale=0.09]{figs/exp_with_eta_2011/pid_0p61_0p71geo0_0p26.png} \\
  258. \column{1.25in}
  259. \includegraphics[scale=0.09]{figs/exp_with_eta_2011/pid_0p61_0p71geo0p34_0p45.png} \\
  260. \end{columns}
  261.  
  262. \textref {M.Chrz\k{a}szcz, N.Serra 2014}
  263. \end{frame}
  264.  
  265.  
  266.  
  267.  
  268.  
  269. \begin{frame}\frametitle{Expected limit}
  270. \begin{itemize}
  271. \item Note was send to conveners on Monday.
  272. \end{itemize}
  273. \includegraphics[scale=1.4]{hahaha.jpg}
  274.  
  275. \begin{itemize}
  276. \item We decided to give two limits with $\PDs \to \eta(\mu\mu\gamma)\mu \nu$ and with $\eta$ veto.
  277. \end{itemize}
  278. V0 of the note(no systematics in the limit):
  279. \begin{enumerate}
  280. \item $\eta$ veto: $Br(\mu\mu\mu)<4.8\times 10^{-8}$
  281. \item $\eta$: $Br(\mu\mu\mu)<4.7\times 10^{-8}$
  282. \end{enumerate}
  283. Yesterday I evaluated the limits with background systematics. The limits gets around: $5.1\times 10^{-8}$
  284.  
  285.  
  286.  
  287.  
  288. \textref {M.Chrz\k{a}szcz, N.Serra 2014}
  289. \end{frame}
  290.  
  291.  
  292.  
  293. \section{$\PKstar\mu\mu$}
  294.  
  295.  
  296. \begin{frame}\frametitle{Unfolding for $\PKstar \mu \mu$}
  297. \begin{itemize}
  298. \item Recently every one had statistics problems.
  299. \item I felt alienated that i have none.
  300. \item Thank god that Nico provided some problem :)
  301. \end{itemize}
  302.  
  303.  
  304.  
  305. \textref {M.Chrz\k{a}szcz, N.Serra 2014}
  306. \end{frame}
  307.  
  308.  
  309.  
  310.  
  311.  
  312. \begin{frame}\frametitle{Nico hypothesis}
  313. We have our PDF:
  314. \begin{multline}
  315. PDF=\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( J_{1s}sin^2 \theta_k + J_{1c}cos^2 \theta_k + (J_{2s}sin^2 \theta_k + \\ J_{2c}cos^2) cos 2\theta_l + J_3 sin^2 \theta_k sin^2 \theta_l cos2\phi + J_4 sin2 \theta_k sin \theta_l cos\phi +\\ J_5 sin2 \theta_k sin \theta_l cos \phi + (J_{6s} sin^2 \theta_k + J_{6c} cos^2 \theta_k) cos \theta_l + \\ J_7 sin 2\theta_k sin \theta_l sin \phi + J_8 sin 2 \theta_k sin 2 \theta_l sin phi + J_9 sin^2 \theta_k sin^2 \theta_l sin 2 \phi)
  316. \end{multline}
  317. And corresponding moments measured moments: $M^{R}_i$ corresponding to the $i^{th}$ moment.
  318. Nicos hypothesis:
  319. The true Moments: $M^{T}_i = A^i_j M^{R}_j$.
  320. But he can't prove it and it looks insane at the first looks. So in the process of proving he is wrong I proved that this is true.
  321.  
  322.  
  323.  
  324.  
  325. \textref {M.Chrz\k{a}szcz, N.Serra 2014}
  326. \end{frame}
  327.  
  328. \begin{frame}\frametitle{Nico hypothesis, proof}
  329. So the true moments:
  330. $M^{T}_i = \int PDF f_i = J_i \int f_i^2= J_i \times const$
  331. Now for the measurements you need to have some efficiency: $\epsilon(dcos\theta_k, dcos\theta_l, d\phi)$, we assume it is $C^{\infty}$. So one can Taylor expand this function. \\
  332. The only thing I need to proof now is that the arbitrary element in the Taylor expansion can be write using all $J_i$ in the first order:
  333. $M^{R}_i=\int PDF f_i \cos\theta^x_k \cos^y\theta_l \phi^z = \sum_j J_j \int f_i f_j \cos\theta^x_k \cos^y\theta_l \phi^z = \sum_j J_j const_j$
  334. Which ends the proof. I calculated explicit matrix element correspond to $\cos\theta^x_k \cos^y\theta_l \phi^z $, but it's 3 pages long(in the attachment if one likes horrors).
  335.  
  336.  
  337.  
  338.  
  339.  
  340.  
  341. \textref {M.Chrz\k{a}szcz, N.Serra 2014}
  342. \end{frame}
  343.  
  344.  
  345.  
  346.  
  347. \begin{frame}\frametitle{Back to the unfolding}
  348.  
  349. The unfolding for the method of moments can(and will) be done with 2 unfolding approaches.
  350.  
  351. \begin{itemize}
  352. \item Unfolding using matrix.
  353. \item Unfolding using event weighting using the same weights as for the fits.
  354. \item We can check internal consistency.
  355. \end{itemize}
  356.  
  357.  
  358.  
  359.  
  360.  
  361.  
  362.  
  363. \textref {M.Chrz\k{a}szcz, N.Serra 2014}
  364. \end{frame}
  365.  
  366.  
  367.  
  368. \end{document}