\documentclass[hyperref=pdftex, presentation,9pt]{beamer}
% Replacing 'presentation' with 'handout' in the above line
% will produce 4 slides per page.
% The hyperref option makes it possible to include hyperlinks.

\mode<presentation> {
\usetheme{Boadilla}
\setbeamercovered{transparent}
}

\usepackage[english]{babel}
\usepackage[latin1]{inputenc}
\usepackage{times}
\usepackage[T1]{fontenc}
\usepackage{wrapfig}
\usepackage{graphicx}

\mode<handout>{
\usepackage{pgfpages}
\pgfpagesuselayout{4 on 1}[letterpaper,landscape,border shrink=5mm]
\setbeamercolor{background canvas}{bg=black!10} }

\setbeamertemplate{footline}
{
\leavevmode%
\hbox{%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{author
	in head/foot}%
	\usebeamerfont{author in head/ foot}\insertshortauthor%&\approx& (\insertshorti
\end{beamercolorbox}%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{title
	in head/foot}%
	\usebeamerfont{title in head/foot}\insertshorttitle
\end{beamercolorbox}%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{date in
	head/foot}%
	\usebeamerfont{date in head/foot}\insertshortdate\hspace*{2em}
	\insertframenumber / \inserttotalframenumber\hspace*{2ex}
\end{beamercolorbox}}%
\vskip0pt%
}

\newcommand{\backupbegin}{
\newcounter{framenumberappendix}
\setcounter{framenumberappendix}{\value{framenumber}}
}
\newcommand{\backupend}{
\addtocounter{framenumberappendix}{-\value{framenumber}}
\addtocounter{framenumber}{\value{framenumberappendix}} 
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\title[GEANT4/EGS5]{GEANT4/EGS5}

\title{Vertexing status and plans}

\author{Sho Uemura}
\institute{SLAC}
\date[July 5, 2016]

\begin{document}

\begin{frame}
	\titlepage
\end{frame}

\begin{frame}{Overview}
	\begin{itemize}
		\item How should the analysis work?
		\item What's been going on
		\item What I'm worried about
	\end{itemize}
\end{frame}

\begin{frame}{The analysis}
	\begin{itemize}
		\item We want to set exclusion regions in mass vs. $\epsilon^2$ for visibly decaying A'
			\begin{itemize}
				\item Find limits on production cross-section (relative to radiative) as a function of mass and $c\tau$, then exclude based on compatibility with the cross-section predicted by $\epsilon^2$
			\end{itemize}
		\item Find significance and a preferred region for any observed signal
		\item Anything else?
	\end{itemize}
\end{frame}

\begin{frame}{Limit setting}
	\begin{itemize}
		\item Inputs:
			\begin{itemize}
				\item Vertex Z vs. mass
				\item Efficiency vs. Z at each A' mass (from MC)
				\item A' vertex distributions (production$\times$decay$\times$efficiency) as a function of mass and coupling
			\end{itemize}
		\item First step: take a resolution-limited mass slice (2.5 $\sigma_m$ wide), get a 1-D data set
		\item Can take sideband slices, fit those and interpolate to get a background model for the slice
			\begin{itemize}
				\item Gaussian with exponential tail seems to work
				\item What if that's not all there is to the tail?
			\end{itemize}
		\item Then what?
	\end{itemize}
	\begin{center}
		\includegraphics[width=0.5\textwidth]{zvsmass}
		\includegraphics[width=0.5\textwidth]{slice-6_roofit}
	\end{center}
\end{frame}

\begin{frame}{Cut-and-count}
	\begin{itemize}
		\item Define a zcut such that we expect $b$ events above the cut, count events above the cut, get a confidence interval for the signal rate past the zcut: makes no assumptions about signal shape
			\begin{itemize}
				\item Feldman-Cousins intervals?
				\item What's optimal $b$? 0.5? Does the answer change if there are irreducible backgrounds?
			\end{itemize}
		\item For each $c\tau$, this sets an interval for the production cross-section
		\item Check for consistency with the appropriate $\epsilon^2$
	\end{itemize}
\end{frame}

\begin{frame}{Optimum interval (Yellin, arXiv:physics/0203002)}
	\begin{columns}
		\column{0.7\textwidth}
		\begin{itemize}
			\item Sets a limit on A' production cross-section for a given $c\tau$
			\item Assume a production cross-section, then the expected trident distribution (background plus A's) $dN/dz$ is known: do a change of variables from $z$ to $N$, so the expected distribution is uniform in $N$ and has total length $\mu$ (= total expected events)
			\item For every interval between two events (of width $x$ expected events and containing $n$ observed events), compute the probability $C_n(x,\mu)$ given the expected distribution that all intervals containing $n$ events are narrower than this one; take the interval with largest $C$ to be the ``optimum interval'' that most strongly rejects the proposed cross-section; that value of $C$ is called $C_{max}$
			\item You pay a statistical penalty for picking the best interval and the best $n$; if you want a 90\% confidence interval on the cross-section, the $C_{max}$ threshold for excluding a cross-section is larger than 0.9
			\item If there's an unexpected background (or one where we just don't know the spatial distribution), the optimum interval automatically avoids it
		\end{itemize}
		\column{0.3\textwidth}
		\includegraphics[width=\textwidth]{maxgap}
	\end{columns}
\end{frame}

\begin{frame}{We found a signal \ldots now what?}
	\begin{itemize}
		\item Do a profile likelihood ratio to get a local p-value for a nonzero signal at given mass and $c\tau$
		\item Also get a p-value for consistency with the predicted production cross-section
		\item Significance: toys should work (since any signal strength we find is likely to be weak --- we're not going to find a 5$\sigma$ signal)
			\begin{itemize}
				\item The ``upcrossings'' method of estimating the look-elsewhere effect for strong signals is specific to 1D searches, but can be generalized to 2D (arXiv:1105.4355)
			\end{itemize}
		\item Look at esum distribution? Can we compare goodness of fit with full-diagram and A'?
	\end{itemize}
\end{frame}

\begin{frame}{Events without L1 hits}
	\begin{itemize}
		\item We need these to get acceptance past $Z=50$ mm or so; on the other hand no-L1 events have significantly worse mass and vertex resolution, and tails that extend an additional 10-20 mm 
		\item I think we need to split the data set
		\item Can't trust that L1 efficiency is the same in data and MC: how do you split A' production between data sets?
			\begin{itemize}
				\item Use total trident rate (all tracking strategies, double-counting excluded) in both data sets?
			\end{itemize}
		\item Need to combine L1 and no-L1 datasets: doable for both cut-and-count and optimum interval methods
	\end{itemize}
	\begin{center}
		\includegraphics[width=0.5\textwidth]{efficiency_L1}
		\includegraphics[width=0.5\textwidth]{efficiency_L1_2}
	\end{center}
\end{frame}

\begin{frame}{Setting cuts}
	\begin{itemize}
		\item Vertex tails mostly come from L1 scatters
		\item Using data to test cuts: reject high-Z fakes (``background''), keep low-Z tridents (``signal'')
		\item Need to check with MC to make sure these cuts don't reject high-Z A', and maybe find more variables to cut on
		\item Should check mass dependence of cuts
		\item Eventually (soon) we will need to use the analysis to tune the cuts for best sensitivity
	\end{itemize}
	\begin{center}
		\includegraphics[width=0.3\textwidth,page=1]{vertcuts}
		\includegraphics[width=0.3\textwidth]{old-zcut}
		\includegraphics[width=0.3\textwidth]{new-zcut}
	\end{center}
\end{frame}

\begin{frame}{Software, MC, other stuff}
	\begin{itemize}
		\item A' MC: Brad has made displaced vertex A'
			\begin{itemize}
				\item Only making $c\tau=1$ mm (for now?), since I just want to get good coverage in $Z$ for getting efficiencies
			\end{itemize}
		\item Big sample of trident MC: it'd be nice to have an MC sample of the same size as the full data set (current MC is about 1/5 the lumi of the unblinded 10\%)
			\begin{itemize}
				\item May be the only way we're going to see (and be prepared to cut out) a small background, O(10) events
				\item But we'll never know if it has everything
			\end{itemize}
		\item Unblinding $Z<0$: no reason not to
			\begin{itemize}
				\item May tell us something about vertex tails
				\item But maybe there are too many differences
			\end{itemize}
	\end{itemize}
\end{frame}

\begin{frame}{What I'm worried about}
	\begin{itemize}
		\item Background from L1
		\item What if there's background not accounted for in our model?
		\item The yield is too low (lower than expected, too low to set limits)
	\end{itemize}
	\begin{center}
		\includegraphics[width=0.7\textwidth,page=8]{goldenhalo}
	\end{center}
\end{frame}

\begin{frame}{Known sources of tridents at large Z}
	\begin{itemize}
		\item Beam-gas
			\begin{itemize}
				\item Expected to be a few events at most; should get a real estimate from Takashi
			\end{itemize}
		\item Beam halo/scattered beam from target hitting L1
			\begin{itemize}
				\item We see tridents being made in inactive L1 silicon: beam halo electrons, or electrons scattered by the target
				\item This will be O(2000) tridents in the full data set, but concentrated near Z=100 mm: hopefully we can reject these without throwing out too much of our A' space
			\end{itemize}
	\end{itemize}
	\begin{center}
		\includegraphics[width=0.7\textwidth,page=8]{goldenhalo}
	\end{center}
\end{frame}

\begin{frame}{What if we have an unexpected background?}
	\begin{itemize}
		\item Suppose we have a background at large Z, slowly varying with mass
			\begin{itemize}
				\item Real vertices, like beam-gas tridents
				\item Fake vertices, like some kind of subexponential vertex tail
			\end{itemize}
		\item It's not obvious now in 10\% of the data, so if we have something like this it's going to be small --- O(50) events, O(5) events in a mass slice
		\item Count events past zcut, fit to a low-order polynomial? Could this improve our limit?
			\begin{itemize}
				\item Doesn't work very well for edges of the mass distribution (similar problem to bumphunt)
				\item Seems dangerous, too easy to really screw things up
				\item I'd prefer to take the hit to our limit, but use this when calculating significance (we can quote signal significance over known low-Z backgrounds and over low-Z+high-Z backgrounds)
			\end{itemize}
	\end{itemize}
\end{frame}

\begin{frame}{Yield}
	\begin{itemize}
		\item Yield (A' past zcut) $\log{\epsilon^2}$ vs. mass (15-60 MeV)
		\item Assuming A' efficiency constant to $z=\infty$ (obviously not true), radiative fraction 15\%
		\item Left to right:
			\begin{itemize}
				\item Real data (L1 required, reasonable cuts), zcut derived from data
				\item Real data (L1 required, reasonable cuts), zcut 35 mm
				\item Loose data (L1 not required, loose bumphunt-style cuts), zcut 35 mm
			\end{itemize}
		\item Not good enough! That's way under $2\sigma$ even with very optimistic assumptions
	\end{itemize}
	\begin{center}
		\includegraphics[width=0.3\textwidth,page=8]{yield_realcuts_realzcut}
		\includegraphics[width=0.3\textwidth,page=8]{yield_realcuts}
		\includegraphics[width=0.3\textwidth,page=8]{yield_loosecuts}
	\end{center}
\end{frame}

\begin{frame}{Why is the yield so low?}
	\begin{itemize}
		\item Matt G. estimated $6\sigma$ significance at 3 PAC days; we got 1.9
		\item The trident yield in data is lower than MC, but less than a factor of 2
		\item We should figure out what's wrong
	\end{itemize}
	\begin{center}
		\includegraphics[width=0.3\textwidth,page=8]{significance_3e-9}
		\includegraphics[width=0.3\textwidth,page=8]{significance_1e-9}
		\includegraphics[width=0.3\textwidth,page=8]{rate}
	\end{center}
\end{frame}

\end{document}