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9b0da9b..e8ad7e5 100644 --- a/Kstmumu/Face2Face_meeting/Comparison/Comparison.out +++ b/Kstmumu/Face2Face_meeting/Comparison/Comparison.out @@ -1,5 +1 @@ \BOOKMARK [2][]{Outline0.1}{Introduction}{} -\BOOKMARK [2][]{Outline0.2}{Method of Moments - Theory}{} -\BOOKMARK [2][]{Outline0.3}{Moments of Ss}{} -\BOOKMARK [2][]{Outline0.4}{Toy MC study}{} -\BOOKMARK [2][]{Outline0.5}{S-wave}{} diff --git a/Kstmumu/Face2Face_meeting/Comparison/Comparison.pdf b/Kstmumu/Face2Face_meeting/Comparison/Comparison.pdf index cb262eb..3eab7ae 100644 --- a/Kstmumu/Face2Face_meeting/Comparison/Comparison.pdf +++ b/Kstmumu/Face2Face_meeting/Comparison/Comparison.pdf Binary files differ diff --git a/Kstmumu/Face2Face_meeting/Comparison/Comparison.synctex.gz b/Kstmumu/Face2Face_meeting/Comparison/Comparison.synctex.gz index 753bb0a..014b11e 100644 --- a/Kstmumu/Face2Face_meeting/Comparison/Comparison.synctex.gz +++ b/Kstmumu/Face2Face_meeting/Comparison/Comparison.synctex.gz Binary files differ diff --git a/Kstmumu/Face2Face_meeting/Comparison/Comparison.tex b/Kstmumu/Face2Face_meeting/Comparison/Comparison.tex index 8183995..f220aa0 100644 --- a/Kstmumu/Face2Face_meeting/Comparison/Comparison.tex +++ b/Kstmumu/Face2Face_meeting/Comparison/Comparison.tex @@ -10,6 +10,8 @@ \newcommand\abs[1]{\left|#1\right|} \usepackage{hepnicenames} \usepackage{hepunits} +\usepackage{color} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 @@ -44,1029 +46,436 @@ \section{Introduction} -\begin{frame}\frametitle{Introduction} -Why method of moments: -\begin{enumerate} -\item Complementary approach to LL fits. -\item Allows to extract info measuring quantities in event basis depending on the angular distribution. -\item Used in $\PB \to \rho \Plepton \nu$(SLAC-386 UC-414),\\ $\PJpsi \to \PK \PK \gamma$(PRD 71, 032005 (2005) ), etc. -\end{enumerate} - - -\end{frame} -\section{Method of Moments - Theory} -\begin{frame}\frametitle{Method of moments} -{~} -Let's assume we have our pdf with $k$ unknown parameters:~$PDF(x_i, \alpha)$, $dim(\alpha)=k$. One can calculate $k$ moments, which are the functions of $\alpha_i$: -\begin{equation} -\mu_i=f(\alpha_1,..., \alpha_k) = E[W_i] -\end{equation} -For $n$ events, we can estimate: -\begin{equation} -\widehat{\mu}_i=\dfrac{1}{n}\sum_{j=0}^{j=n-1} w_j -\end{equation} -, where $w_j=g(x_i)$ - -\end{frame} - -\begin{frame}\frametitle{Trivial example} -{~} -Lets see how this works in practice: -\begin{equation} -f(x)=\dfrac{x^{a-1}e^{-x/b}} {b^a \Gamma(a)} -\end{equation} -we measure the moments:\\ -\begin{center} $m_1=\dfrac{X_1+X_2+...+X_n}{n}$,\\ $m_2=\dfrac{X_1^2+X_2^2+...+X_n^2}{n}$.\\\end{center} -and calculate them analytically: -\begin{center} $m_1=ab$, $m_2=b^2a(a+1)$\end{center} -So one just needs to solve this and get the answer: -\center $a=\dfrac{m_1^2}{m_2-m_1^2}$, $b=\dfrac{m_2-m_1^2}{m_1}$ -\end{frame} - -\section{Moments of Ss} - - -\begin{frame}\frametitle{Our PDF} -{~} -The angular terms: -\begin{small} -\begin{multline} -PDF(\cos \theta_k ,\cos \theta_l, \phi) =\dfrac{9}{32\pi}( \dfrac{3}{4}(1-F_l)\sin^2 \theta_k + F_l \cos^2 \theta_k + (\dfrac{1}{4}(1-F_l)\sin^2 \theta_k \\ -F_l\cos^2) \cos 2\theta_l + S_3 \sin^2 \theta_k \sin^2 \theta_l cos2\phi + S_4 \sin2 \theta_k \sin \theta_l \cos\phi +\\ S_5 \sin 2 \theta_k \sin \theta_l \cos \phi + (S_{6s} \sin^2 \theta_k + S_{6c} \cos^2 \theta_k) \cos \theta_l + \\ S_7 \sin 2\theta_k \sin \theta_l \sin \phi + S_8 \sin 2 \theta_k \sin 2 \theta_l \sin \phi + S_9 \sin^2 \theta_k \sin^2 \theta_l \sin 2 \phi) -\end{multline} -\end{small} -\only<1>{ -Since we are fitting a PDF we need to ensure it is normalized: -\begin{equation} -\int_{-\pi}^{\pi} d\phi \int_{-1}^{1} d cos\theta_l \int_{-1}^{1} d cos\theta_k \dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=1 -\end{equation} -} -\only<2> -{ -\begin{small} -For further use let's introduce a notation: -\begin{multline} -PDF(\cos \theta_k ,\cos \theta_l, \phi) =\dfrac{9}{32\pi}( \dfrac{3}{4}(1-F_l)\sin^2 \theta_k + F_l \cos^2 \theta_k + \\(\dfrac{1}{4}(1-F_l)\sin^2 \theta_k -F_l\cos^2) \cos 2\theta_l + \sum_{x=3}^{9} S_x f_x(\cos \theta_k ,\cos \theta_l, \phi) -\end{multline} -\end{small} -} - -\end{frame} - -\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$ 1/2} -{~} -\begin{footnotesize} - - - -Let's calculate the moments(means of the given distribution): -\begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) \sin^2 \theta_k =\frac{2}{5} (2-F_l) -\end{equation} -\begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) \cos^2 \theta_k =\frac{1}{5} (2F_l+1) -\end{equation} -\begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) \cos^2 \theta_k =-\dfrac{2}{25}(2 + F_l) -\end{equation} -\begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) \sin^2 \theta_k =-\dfrac{1}{25}(1+8F_l) -\end{equation} -\end{footnotesize} - -\end{frame} - - -\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$ 2/2} -{~} - - -\begin{small} - -Let's calculate the moments(means of the given distribution): -\begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) f_{S_x}= \frac{8}{25}S_x, -\end{equation} -for $x=3,4,8,9$, and: - -%% -\begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) f_{S_x}= \frac{2}{5}S_x, -\end{equation} -for $x=5,6,7$.\\ -New physics apparently as we like orthogonal world: -\begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi~( f_{S_x} \times f_{S_y}) = \alpha_{xy} \delta_{x~y} -\end{equation} - -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} -{~} -\begin{itemize} -\item We are abusing the fact that the basis is orthogonal and moments do not mix. -\item Makes live easier and reduces the systematics. -\item Each of the S does not know about other. -\item In case of full PDF, $S_{1s}$, $S_{2s}$, $S_{1c}$, $S_{2c}$ $S_{6s}$, $S_{6c}$ are not orthogonal. -\item Still we can get them solving equation system: -\end{itemize} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin^2 \theta_k cos \theta_l = 0.1(S_6c+4S_6s) -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} cos \theta_l = 0.25(S_{6}c+2S_{6s}) -\end{equation} - -\small solution: $S_{6c}=2 (4 M_{S_{6c}} - 5 M_{S_{6s}})$, $S_{6s}= -2 M_{S_{6c}} + 5 M_{S_{6s}}$ - - - -\end{frame} - - - -\section{Toy MC study} - -\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} -{~} -Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.25]{images/J3.png} - -\column{2.5in} -\includegraphics[scale=0.25]{images/J9.png} - - -\end{columns} - -\end{frame} - - - - - -\begin{frame}\frametitle{Error Estimation} -{~} -\begin{itemize} -\item Since moment is the mean of a given distribution the error can be estimated as $mean/RMS$ -\item use TOY MC to check this assumption -\item Do not worry, detail description an numbers will come in other presentation. -\end{itemize} - -\includegraphics[scale=0.3]{plots/conw.png}\\ - - -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%5 -\begin{frame}\frametitle{Correlation check} -{~} -\begin{itemize} -\item In theory $S_i$ shouldn't be correlated to $S_j$ in the moment calculation. -\item Lets put this to a test. -\end{itemize} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.2]{plots/J9J4.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.2]{plots/J8J5.png}\\ - - -\end{columns} - - -\end{frame} - - -%%%%%%%%%%%%%%%%%%%%%%%%5 -\begin{frame}\frametitle{Correlation check 2} -{~} -\begin{itemize} -\item Let's now FIX $J_x$ and simulate different $J_y$ -\item Again theory would suggest that one J shouldn't know about the other, so $J_x$ shouldn't change with scanning $J_y$ parameter -\end{itemize} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.24]{plots/J5_vs_J9_300.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.24]{plots/J3_vs_J9_300.png}\\ - - -\end{columns} - - -\end{frame} - - - -\section{S-wave} - - - -\begin{frame}\frametitle{S-wave pollution} -{~} +\begin{frame}\frametitle{How to use Moments} \begin{columns} \column{3in} +\begin{enumerate} +\item Method of moments still uses fits. +\item Extended likelihood fit is used to extract number of signal and background events. +\item Calculate raw moments in bck window$~masss>5350$ and signal window$~mass\in[5230,5330]$ +\only<1>{\item Use a simple weighted average:} +\only<2>{\item Extract signal moments:} +\end{enumerate} + +\column{2.2in} +\includegraphics[width=0.9\textwidth]{mass3.png} + +\end{columns} +{~}\\ +\only<1>{ +\begin{equation} +M_{mix}= \dfrac{n_{sig} M_{sig}+n_{bkg}M_{bkg}}{n_{sig}+n_{bkg}} +\end{equation} +} +\only<2>{ +\begin{equation} +M_{sig}=\dfrac{ (n_{sig}+n_{bkg}) M_{mix}}{n_{sig}} - \dfrac{n_{bkg} m_{bkg}}{n_{sig}} +\end{equation} +} + +\end{frame} + +\begin{frame}\frametitle{How to use fits 1/2} +\begin{columns} +\column{3.0in} \begin{itemize} -\item Unfortunately in our perfect orthogonal world lives an imposter. -\item This imposter is $\PBzero \to (\PK \Ppi)_{S-wave}~\mu \mu$ -\item This "ghost" dilutes our NP! Like dark matter the universe. -\item We need something to bust this ghost away +\item Assuming we can decouple in the PDF the angular and mass part: +$PDF(\theta_l, \theta_k, \phi, m)= PDF_1(\theta_l, \theta_k, \phi) \times PDF_2(m)$ + +\item $PDF_1$ is our PDF defined in previous presentation. +\item $PDF_2$ is double CB as defined in Christoph toy creation. +\item For background we assume 2nd order Chebyshev polynomials($PDF_{1,bck}$) +\item And single exponential for bkg part($PDF_{2,bck}$) \end{itemize} -\column{2in} -\includegraphics[width=0.95\textwidth]{P5.png}\\ - -\includegraphics[width=0.5\textwidth]{gb.jpg} +\column{2.2in} +\includegraphics[width=0.6\textwidth]{cosk_tmp.png}\\ +\includegraphics[width=0.6\textwidth]{cosl_tmp.png} \end{columns} - \end{frame} - - - - -%%%%%%%%%%%%%%%%%%%5 -\begin{frame}\frametitle{S-wave hunting} -{~} -Our PDF with the S-wave will look as follows: -\begin{multline} -PDF_{full}(\cos \theta_k ,\cos \theta_l, \phi) =\dfrac{9}{32\pi}( \textcolor{red}{(1-F_s)}(\dfrac{3}{4}(1-F_l)\sin^2 \theta_k + F_l \cos^2 \theta_k + \\ (\dfrac{1}{4}(1-F_l)\sin^2 \theta_k -F_l\cos^2) \cos 2\theta_l + S_3 \sin^2 \theta_k \sin^2 \theta_l cos2\phi + \\S_4 \sin2 \theta_k \sin \theta_l \cos\phi + S_5 \sin 2 \theta_k \sin \theta_l \cos \phi + \\ (S_{6s} \sin^2 \theta_k + S_{6c} \cos^2 \theta_k) \cos \theta_l + S_7 \sin 2\theta_k \sin \theta_l \sin \phi + \\ S_8 \sin 2 \theta_k \sin 2 \theta_l \sin \phi + S_9 \sin^2 \theta_k \sin^2 \theta_l \sin 2 \phi) + \\ -\textcolor{red}{\dfrac{2}{3} F_s \sin^2 \theta_l + \frac{4}{3} A_s \sin^2 \theta_l \cos \theta_k + I_4 \sin \theta_k \sin 2 \theta_l \cos \phi} \\ \textcolor{red}{+ I_5 \sin \theta_k \sin \theta_l \cos \phi + I_7 \sin \theta_k \sin \theta_l + \sin \phi + I_8 \sin \theta_k \sin 2\theta_l \sin\phi}) -\end{multline} - -\small In this form we ensure normalization. -\end{frame} - -\begin{frame}\frametitle{How does the dilution work? 1/2} -{~} -\begin{small} -\begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF_{full}(\cos \theta_k ,\cos \theta_l, \phi) f_{S_x}= \frac{8}{25}S_x\textcolor{red}{(1-F_s)}, -\end{equation} -for $x=3,4,8,9$, and: - -%% -\begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF_{full}(\cos \theta_k ,\cos \theta_l, \phi) f_{S_x}= \frac{2}{5}S_x\textcolor{red}{(1-F_s)}, -\end{equation} -for $x=5,6,7$.\\ -Not much harm and easy to control. -\end{small} - -\end{frame} - -\begin{frame}\frametitle{How does the dilution work? 2/2} -{~} -\begin{small} -Unfortunately $F_l$ and $F_s$ will mix with each other: -\begin{multline} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF_{full}(\cos \theta_k ,\cos \theta_l, \phi) \sin^2 \theta_k= \\ \frac{2}{15} (6 + 3 F_l (F_s-1) - F_s)=M_{F_l} -\end{multline} -\begin{multline} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF_{full}(\cos \theta_k ,\cos \theta_l, \phi) \sin^2 \theta_l= \\ \frac{1}{5} (3 + F_l + F_s - F_l F_s)=M_{F_s} -\end{multline} - -They can solve this system: - -$ \begin{cases} F_s = \frac{15}{4} (M_{F_l} + 2 M_{F_s}) \\ F_l = \frac{(15 M_{F_l} + 10 M_{F_s}-18)}{(15 M_{F_l} + 30 M_{F_s}-34)} \end{cases}$ - - -\end{small} - -\end{frame} - - -\begin{frame}\frametitle{S-wave moments} -{~} -We can even measure directly the S-wave: -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_l cos \theta_k = \dfrac{32 I_{1b} }{45} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin \theta_k sin 2 \theta_l cos \phi = \dfrac{16 I_4 }{45} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin\theta_k sin\theta_l cos\phi = \dfrac{4 I_5 }{9} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin 2 \theta_l sin \phi = \dfrac{4 I_7 }{9} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin2 \theta_l sin \phi = \dfrac{16 S_8 }{45} -\end{equation} - - - -\end{frame} - - -\begin{frame}\frametitle{Conclusions} -{~} +\begin{frame}\frametitle{How to use fits 2/2} +\begin{columns} +\column{3.2in} +What is left free in the fit: \begin{itemize} -\item Method of moments very suitable for $\PBzero \to \PKstar \mu \mu$. -\item The method converge fast and works for the "simple case", i.e. signal only. -\item Method very insensitive to S-wave component, thanks to orthogonality. -\item Complementary one can measure in-depended S-wave component. -\item No problem with boundary problems. +\item $\lambda$ for exponent. +\item $F_l$, $S_x$ for angular distribution. +\item Relative normalization of signal and bkg. +\end{itemize} +Other remarks: +\begin{enumerate} +\item I am using good old Roofit, not custom developed fitter. +\item No s-wave in the fits, or systematics include in this study. +\item individual toys are now provided by Christoph, so one can compare $1:1$. +\end{enumerate} +\column{2.2in} +\includegraphics[width=0.6\textwidth]{phi_tmp.png}\\ +\includegraphics[width=0.6\textwidth]{mass.png} +\end{columns} + +\end{frame} + + +\begin{frame}\frametitle{Small things} +General remark: +\begin{itemize} +\item All pull plots/fits are available: \href{http://nz17-p1.ifj.edu.pl/work_public/LHCb/Kst_mumu/Face2Face_meeting/}{LINK} +\item User: lhcb, password: $2924$. + \end{itemize} -What comes in the next talks(stay tuned): +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{MM results $1GeV$ binning, Mean bias} + + + \tiny{ + \begin{tabular}{|*{10}{c|}} + + \hline +$Q^2$ & \scalebox{0.5}{$F_l$} & \scalebox{0.5}{$S_3$} & \scalebox{0.5}{$S_4$} & \scalebox{0.5}{$S_5$} & \scalebox{0.5}{$S_6$} \\ \hline +0 & \scalebox{0.5}{\textcolor{blue}{$-0.431 \pm 0.0184(-23.4)$}} & \scalebox{0.5}{$0.00218 \pm 0.0186(0.118)$} & \scalebox{0.5}{$0.0389 \pm 0.0183(2.13)$} & \scalebox{0.5}{$0.0104 \pm 0.0183(0.564)$} & \scalebox{0.5}{$0.0357 \pm 0.0183(1.96)$} \\ \hline +1 & \scalebox{0.5}{$-0.029 \pm 0.0188(-1.56)$} & \scalebox{0.5}{$0.0247 \pm 0.0187(1.32)$} & \scalebox{0.5}{$0.016 \pm 0.0184(0.872)$} & \scalebox{0.5}{$-0.0125 \pm 0.0191(-0.657)$} & \scalebox{0.5}{$-0.00833 \pm 0.0186(-0.449)$} \\ \hline +2 & \scalebox{0.5}{$0.0090 \pm 0.0181(0.501)$} & \scalebox{0.5}{$-0.0226 \pm 0.0186(-1.21)$} & \scalebox{0.5}{$-0.00623 \pm 0.018(-0.347)$} & \scalebox{0.5}{$-0.0235 \pm 0.018(-1.3)$} & \scalebox{0.5}{$-0.0201 \pm 0.0183(-1.1)$} \\ \hline +3 & \scalebox{0.5}{$-0.046 \pm 0.0183(-2.56)$} & \scalebox{0.5}{$-0.00942 \pm 0.0183(-0.515)$} & \scalebox{0.5}{$-0.00109 \pm 0.0188(-0.0579)$} & \scalebox{0.5}{$0.0108 \pm 0.0188(0.577)$} & \scalebox{0.5}{$-0.0519 \pm 0.0184(-2.83)$} \\ \hline +4 & \scalebox{0.5}{$-0.031 \pm 0.0183(-1.71)$} & \scalebox{0.5}{$0.0268 \pm 0.0181(1.48)$} & \scalebox{0.5}{$-0.00687 \pm 0.0182(-0.378)$} & \scalebox{0.5}{$-0.00106 \pm 0.0187(-0.0568)$} & \scalebox{0.5}{$0.00908 \pm 0.0189(0.481)$} \\ \hline +5 & \scalebox{0.5}{$-0.034 \pm 0.0178(-1.96)$} & \scalebox{0.5}{$0.0231 \pm 0.0189(1.22)$} & \scalebox{0.5}{$-0.0169 \pm 0.0183(-0.92)$} & \scalebox{0.5}{$-0.0138 \pm 0.0183(-0.75)$} & \scalebox{0.5}{$9.56e-05 \pm 0.0184(0.00521)$} \\ \hline +6 & \scalebox{0.5}{$-0.031 \pm 0.0186(-1.69)$} & \scalebox{0.5}{$0.0184 \pm 0.0183(1)$} & \scalebox{0.5}{$-0.000709 \pm 0.0182(-0.039)$} & \scalebox{0.5}{$-0.00728 \pm 0.0189(-0.386)$} & \scalebox{0.5}{$0.0223 \pm 0.0182(1.22)$} \\ \hline +7 & \scalebox{0.5}{$0.0042 \pm 0.0188(0.22)$} & \scalebox{0.5}{$0.022 \pm 0.0181(1.22)$} & \scalebox{0.5}{$-0.00412 \pm 0.0188(-0.22)$} & \scalebox{0.5}{$0.0044 \pm 0.0187(0.236)$} & \scalebox{0.5}{$0.0291 \pm 0.0188(1.55)$} \\ \hline +8 & \scalebox{0.5}{$0.0061 \pm 0.018(0.34)$} & \scalebox{0.5}{$0.0118 \pm 0.0184(0.643)$} & \scalebox{0.5}{$-0.0169 \pm 0.0185(-0.915)$} & \scalebox{0.5}{$0.0244 \pm 0.0182(1.34)$} & \scalebox{0.5}{$0.00532 \pm 0.0188(0.283)$} \\ \hline +9 & \scalebox{0.5}{$0.0056 \pm 0.0184(0.30)$} & \scalebox{0.5}{$-0.00938 \pm 0.0182(-0.514)$} & \scalebox{0.5}{$-0.0405 \pm 0.0182(-2.22)$} & \scalebox{0.5}{$0.00885 \pm 0.0182(0.487)$} & \scalebox{0.5}{$0.0361 \pm 0.0185(1.96)$} \\ \hline +10 & \scalebox{0.5}{$-0.0156 \pm 0.0185(-0.84)$} & \scalebox{0.5}{$-0.00611 \pm 0.018(-0.34)$} & \scalebox{0.5}{$-0.0241 \pm 0.0184(-1.31)$} & \scalebox{0.5}{$0.0204 \pm 0.0186(1.09)$} & \scalebox{0.5}{$-0.00378 \pm 0.0189(-0.201)$} \\ \hline +11 & \scalebox{0.5}{$-0.0079 \pm 0.018(-0.44)$} & \scalebox{0.5}{$0.0539 \pm 0.0182(2.96)$} & \scalebox{0.5}{$-0.0063 \pm 0.0189(-0.334)$} & \scalebox{0.5}{$-0.0297 \pm 0.019(-1.57)$} & \scalebox{0.5}{$-0.00305 \pm 0.0183(-0.166)$} \\ \hline + + \end{tabular} + + \begin{tabular}{|*{10}{c|}} + \hline +$Q^2$ & \scalebox{0.5}{$S_7$} & \scalebox{0.5}{$S_8$} & \scalebox{0.5}{$S_9$} \\ \hline +0 & \scalebox{0.5}{$-0.0179 \pm 0.018(-0.997)$} & \scalebox{0.5}{$-0.0311 \pm 0.0187(-1.66)$} & \scalebox{0.5}{$0.0274 \pm 0.0184(1.49)$} \\ \hline +1 & \scalebox{0.5}{$-0.0221 \pm 0.0183(-1.21)$} & \scalebox{0.5}{$-0.0592 \pm 0.0185(-3.2)$} & \scalebox{0.5}{$0.0151 \pm 0.0181(0.836)$} \\ \hline +2 & \scalebox{0.5}{$-0.00449 \pm 0.0185(-0.243)$} & \scalebox{0.5}{$-0.00996 \pm 0.0188(-0.529)$} & \scalebox{0.5}{$0.00609 \pm 0.0186(0.328)$} \\ \hline +3 & \scalebox{0.5}{$0.0274 \pm 0.0177(1.55)$} & \scalebox{0.5}{$-0.00217 \pm 0.0186(-0.117)$} & \scalebox{0.5}{$-0.00915 \pm 0.0187(-0.49)$} \\ \hline +4 & \scalebox{0.5}{$0.0156 \pm 0.0181(0.861)$} & \scalebox{0.5}{$-0.0141 \pm 0.0186(-0.759)$} & \scalebox{0.5}{$0.00498 \pm 0.0178(0.279)$} \\ \hline +5& \scalebox{0.5}{$0.0158 \pm 0.0186(0.848)$} & \scalebox{0.5}{$0.00727 \pm 0.0191(0.381)$} & \scalebox{0.5}{$0.029 \pm 0.0185(1.57)$} \\ \hline +6& \scalebox{0.5}{$-0.00232 \pm 0.0186(-0.125)$} & \scalebox{0.5}{$0.00974 \pm 0.0177(0.551)$} & \scalebox{0.5}{$-0.00613 \pm 0.018(-0.341)$}\\ \hline +7& \scalebox{0.5}{$-0.00853 \pm 0.0184(-0.463)$} & \scalebox{0.5}{$-0.00649 \pm 0.0182(-0.356)$} & \scalebox{0.5}{$0.00402 \pm 0.0183(0.22)$} \\ \hline +8& \scalebox{0.5}{$-0.0137 \pm 0.0185(-0.739)$} & \scalebox{0.5}{$-0.0167 \pm 0.0185(-0.903)$} & \scalebox{0.5}{$-0.0278 \pm 0.0183(-1.52)$} \\ \hline +9& \scalebox{0.5}{$-0.0229 \pm 0.019(-1.2)$} & \scalebox{0.5}{$-0.0506 \pm 0.0183(-2.77)$} & \scalebox{0.5}{$-0.0269 \pm 0.0183(-1.46)$} \\ \hline +10& \scalebox{0.5}{$-0.0155 \pm 0.0185(-0.84)$} & \scalebox{0.5}{$0.0276 \pm 0.0184(1.5)$} & \scalebox{0.5}{$0.0137 \pm 0.0185(0.742)$} \\ \hline +11& \scalebox{0.5}{$-0.0503 \pm 0.0183(-2.75)$} & \scalebox{0.5}{$-0.0137 \pm 0.0181(-0.758)$} & \scalebox{0.5}{$0.0169 \pm 0.0187(0.902)$} \\ \hline + + \end{tabular} + } + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{MM results $1GeV$ binning, Sigma bias} + + + \tiny{ + \begin{tabular}{|*{10}{c|}} + \hline +$Q^2$ & \scalebox{0.5}{$F_l$} & \scalebox{0.5}{$S_3$} & \scalebox{0.5}{$S_4$} & \scalebox{0.5}{$S_5$} & \scalebox{0.5}{$S_6$} \\ \hline +0 & \scalebox{0.5}{$0.969 \pm 0.014(2.24)$} & \scalebox{0.5}{$0.979 \pm 0.0142(1.45)$} & \scalebox{0.5}{$0.958 \pm 0.0136(3.11)$} & \scalebox{0.5}{$0.969 \pm 0.0139(2.21)$} & \scalebox{0.5}{$0.975 \pm 0.014(1.8)$} \\ \hline +1 & \scalebox{0.5}{$0.998 \pm 0.0154(0.128)$} & \scalebox{0.5}{$0.99 \pm 0.0141(0.684)$} & \scalebox{0.5}{$0.982 \pm 0.014(1.31)$} & \scalebox{0.5}{$1 \pm 0.0142(-0.327)$} & \scalebox{0.5}{$0.988 \pm 0.0152(0.812)$} \\ \hline +2 & \scalebox{0.5}{$0.957 \pm 0.0134(3.23)$} & \scalebox{0.5}{$0.989 \pm 0.0142(0.807)$} & \scalebox{0.5}{$0.96 \pm 0.0142(2.79)$} & \scalebox{0.5}{$0.965 \pm 0.0135(2.6)$} & \scalebox{0.5}{$0.973 \pm 0.0143(1.9)$} \\ \hline +3 & \scalebox{0.5}{$0.971 \pm 0.0139(2.11)$} & \scalebox{0.5}{$0.971 \pm 0.0137(2.1)$} & \scalebox{0.5}{$0.996 \pm 0.0152(0.277)$} & \scalebox{0.5}{$0.995 \pm 0.0142(0.374)$} & \scalebox{0.5}{$0.967 \pm 0.014(2.39)$} \\ \hline +4 & \scalebox{0.5}{$0.971 \pm 0.014(2.09)$} & \scalebox{0.5}{$0.965 \pm 0.0138(2.51)$} & \scalebox{0.5}{$0.966 \pm 0.0137(2.46)$} & \scalebox{0.5}{$0.994 \pm 0.0139(0.44)$} & \scalebox{0.5}{$1 \pm 0.0142(0.00431)$} \\ \hline +5 & \scalebox{0.5}{$0.947 \pm 0.0136(3.88)$} & \scalebox{0.5}{$1 \pm 0.0138(-0.165)$} & \scalebox{0.5}{$0.967 \pm 0.0138(2.4)$} & \scalebox{0.5}{$0.978 \pm 0.0137(1.63)$} & \scalebox{0.5}{$0.981 \pm 0.0132(1.46)$} \\ \hline +6 & \scalebox{0.5}{$0.983 \pm 0.0142(1.19)$} & \scalebox{0.5}{$0.981 \pm 0.0139(1.35)$} & \scalebox{0.5}{$0.967 \pm 0.0134(2.46)$} & \scalebox{0.5}{$1 \pm 0.0145(-0.126)$} & \scalebox{0.5}{$0.969 \pm 0.0134(2.29)$} \\ \hline +7 & \scalebox{0.5}{$1 \pm 0.0144(-0.01)$} & \scalebox{0.5}{$0.968 \pm 0.0142(2.26)$} & \scalebox{0.5}{$0.993 \pm 0.0143(0.474)$} & \scalebox{0.5}{$0.989 \pm 0.0136(0.775)$} & \scalebox{0.5}{$0.991 \pm 0.0138(0.671)$} \\ \hline +8 & \scalebox{0.5}{$0.956 \pm 0.0133(3.33)$} & \scalebox{0.5}{$0.98 \pm 0.0138(1.43)$} & \scalebox{0.5}{$0.983 \pm 0.0145(1.18)$} & \scalebox{0.5}{$0.966 \pm 0.0136(2.46)$} & \scalebox{0.5}{$0.996 \pm 0.0145(0.309)$} \\ \hline +9 & \scalebox{0.5}{$0.959 \pm 0.013(3.14)$} & \scalebox{0.5}{$0.968 \pm 0.0145(2.21)$} & \scalebox{0.5}{$0.954 \pm 0.0128(3.64)$} & \scalebox{0.5}{$0.963 \pm 0.013(2.8)$} & \scalebox{0.5}{$0.985 \pm 0.0142(1.03)$} \\ \hline +10 & \scalebox{0.5}{$0.972 \pm 0.0131(2.11)$} & \scalebox{0.5}{$0.955 \pm 0.0131(3.46)$} & \scalebox{0.5}{$0.978 \pm 0.0141(1.59)$} & \scalebox{0.5}{$0.991 \pm 0.014(0.635)$} & \scalebox{0.5}{$1.01 \pm 0.0137(-0.502)$} \\ \hline +11 & \scalebox{0.5}{$0.952 \pm 0.014(3.43)$} & \scalebox{0.5}{$0.969 \pm 0.0141(2.22)$} & \scalebox{0.5}{$0.999 \pm 0.0146(0.0445)$} & \scalebox{0.5}{$1 \pm 0.0144(-0.22)$} & \scalebox{0.5}{$0.979 \pm 0.0143(1.45)$} \\ \hline + + + + \end{tabular} + \begin{columns} + \column{2in} +\begin{tabular}{|c|c|c|c|} + \hline +$Q^2$ & \scalebox{0.5}{$S_7$} & \scalebox{0.5}{$S_8$} & \scalebox{0.5}{$S_9$} \\ \hline + +0 & \scalebox{0.5}{$0.958 \pm 0.0139(2.98)$} & \scalebox{0.5}{$0.994 \pm 0.0151(0.42)$} & \scalebox{0.5}{$0.972 \pm 0.0145(1.91)$} \\ \hline +1 & \scalebox{0.5}{$0.969 \pm 0.0138(2.24)$} & \scalebox{0.5}{$0.98 \pm 0.0145(1.4)$} & \scalebox{0.5}{$0.963 \pm 0.0137(2.74)$} \\ \hline +2 & \scalebox{0.5}{$0.983 \pm 0.0145(1.17)$} & \scalebox{0.5}{$0.998 \pm 0.0146(0.147)$} & \scalebox{0.5}{$0.986 \pm 0.0143(0.98)$} \\ \hline +3 & \scalebox{0.5}{$0.942 \pm 0.013(4.43)$} & \scalebox{0.5}{$0.987 \pm 0.0132(0.957)$} & \scalebox{0.5}{$0.996 \pm 0.0145(0.295)$} \\ \hline +4 & \scalebox{0.5}{$0.965 \pm 0.0137(2.58)$} & \scalebox{0.5}{$0.986 \pm 0.0138(1)$} & \scalebox{0.5}{$0.965 \pm 0.0131(2.24)$} \\ \hline +5 & \scalebox{0.5}{$0.979 \pm 0.0135(1.55)$} & \scalebox{0.5}{$0.978 \pm 0.0149(1.46)$} & \scalebox{0.5}{$0.981 \pm 0.0143(1.33)$} \\ \hline +6 & \scalebox{0.5}{$0.983 \pm 0.0139(1.22)$} & \scalebox{0.5}{$0.942 \pm 0.013(4.48)$} & \scalebox{0.5}{$0.955 \pm 0.0136(3.33)$} \\ \hline +7 & \scalebox{0.5}{$0.979 \pm 0.0129(1.63)$} & \scalebox{0.5}{$0.97 \pm 0.0145(2.06)$} & \scalebox{0.5}{$0.972 \pm 0.0135(2.05)$} \\ \hline +8 & \scalebox{0.5}{$0.979 \pm 0.014(1.5)$} & \scalebox{0.5}{$0.985 \pm 0.0139(1.08)$} & \scalebox{0.5}{$0.971 \pm 0.0136(2.13)$} \\ \hline +9 & \scalebox{0.5}{$0.995 \pm 0.0139(0.368)$} & \scalebox{0.5}{$0.975 \pm 0.0142(1.73)$} & \scalebox{0.5}{$0.975 \pm 0.0137(1.82)$} \\ \hline +10 & \scalebox{0.5}{$0.988 \pm 0.0132(0.907)$} & \scalebox{0.5}{$0.977 \pm 0.0142(1.59)$} & \scalebox{0.5}{$0.978 \pm 0.0142(1.56)$} \\ \hline +11 & \scalebox{0.5}{$0.971 \pm 0.0149(1.97)$} & \scalebox{0.5}{$0.968 \pm 0.0142(2.25)$} & \scalebox{0.5}{$0.988 \pm 0.0137(0.886)$} \\ \hline + \end{tabular} + \column{2in} +Conclusions: \begin{itemize} -\item This method reduces the error on unfolding. -\item No problem with convergence. -\item Systematics easy accessible. +\item MM does not bias the mean! +\item There is a trend that it overestimates the errors. +\item From all possible things that could go wrong this is the best. \end{itemize} - - -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%55 -\begin{frame}\frametitle{~} -{~} -\center \Huge BACKUPS - -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1c_50.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1c_75.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1c_50E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1c_75E.png} - - \end{columns} -\end{frame} + } + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Fit $1GeV$ binning, Mean bias} +\tiny{ + \begin{tabular}{|*{10}{c|}} + +\hline +$Q^2$ & \scalebox{0.6}{$F_l$} & \scalebox{0.6}{$S_3$} & \scalebox{0.6}{$S_4$} & \scalebox{0.6}{$S_5$} & \scalebox{0.6}{$S_6$} \\ \hline -\begin{frame} -{~} +0 & \scalebox{0.6}{$-0.54 \pm 0.02091(-25.82)$} & \scalebox{0.6}{$0.01246 \pm 0.0213(0.585)$} & \scalebox{0.6}{$0.01828 \pm 0.02126(0.8598)$} & \scalebox{0.6}{$0.02513 \pm 0.02078(1.209)$} & \scalebox{0.6}{$0.0646 \pm 0.02081(3.104)$} \\ \hline +1 & \scalebox{0.6}{$-0.27 \pm 0.02232(-12.1)$} & \scalebox{0.6}{$0.03261 \pm 0.02401(1.358)$} & \scalebox{0.6}{$0.08175 \pm 0.02376(3.441)$} & \scalebox{0.6}{$-0.1473 \pm 0.0246(-5.987)$} & \scalebox{0.6}{$-0.244 \pm 0.02276(-10.72)$} \\ \hline +2 & \scalebox{0.6}{$-0.7574 \pm 0.02208(-34.3)$} & \scalebox{0.6}{$-0.0307 \pm 0.02267(-1.354)$} & \scalebox{0.6}{$-0.07512 \pm 0.02344(-3.204)$} & \scalebox{0.6}{$0.03054 \pm 0.02523(1.21)$} & \scalebox{0.6}{$-0.2317 \pm 0.02327(-9.957)$} \\ \hline +3 & \scalebox{0.6}{$-0.7548 \pm 0.02333(-32.35)$} & \scalebox{0.6}{$-0.01416 \pm 0.02193(-0.6458)$} & \scalebox{0.6}{$-0.1786 \pm 0.02354(-7.588)$} & \scalebox{0.6}{$0.2604 \pm 0.02232(11.67)$} & \scalebox{0.6}{$-0.05868 \pm 0.02325(-2.524)$} \\ \hline +4 & \scalebox{0.6}{$-0.5667 \pm 0.02163(-26.2)$} & \scalebox{0.6}{$0.0153 \pm 0.02265(0.6756)$} & \scalebox{0.6}{$-0.2313 \pm 0.02105(-10.99)$} & \scalebox{0.6}{$0.4372 \pm 0.02207(19.81)$} & \scalebox{0.6}{$0.03735 \pm 0.02385(1.566)$} \\ \hline +5 & \scalebox{0.6}{$-0.4589 \pm 0.02156(-21.29)$} & \scalebox{0.6}{$0.0305 \pm 0.02265(1.347)$} & \scalebox{0.6}{$-0.2186 \pm 0.02141(-10.21)$} & \scalebox{0.6}{$0.5118 \pm 0.02161(23.69)$} & \scalebox{0.6}{$0.1218 \pm 0.02321(5.249)$} \\ \hline +6 & \scalebox{0.6}{$-0.3408 \pm 0.02351(-14.5)$} & \scalebox{0.6}{$-0.005133 \pm 0.0235(-0.2184)$} & \scalebox{0.6}{$-0.3205 \pm 0.02116(-15.15)$} & \scalebox{0.6}{$0.628 \pm 0.02207(28.45)$} & \scalebox{0.6}{$0.2972 \pm 0.02256(13.17)$}\\ \hline +7 & \scalebox{0.6}{$-0.2309 \pm 0.02362(-9.778)$} & \scalebox{0.6}{$-0.003081 \pm 0.02186(-0.1409)$} & \scalebox{0.6}{$-0.4115 \pm 0.02268(-18.14)$} & \scalebox{0.6}{$0.6794 \pm 0.02274(29.88)$} & \scalebox{0.6}{$0.4305 \pm 0.02204(19.53)$} \\ \hline +8 & \scalebox{0.6}{$0.3543 \pm 0.02837(12.49)$} & \scalebox{0.6}{$0.157 \pm 0.02254(6.969)$} & \scalebox{0.6}{$-0.3984 \pm 0.02223(-17.93)$} & \scalebox{0.6}{$0.3877 \pm 0.02171(17.86)$} & \scalebox{0.6}{$0.8208 \pm 0.02474(33.18)$} \\ \hline +9 & \scalebox{0.6}{$0.2385 \pm 0.02778(8.586)$} & \scalebox{0.6}{$0.1185 \pm 0.02156(5.499)$} & \scalebox{0.6}{$-0.3564 \pm 0.02171(-16.42)$} & \scalebox{0.6}{$0.3164 \pm 0.02264(13.98)$} & \scalebox{0.6}{$0.7744 \pm 0.02437(31.78)$} \\ \hline +10 & \scalebox{0.6}{$0.2395 \pm 0.0273(8.774)$} & \scalebox{0.6}{$0.2025 \pm 0.02106(9.617)$} & \scalebox{0.6}{$-0.3328 \pm 0.02126(-15.66)$} & \scalebox{0.6}{$0.2583 \pm 0.02247(11.5)$} & \scalebox{0.6}{$0.5419 \pm 0.02453(22.09)$} \\ \hline +11 & \scalebox{0.6}{$0.139 \pm 0.02676(5.194)$} & \scalebox{0.6}{$0.3433 \pm 0.02149(15.98)$} & \scalebox{0.6}{$-0.3043 \pm 0.02151(-14.15)$} & \scalebox{0.6}{$0.1217 \pm 0.02339(5.205)$} & \scalebox{0.6}{$0.3523 \pm 0.02402(14.67)$} \\ \hline + +\end{tabular} + + \begin{columns} + \column{3in} + \begin{tabular}{|*{10}{c|}} + \hline +$Q^2$ & \scalebox{0.6}{$S_7$} & \scalebox{0.6}{$S_8$} & \scalebox{0.6}{$S_9$} \\ \hline +0 & \scalebox{0.6}{$-0.03252 \pm 0.02039(-1.595)$} & \scalebox{0.6}{$-0.02852 \pm 0.02148(-1.328)$} & \scalebox{0.6}{$0.03152 \pm 0.0207(1.523)$} \\ \hline +1 & \scalebox{0.6}{$-0.01799 \pm 0.02456(-0.7325)$} & \scalebox{0.6}{$-0.03414 \pm 0.02435(-1.402)$} & \scalebox{0.6}{$0.04347 \pm 0.02277(1.909)$} \\ \hline +2 & \scalebox{0.6}{$-0.1108 \pm 0.02502(-4.429)$} & \scalebox{0.6}{$-0.007344 \pm 0.02559(-0.287)$} & \scalebox{0.6}{$0.04804 \pm 0.02257(2.129)$} \\ \hline +3 & \scalebox{0.6}{$-0.009689 \pm 0.02367(-0.4093)$} & \scalebox{0.6}{$0.03343 \pm 0.0234(1.429)$} & \scalebox{0.6}{$-0.01668 \pm 0.0209(-0.7982)$} \\ \hline +4 & \scalebox{0.6}{$-0.03027 \pm 0.02361(-1.282)$} & \scalebox{0.6}{$0.05424 \pm 0.02354(2.304)$} & \scalebox{0.6}{$-0.02207 \pm 0.02167(-1.018)$} \\ \hline +5 & \scalebox{0.6}{$-0.07159 \pm 0.02324(-3.08)$} & \scalebox{0.6}{$0.02229 \pm 0.02396(0.9304)$} & \scalebox{0.6}{$-0.03396 \pm 0.02147(-1.582)$} \\ \hline +6 & \scalebox{0.6}{$-0.06034 \pm 0.02395(-2.52)$} & \scalebox{0.6}{$0.04234 \pm 0.02284(1.854)$} & \scalebox{0.6}{$-0.01762 \pm 0.02174(-0.8102)$} \\ \hline +7 & \scalebox{0.6}{$-0.05002 \pm 0.02386(-2.097)$} & \scalebox{0.6}{$0.03382 \pm 0.02289(1.477)$} & \scalebox{0.6}{$0.009742 \pm 0.02147(0.4538)$} \\ \hline +8 & \scalebox{0.6}{$-0.05097 \pm 0.0245(-2.08)$} & \scalebox{0.6}{$-0.02328 \pm 0.02359(-0.9872)$} & \scalebox{0.6}{$-0.03285 \pm 0.023(-1.428)$} \\ \hline +9 & \scalebox{0.6}{$-0.03206 \pm 0.02543(-1.261)$} & \scalebox{0.6}{$-0.009805 \pm 0.02334(-0.4201)$} & \scalebox{0.6}{$-0.04927 \pm 0.02272(-2.169)$} \\ \hline +10 & \scalebox{0.6}{$-0.02589 \pm 0.02487(-1.041)$} & \scalebox{0.6}{$-0.005148 \pm 0.02376(-0.2166)$} & \scalebox{0.6}{$-0.02395 \pm 0.02422(-0.9889)$} \\ \hline +11 & \scalebox{0.6}{$-0.04134 \pm 0.02664(-1.552)$} & \scalebox{0.6}{$-0.03522 \pm 0.02517(-1.399)$} & \scalebox{0.6}{$-0.02359 \pm 0.0246(-0.9592)$} \\ \hline + + \end{tabular} + +\column{1.5in} +\begin{itemize} +\item With agreement with Michel previous studies \href{https://indico.cern.ch/event/290857/contribution/3/material/slides/0.pdf}{LINK} +\end{itemize} + + + \end{columns} +} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Conclusion on $1GeV$ binning} \begin{columns} \column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1c_125.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1c_175.png}\\ - - +\begin{itemize} +\item Fits Highly bias and not usable. +\item MM work fine. +\item Christian developed his own fitter +\item Let's try comparing those(not very fair comparison)! +\end{itemize} \column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1c_125E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1c_175E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1c_225.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1c_300.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1c_225E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1c_300E.png} - - -\end{columns} -\end{frame} - - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1c_400.png}\\ - - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1c_400E.png}\\ - - - -\end{columns} -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1s_50.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1s_75.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1s_50E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1s_75E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1s_125.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1s_175.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1s_125E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1s_175E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1s_225.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1s_300.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1s_225E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1s_300E.png} - - -\end{columns} -\end{frame} - - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1s_400.png}\\ - - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1s_400E.png}\\ - - - -\end{columns} -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J2c_50.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J2c_75.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J2c_50E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J2c_75E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J2c_125.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J2c_175.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J2c_125E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J2c_175E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J2c_225.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J2c_300.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J2c_225E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J2c_300E.png} - - -\end{columns} -\end{frame} - - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J2c_400.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J2c_500.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J2c_400E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J2c_500E.png}\\ - - -\end{columns} -\end{frame} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J3_50.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J3_75.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J3_50E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J3_75E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J3_125.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J3_175.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J3_125E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J3_175E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J3_225.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J3_300.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J3_225E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J3_300E.png} - - -\end{columns} -\end{frame} - - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J3_400.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J3_500.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J3_400E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J3_500E.png}\\ - - -\end{columns} -\end{frame} - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J4_50.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J4_75.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J4_50E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J4_75E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J4_125.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J4_175.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J4_125E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J4_175E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J4_225.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J4_300.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J4_225E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J4_300E.png} - - -\end{columns} -\end{frame} - - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J4_400.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J4_500.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J4_400E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J4_500E.png}\\ - - -\end{columns} -\end{frame} - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J5_50.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J5_75.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J5_50E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J5_75E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J5_125.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J5_175.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J5_125E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J5_175E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J5_225.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J5_300.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J5_225E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J5_300E.png} - - -\end{columns} -\end{frame} - - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J5_400.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J5_500.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J5_400E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J5_500E.png}\\ - - -\end{columns} -\end{frame} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J7_50.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J7_75.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J7_50E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J7_75E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J7_125.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J7_175.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J7_125E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J7_175E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J7_225.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J7_300.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J7_225E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J7_300E.png} - - -\end{columns} -\end{frame} - - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J7_400.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J7_500.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J7_400E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J7_500E.png}\\ - - -\end{columns} -\end{frame} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J8_50.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J8_75.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J8_50E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J8_75E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J8_125.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J8_175.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J8_125E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J8_175E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J8_225.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J8_300.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J8_225E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J8_300E.png} - - -\end{columns} -\end{frame} - - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J8_400.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J8_500.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J8_400E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J8_500E.png}\\ - - -\end{columns} -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J9_50.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J9_75.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J9_50E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J9_75E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J9_125.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J9_175.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J9_125E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J9_175E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J9_225.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J9_300.png}\\ - - -\column{2.5in} 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-\includegraphics[scale=0.2]{plots/J8J5.png}\\ -\includegraphics[scale=0.2]{plots/J8J4.png}\\ +\includegraphics[width=0.8\textwidth]{Q2_4_S8.png}\\ +\includegraphics[width=0.8\textwidth]{Q2_5_S5.png} \end{columns} \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{MM vs Fit\footnote{Taken form Christoph's presentation}} +\begin{tiny} +\begin{columns} +\column{1in} + \begin{tabular}{|c|c|c|} + \hline + $Q^2$ & $F_l^{MM}$ & $F_l^{Fit}$ \\ \hline + $0$ & $0.0397$ & $0.025$\\ \hline + $1$ & $0.0802$ & $0.051$\\ \hline + $2$ & $0.0869$ & $0.057$\\ \hline + $3$ & $0.0893$ & $0.050$\\ \hline + $4$ & $0.0878$ & $0.051$\\ \hline + $5$ & $0.0848$ & $0.048$\\ \hline + $6$ & $0.0812$ & $0.047$\\ \hline + $7$ & $0.0775$ & $0.046$\\ \hline + $8$ & $0.0657$ & $0.041$\\ \hline + $9$ & $0.0687$ & $0.044$\\ \hline + $10$ & $0.0755$ & $0.045$\\ \hline + $11$ & $0.0967$ & $0.061$\\ \hline + \end{tabular} +\column{1in} + \begin{tabular}{|c|c|c|} + \hline + $Q^2$ & $S_3^{MM}$ & $S_3^{Fit}$ \\ \hline + $0$ & $0.0656$ & $0.058$\\ \hline + $1$ & $0.109$ & $0.100$\\ \hline + $2$ & $0.116$ & $0.102$\\ \hline + $3$ & $0.12$ & $0.102$\\ \hline + $4$ & $0.118$ & $0.101$\\ \hline + $5$ & $0.115$ & $0.098$\\ \hline + $6$ & $0.112$ & $0.092$\\ \hline + $7$ & $0.108$ & $0.087$\\ \hline + $8$ & $0.0989$ & $0.090$\\ \hline + $9$ & $0.104$ & $0.098$\\ \hline + $10$ & $0.114$ & $0.108$\\ \hline + $11$ & $0.146$ & $0.155$\\ \hline + \end{tabular} +\column{1in} + \begin{tabular}{|c|c|c|} + \hline + $Q^2$ & $S_4^{MM}$ & $S_4^{Fit}$ \\ \hline + $0$ & $0.0639$ & $0.054$\\ \hline + $1$ & $0.123$ & $0.115$\\ \hline + $2$ & $0.134$ & $0.114$\\ \hline + $3$ & $0.137$ & $0.123$\\ \hline + $4$ & $0.134$ & $0.116$\\ \hline + $5$ & $0.129$ & $0.112$\\ \hline + $6$ & $0.123$ & $0.104$\\ \hline + $7$ & $0.117$ & $0.100$\\ \hline + $8$ & $0.099$ & $0.086$\\ \hline + $9$ & $0.103$ & $0.098$\\ \hline + $10$ & $0.112$ & $0.109$\\ \hline + $11$ & $0.144$ & $0.160$\\ \hline + \end{tabular} +\column{1in} + \begin{tabular}{|c|c|c|} + \hline + $Q^2$ & $S_5^{MM}$ & $S_5^{Fit}$ \\ \hline + $0$ & $ 0.0563$ & $0.050$\\ \hline + $1$ & $0.118$ & $0.114$\\ \hline + $2$ & $0.131$ & $0.108$\\ \hline + $3$ & $0.133$ & $0.117$\\ \hline + $4$ & $0.129$ & $0.105$\\ \hline + $5$ & $0.122$ & $0.106$\\ \hline + $6$ & $0.116$ & $0.097$\\ \hline + $7$ & $0.109$ & $0.094$\\ \hline + $8$ & $0.0884$ & $0.080$\\ \hline + $9$ & $0.0925$ & $0.085$\\ \hline + $10$ & $0.101$ & $0.096$\\ \hline + $11$ & $0.13$ & $0.144$\\ \hline + \end{tabular} + + + + \end{columns} + + + + +\begin{columns} +\column{1in} + \begin{tabular}{|c|c|c|} + \hline + $Q^2$ & $S_6^{MM}$ & $S_6^{Fit}$ \\ \hline + $0$ & $0.0632$ & $0.058$\\ \hline + $1$ & $0.0936$ & $0.085$\\ \hline + $2$ & $0.097$ & $0.093$\\ \hline + $3$ & $0.101$ & $0.085$\\ \hline + $4$ & $0.101$ & $0.083$\\ \hline + $5$ & $0.0999$ & $0.085$\\ \hline + $6$ & $0.0975$ & $0.080$\\ \hline + $7$ & $0.0941$ & $0.079$\\ \hline + $8$ & $0.0873$ & $0.073$\\ \hline + $9$ & $0.0925$ & $0.080$\\ \hline + $10$ & $0.104$ & $0.100$\\ \hline + $11$ & $0.137$ & $0.121$\\ \hline + \end{tabular} +\column{1in} + \begin{tabular}{|c|c|c|} + \hline + $Q^2$ & $S_7^{MM}$ & $S_7^{Fit}$ \\ \hline + $0$ & $0.0574$ & $0.051$\\ \hline + $1$ & $0.118$ & $0.100$\\ \hline + $2$ & $0.131$ & $0.105$\\ \hline + $3$ & $0.134$ & $0.111$\\ \hline + $4$ & $0.131$ & $0.111$\\ \hline + $5$ & $0.125$ & $0.104$\\ \hline + $6$ & $0.119$ & $0.102$\\ \hline + $7$ & $0.113$ & $0.097$\\ \hline + $8$ & $0.0958$ & $0.085$\\ \hline + $9$ & $0.101$ & $0.091$\\ \hline + $10$ & $0.112$ & $0.101$\\ \hline + $11$ & $0.144$ & $0.136$\\ \hline + \end{tabular} +\column{1in} + \begin{tabular}{|c|c|c|} + \hline + $Q^2$ & $S_8^{MM}$ & $S_8^{Fit}$ \\ \hline + $0$ & $0.0641$ & $0.058$\\ \hline + $1$ & $0.123$ & $0.113$\\ \hline + $2$ & $0.134$ & $0.120$\\ \hline + $3$ & $0.138$ & $0.119$\\ \hline + $4$ & $0.135$ & $0.112$\\ \hline + $5$ & $0.13$ & $0.108$\\ \hline + $6$ & $0.124$ & $0.103$\\ \hline + $7$ & $0.118$ & $0.101$\\ \hline + $8$ & $0.104$ & $0.092$\\ \hline + $9$ & $0.109$ & $0.095$\\ \hline + $10$ & $0.121$ & $0.115$\\ \hline + $11$ & $0.156$ & $0.149$\\ \hline + \end{tabular} +\column{1in} + \begin{tabular}{|c|c|c|} + \hline + $Q^2$ & $S_9^{MM}$ & $S_9^{Fit}$ \\ \hline + $0$ & $0.0656$ & $0.057$\\ \hline + $1$ & $0.109$ & $0.099$\\ \hline + $2$ & $0.116$ & $0.109$\\ \hline + $3$ & $0.12$ & $0.104$\\ \hline + $4$ & $0.119$ & $0.102$\\ \hline + $5$ & $0.116$ & $0.097$\\ \hline + $6$ & $0.112$ & $0.094$\\ \hline + $7$ & $0.108$ & $0.091$\\ \hline + $8$ & $0.0993$ & $0.079$\\ \hline + $9$ & $0.105$ & $0.088$\\ \hline + $10$ & $0.115$ & $0.103$\\ \hline + $11$ & $0.149$ & $0.143$\\ \hline + \end{tabular} + + + + \end{columns} +\end{tiny} +\end{frame} % ------------------------------------------------------------------------------ + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Conclusion} + +\begin{itemize} +\item Method of moments a bit worse($\sim 15\%$) then optimistic fit. +\item MM overestimates the error by fiew \%, fits understimates the error by fiew \%. +\item Fit needs more study to understand why roofit is biased and Christoph fit is not. +\end{itemize} + + +\end{frame} + + + + + + \end{document} diff --git a/Kstmumu/Face2Face_meeting/Comparison/Comparison.toc b/Kstmumu/Face2Face_meeting/Comparison/Comparison.toc index bedbea4..bc756c5 100644 --- a/Kstmumu/Face2Face_meeting/Comparison/Comparison.toc +++ b/Kstmumu/Face2Face_meeting/Comparison/Comparison.toc @@ -1,7 +1,3 @@ \beamer@endinputifotherversion {3.10pt} \select@language {english} \beamer@sectionintoc {1}{Introduction}{4}{0}{1} -\beamer@sectionintoc {2}{Method of Moments - Theory}{5}{0}{2} -\beamer@sectionintoc {3}{Moments of Ss}{7}{0}{3} -\beamer@sectionintoc {4}{Toy MC study}{12}{0}{4} -\beamer@sectionintoc {5}{S-wave}{16}{0}{5} diff --git a/Kstmumu/Face2Face_meeting/Comparison/Q2_4_S8.png 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