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talk/slides.tex
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@ -16,7 +16,6 @@ labelformat=brace, position=top]{subcaption}
\usepackage{ifdraft} \usepackage{ifdraft}
\usepackage{appendixnumberbeamer} \usepackage{appendixnumberbeamer}
\usetikzlibrary{arrows,shapes,angles,quotes,arrows.meta,external} \usetikzlibrary{arrows,shapes,angles,quotes,arrows.meta,external}
\tikzexternalize[prefix=tikz/]
\graphicspath{ {figs/} } \graphicspath{ {figs/} }
\addbibresource{thesis.bib} \addbibresource{thesis.bib}
@ -171,12 +170,13 @@ labelformat=brace, position=top]{subcaption}
\begin{block}{Diphoton Process \(\qqgg\)} \begin{block}{Diphoton Process \(\qqgg\)}
\begin{itemize} \begin{itemize}
\item simple QED process, calculable by hand \item simple QED process, calculable by hand
\item higgs decay channel: \(H\rightarrow \gamma\gamma\) \item background for important higgs decay channel:
\(H\rightarrow \gamma\gamma\)
\begin{itemize} \begin{itemize}
\item instrumental in its \item instrumental in its
discovery~\cite{Aad:2012tfa,Chatrchyan:2012ufa} discovery~\cite{Aad:2012tfa,Chatrchyan:2012ufa}
\end{itemize} \end{itemize}
\item dihiggs decay \(HH\rightarrow b\bar{b}\gamma\gamma\) \item partial background for dihiggs decay \(HH\rightarrow b\bar{b}\gamma\gamma\)
\begin{itemize} \begin{itemize}
\item process of recent interest~\cite{aaboud2018:sf} \item process of recent interest~\cite{aaboud2018:sf}
\end{itemize} \end{itemize}
@ -306,8 +306,8 @@ labelformat=brace, position=top]{subcaption}
\pause \pause
\begin{block}{Concrete Applicationss} \begin{block}{Concrete Applicationss}
\begin{enumerate} \begin{enumerate}
\item<+-> integrate \(f\) over some volume \(\Omega\) \item integrate \(f\) over some volume \(\Omega\)
\item<+-> treat \(f\) as distribution and take random samples \item treat \(f\) as distribution and take random samples
\end{enumerate} \end{enumerate}
\end{block} \end{block}
\end{frame} \end{frame}
@ -345,13 +345,13 @@ labelformat=brace, position=top]{subcaption}
\item<+-> integration error: \item<+-> integration error:
\begin{align} \begin{align}
\sigma_I^2 &= \frac{\textcolor<+->{blue}{\sigma^2}}{\textcolor<.->{red}{N}} \\ \sigma_I^2 &= \frac{\textcolor<+->{blue}{\sigma^2}}{\textcolor<.->{red}{N}} \\
\sigma^2 &= \VAR{\frac{F}{\Rho}} = \int_{\textcolor<+(3)->{blue}{\Omega}} \qty[I - \sigma^2 &= \VAR{\frac{F}{\Rho}} = \int_{\textcolor<+(2)->{blue}{\Omega}} \qty[I -
\frac{f(\vb{x})}{\textcolor<+->{blue}{\rho(\vb{x})}}]^2 \frac{f(\vb{x})}{\textcolor<.->{blue}{\rho(\vb{x})}}]^2
\textcolor<.->{blue}{\rho(\vb{x})} \textcolor<+->{blue}{\dd{\vb{x}}} \approx \frac{1}{N - 1}\sum_i \qty[I - \textcolor<.->{blue}{\rho(\vb{x})} \textcolor<+->{blue}{\dd{\vb{x}}} \approx \frac{1}{N - 1}\sum_i \qty[I -
\frac{f(\vb{x_i})}{\rho(\vb{x_i})}]^2 \label{eq:varI-approx} \frac{f(\vb{x_i})}{\rho(\vb{x_i})}]^2 \label{eq:varI-approx}
\end{align} \end{align}
\pause \pause
\item<+-> No mention of dimensionality :) \item<+-> independent of dimensionality :)
\end{itemize} \end{itemize}
\end{frame} \end{frame}
@ -365,7 +365,7 @@ labelformat=brace, position=top]{subcaption}
\begin{results} \begin{results}
\begin{itemize} \begin{itemize}
\item<3-> integrating \(\dv{\sigma}{\theta}\) with target error of \item<3-> integrating \(\dv{\sigma}{\theta}\) with target error of
\(\sigma = \SI{1e-3}{\pico\barn}\) takes \(\SI{1e-3}{\pico\barn}\) takes
\result{xs/python/xs_mc_N} samples \result{xs/python/xs_mc_N} samples
\item<4-> integrating \(\dv{\sigma}{\eta}\) takes just \item<4-> integrating \(\dv{\sigma}{\eta}\) takes just
\result{xs/python/xs_mc_eta_N} samples \result{xs/python/xs_mc_eta_N} samples
@ -402,11 +402,12 @@ labelformat=brace, position=top]{subcaption}
\end{enumerate} \end{enumerate}
\end{block} \end{block}
\pause \pause
\begin{results} \begin{results}[Results: Application to \(\dd{\sigma}/\dd{\theta}\)]
\begin{itemize} \begin{itemize}
\item Total function evaluations: \item total function evaluations:
\result{xs/python/xs_mc_θ_vegas_N}\\ \result{xs/python/xs_mc_θ_vegas_N}\\
(for same accuracy as before) (for same accuracy as before)
\item without \vegas\: \result{xs/python/xs_mc_N}
\end{itemize} \end{itemize}
\end{results} \end{results}
\end{column} \end{column}
@ -424,7 +425,7 @@ labelformat=brace, position=top]{subcaption}
\begin{frame}{Why Samples?} \begin{frame}{Why Samples?}
\begin{itemize}[<+->] \begin{itemize}[<+->]
\item same format as experimental data: direct comparison \item same format as experimental data: direct comparison possible
\item easy to generate distributions for other observables \item easy to generate distributions for other observables
\item events can be ``dressed'' with additional effects \item events can be ``dressed'' with additional effects
\end{itemize} \end{itemize}
@ -451,13 +452,13 @@ labelformat=brace, position=top]{subcaption}
\item let \(F\) be the antiderivative of \(f\), then \item let \(F\) be the antiderivative of \(f\), then
\(y=F^{-1}(x\cdot A + F(0))\) \(y=F^{-1}(x\cdot A + F(0))\)
\begin{itemize} \begin{itemize}
\item sometimes analytical form available \item<.-> sometimes analytical form available
\item otherwise tackle that numerically \item<.-> otherwise tackle that numerically
\end{itemize} \end{itemize}
\end{itemize} \end{itemize}
\end{block} \end{block}
\end{column} \end{column}
\begin{column}{.5\textwidth}<.(-3)-> \begin{column}{.5\textwidth}<.(-1)->
\begin{figure} \begin{figure}
\centering \centering
\includegraphics[width=\columnwidth]{figs/normal_cdf.pdf} \includegraphics[width=\columnwidth]{figs/normal_cdf.pdf}
@ -469,7 +470,7 @@ labelformat=brace, position=top]{subcaption}
\begin{frame}{Hit or Miss} \begin{frame}{Hit or Miss}
\begin{block}{Basic Idea} \begin{block}{Basic Idea}
\begin{itemize}[<+->] \begin{itemize}
\item take samples \({x_i}\) distributed according to \(g/B\), \item take samples \({x_i}\) distributed according to \(g/B\),
where \(B=\int_0^1g(x)\dd{x}\) and where \(B=\int_0^1g(x)\dd{x}\) and
\(\forall x\in\Omega\colon g(x)\geq f(x)\) \(\forall x\in\Omega\colon g(x)\geq f(x)\)
@ -481,9 +482,9 @@ labelformat=brace, position=top]{subcaption}
\item again: efficiency gain through reduction of variance \item again: efficiency gain through reduction of variance
\end{itemize} \end{itemize}
\end{block} \end{block}
\pause
\begin{results}<+->[Results with \(g=f_{\text{max}}\)] \begin{results}[Results with \(g=f_{\text{max}}\)]
\begin{itemize}[<+->] \begin{itemize}
\item<.-> sampling \(\dv{\sigma}{\cos\theta}\): \item<.-> sampling \(\dv{\sigma}{\cos\theta}\):
\result{xs/python/naive_th_samp} \result{xs/python/naive_th_samp}
\item sampling \(\dv{\sigma}{\eta}\): \item sampling \(\dv{\sigma}{\eta}\):
@ -505,7 +506,7 @@ labelformat=brace, position=top]{subcaption}
problems, not discussing now.} problems, not discussing now.}
\begin{itemize} \begin{itemize}
\item<+-> this approach leads to problems when \(f\) is not \item<+-> this approach leads to problems when \(f\) is not
smooth or \emph{very} small some regions smooth or \emph{very} small over larger regions
\end{itemize} \end{itemize}
\end{itemize} \end{itemize}
\end{results} \end{results}
@ -555,8 +556,8 @@ labelformat=brace, position=top]{subcaption}
} }
\begin{itemize} \begin{itemize}
\item we want: distributions of other observables \pause \item we want: distributions of other observables \pause
\item turns out: simply piping samples \(\{x_i\}\) through a map \item turns out: reconstructing full event (kinematics, ...) from
\(\gamma\colon\Omega\mapsto\mathbb{R}\) is enough sampling variables + calculating other observables from that is enough
\end{itemize} \end{itemize}
\pause \pause
\begin{figure}[p] \begin{figure}[p]
@ -592,7 +593,9 @@ labelformat=brace, position=top]{subcaption}
\sigma_{ij} = \int f_i\qty(x_1;Q^2) f_j\qty(x_2;Q^2) \hat{\sigma}_{ij}\qty(x_1, \sigma_{ij} = \int f_i\qty(x_1;Q^2) f_j\qty(x_2;Q^2) \hat{\sigma}_{ij}\qty(x_1,
x_2, Q^2)\dd{x_1}\dd{x_2} x_2, Q^2)\dd{x_1}\dd{x_2}
\end{equation} \end{equation}
\item have to be obtained experimentally (or through lattice QCD\cite{Bhat:2020ktg}) \item have to be obtained experimentally (or through lattice
QCD\cite{Bhat:2020ktg}) at given \(Q^2\) and evolved with the
\emph{DGLAP} equations
\end{itemize} \end{itemize}
\end{block} \end{block}
\end{frame} \end{frame}
@ -646,7 +649,7 @@ labelformat=brace, position=top]{subcaption}
{\huge\result{xs/python/pdf/my_sigma}} {\huge\result{xs/python/pdf/my_sigma}}
\end{center} \end{center}
\begin{itemize} \begin{itemize}
\item compatible with \sherpa\ \item compatible with \sherpa: \result{xs/python/pdf/sherpa_sigma}
\item achieved \result{xs/python/pdf/samp_eff} \item achieved \result{xs/python/pdf/samp_eff}
\item using \result{xs/python/pdf/num_increments} hypercubes \item using \result{xs/python/pdf/num_increments} hypercubes
(\(N=10^7\) samples) (\(N=10^7\) samples)
@ -654,7 +657,7 @@ labelformat=brace, position=top]{subcaption}
\end{frame} \end{frame}
\begin{frame}[allowframebreaks]{Observables} \begin{frame}[allowframebreaks]{Observables}
\pnone{effect of the pt cuts} \pnote{effect of the pt cuts}
\begin{figure}[hp] \begin{figure}[hp]
\centering \centering
\begin{subfigure}{.49\textwidth} \begin{subfigure}{.49\textwidth}
@ -687,9 +690,9 @@ labelformat=brace, position=top]{subcaption}
\item multiple interactions \item multiple interactions
\end{itemize} \end{itemize}
\end{column} \end{column}
\begin{column}{.5\textwidth} \begin{column}{.5\textwidth}<+->
\begin{center} \begin{center}
\pause {\Huge \sherpa\ can model those effects} {\Huge \sherpa\ can model those effects}
\end{center} \end{center}
\end{column} \end{column}
\end{columns} \end{columns}
@ -721,7 +724,7 @@ labelformat=brace, position=top]{subcaption}
\end{frame} \end{frame}
\subsection{Results} \subsection{Results}
\begin{frame}{Cross Sections} \begin{frame}{Fiducial Cross Sections}
\pnote{ \pnote{
- effects of the cuts - effects of the cuts
} }
@ -746,10 +749,45 @@ labelformat=brace, position=top]{subcaption}
\end{figure} \end{figure}
\end{column} \end{column}
\begin{column}{.5\textwidth} \begin{column}{.5\textwidth}
\begin{minipage}[c][.6\textheight][c]{\linewidth}
\begin{itemize} \begin{itemize}
\item photon system acquires recoil momentum \item photon system acquires recoil momentum
\item primordial \(\pt\) enhances xs in low momentum regions \item primordial \(\pt\) enhances xs in low momentum regions
\end{itemize} \end{itemize}
\end{minipage}
\begin{onlyenv}<-+>
\begin{figure}
\centering
\begin{tikzpicture}[remember picture,overlay]
\tikzset{yshift=1.2cm}
\coordinate (origin) at (0,0);
\draw[Latex-] (origin) -- (-2,0) node[left] {\(p_1\)};
\draw[Latex-] (origin) -- (2,0) coordinate (p4) node[right] {\(p_2\)};
\draw[-Latex] (origin) -- (1.32,1.5) coordinate (p2) node[right] {\(p_3\)};
\draw[-Latex] (origin) -- (-1.32,-1.5) node[left] {\(p_4\)};
\draw[fill=black] (origin) circle (.03);
\end{tikzpicture}
\end{figure}
\end{onlyenv}
\begin{onlyenv}<+>
\begin{figure}
\centering
\begin{tikzpicture}[remember picture,overlay]
\tikzset{yshift=1.2cm}
\coordinate (origin) at (0,.1);
\coordinate (right) at (2,0);
\coordinate (left) at (-2,0);
\draw[Latex-] (origin) -- (left) node[left] {\(p_1\)};
\draw[Latex-] (origin) -- (right) coordinate (p4) node[right] {\(p_2\)};
\draw[-Latex] (origin) -- (1.32,1.7) coordinate (p2) node[right] {\(p_3\)};
\draw[-Latex] (origin) -- (-1.32,-1.3) node[left] {\(p_4\)};
\draw[fill=black] (origin) circle (.03);
\draw[dashed] (left) -- (right);
\end{tikzpicture}
\end{figure}
\end{onlyenv}
\end{column} \end{column}
\end{columns} \end{columns}
\pnote{ \pnote{
@ -768,6 +806,9 @@ labelformat=brace, position=top]{subcaption}
\begin{column}{.5\textwidth} \begin{column}{.5\textwidth}
\begin{itemize} \begin{itemize}
\item boost to higher \(\pt\) \item boost to higher \(\pt\)
\item low \(\pt\lesssim \SI{40}{\giga\electronvolt}\) shape
known and expected from QCD resummation of multiple emissions
(parton shower)
\item all but \stone\ stage largely compatible \item all but \stone\ stage largely compatible
\end{itemize} \end{itemize}
\end{column} \end{column}
@ -783,7 +824,8 @@ labelformat=brace, position=top]{subcaption}
\end{column} \end{column}
\begin{column}{.5\textwidth} \begin{column}{.5\textwidth}
\begin{itemize} \begin{itemize}
\item events can be recoiled past the cuts (very rare) \item some events recoiled so both photons acquire
\(\pt > \gev{20}\) (very rare)
\item otherwise shape similar to the \stone\ stage \item otherwise shape similar to the \stone\ stage
\begin{itemize} \begin{itemize}
\item largely governed by the PDF \item largely governed by the PDF