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https://github.com/vale981/bachelor_thesis
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franks improvements
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1 changed files with 75 additions and 33 deletions
100
talk/slides.tex
100
talk/slides.tex
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@ -16,7 +16,6 @@ labelformat=brace, position=top]{subcaption}
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\usepackage{ifdraft}
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\usepackage{appendixnumberbeamer}
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\usetikzlibrary{arrows,shapes,angles,quotes,arrows.meta,external}
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\tikzexternalize[prefix=tikz/]
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\graphicspath{ {figs/} }
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\addbibresource{thesis.bib}
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@ -171,12 +170,13 @@ labelformat=brace, position=top]{subcaption}
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\begin{block}{Diphoton Process \(\qqgg\)}
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\begin{itemize}
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\item simple QED process, calculable by hand
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\item higgs decay channel: \(H\rightarrow \gamma\gamma\)
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\item background for important higgs decay channel:
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\(H\rightarrow \gamma\gamma\)
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\begin{itemize}
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\item instrumental in its
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discovery~\cite{Aad:2012tfa,Chatrchyan:2012ufa}
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\end{itemize}
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\item dihiggs decay \(HH\rightarrow b\bar{b}\gamma\gamma\)
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\item partial background for dihiggs decay \(HH\rightarrow b\bar{b}\gamma\gamma\)
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\begin{itemize}
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\item process of recent interest~\cite{aaboud2018:sf}
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\end{itemize}
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@ -306,8 +306,8 @@ labelformat=brace, position=top]{subcaption}
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\pause
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\begin{block}{Concrete Applicationss}
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\begin{enumerate}
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\item<+-> integrate \(f\) over some volume \(\Omega\)
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\item<+-> treat \(f\) as distribution and take random samples
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\item integrate \(f\) over some volume \(\Omega\)
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\item treat \(f\) as distribution and take random samples
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\end{enumerate}
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\end{block}
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\end{frame}
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@ -345,13 +345,13 @@ labelformat=brace, position=top]{subcaption}
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\item<+-> integration error:
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\begin{align}
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\sigma_I^2 &= \frac{\textcolor<+->{blue}{\sigma^2}}{\textcolor<.->{red}{N}} \\
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\sigma^2 &= \VAR{\frac{F}{\Rho}} = \int_{\textcolor<+(3)->{blue}{\Omega}} \qty[I -
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\frac{f(\vb{x})}{\textcolor<+->{blue}{\rho(\vb{x})}}]^2
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\sigma^2 &= \VAR{\frac{F}{\Rho}} = \int_{\textcolor<+(2)->{blue}{\Omega}} \qty[I -
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\frac{f(\vb{x})}{\textcolor<.->{blue}{\rho(\vb{x})}}]^2
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\textcolor<.->{blue}{\rho(\vb{x})} \textcolor<+->{blue}{\dd{\vb{x}}} \approx \frac{1}{N - 1}\sum_i \qty[I -
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\frac{f(\vb{x_i})}{\rho(\vb{x_i})}]^2 \label{eq:varI-approx}
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\end{align}
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\pause
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\item<+-> No mention of dimensionality :)
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\item<+-> independent of dimensionality :)
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\end{itemize}
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\end{frame}
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@ -365,7 +365,7 @@ labelformat=brace, position=top]{subcaption}
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\begin{results}
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\begin{itemize}
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\item<3-> integrating \(\dv{\sigma}{\theta}\) with target error of
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\(\sigma = \SI{1e-3}{\pico\barn}\) takes
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\(\SI{1e-3}{\pico\barn}\) takes
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\result{xs/python/xs_mc_N} samples
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\item<4-> integrating \(\dv{\sigma}{\eta}\) takes just
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\result{xs/python/xs_mc_eta_N} samples
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@ -402,11 +402,12 @@ labelformat=brace, position=top]{subcaption}
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\end{enumerate}
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\end{block}
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\pause
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\begin{results}
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\begin{results}[Results: Application to \(\dd{\sigma}/\dd{\theta}\)]
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\begin{itemize}
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\item Total function evaluations:
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\item total function evaluations:
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\result{xs/python/xs_mc_θ_vegas_N}\\
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(for same accuracy as before)
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\item without \vegas\: \result{xs/python/xs_mc_N}
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\end{itemize}
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\end{results}
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\end{column}
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@ -424,7 +425,7 @@ labelformat=brace, position=top]{subcaption}
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\begin{frame}{Why Samples?}
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\begin{itemize}[<+->]
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\item same format as experimental data: direct comparison
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\item same format as experimental data: direct comparison possible
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\item easy to generate distributions for other observables
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\item events can be ``dressed'' with additional effects
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\end{itemize}
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@ -451,13 +452,13 @@ labelformat=brace, position=top]{subcaption}
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\item let \(F\) be the antiderivative of \(f\), then
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\(y=F^{-1}(x\cdot A + F(0))\)
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\begin{itemize}
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\item sometimes analytical form available
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\item otherwise tackle that numerically
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\item<.-> sometimes analytical form available
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\item<.-> otherwise tackle that numerically
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\end{itemize}
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\end{itemize}
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\end{block}
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\end{column}
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\begin{column}{.5\textwidth}<.(-3)->
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\begin{column}{.5\textwidth}<.(-1)->
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\begin{figure}
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\centering
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\includegraphics[width=\columnwidth]{figs/normal_cdf.pdf}
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@ -469,7 +470,7 @@ labelformat=brace, position=top]{subcaption}
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\begin{frame}{Hit or Miss}
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\begin{block}{Basic Idea}
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\begin{itemize}[<+->]
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\begin{itemize}
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\item take samples \({x_i}\) distributed according to \(g/B\),
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where \(B=\int_0^1g(x)\dd{x}\) and
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\(\forall x\in\Omega\colon g(x)\geq f(x)\)
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@ -481,9 +482,9 @@ labelformat=brace, position=top]{subcaption}
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\item again: efficiency gain through reduction of variance
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\end{itemize}
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\end{block}
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\begin{results}<+->[Results with \(g=f_{\text{max}}\)]
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\begin{itemize}[<+->]
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\pause
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\begin{results}[Results with \(g=f_{\text{max}}\)]
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\begin{itemize}
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\item<.-> sampling \(\dv{\sigma}{\cos\theta}\):
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\result{xs/python/naive_th_samp}
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\item sampling \(\dv{\sigma}{\eta}\):
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@ -505,7 +506,7 @@ labelformat=brace, position=top]{subcaption}
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problems, not discussing now.}
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\begin{itemize}
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\item<+-> this approach leads to problems when \(f\) is not
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smooth or \emph{very} small some regions
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smooth or \emph{very} small over larger regions
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\end{itemize}
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\end{itemize}
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\end{results}
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@ -555,8 +556,8 @@ labelformat=brace, position=top]{subcaption}
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}
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\begin{itemize}
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\item we want: distributions of other observables \pause
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\item turns out: simply piping samples \(\{x_i\}\) through a map
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\(\gamma\colon\Omega\mapsto\mathbb{R}\) is enough
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\item turns out: reconstructing full event (kinematics, ...) from
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sampling variables + calculating other observables from that is enough
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\end{itemize}
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\pause
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\begin{figure}[p]
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@ -592,7 +593,9 @@ labelformat=brace, position=top]{subcaption}
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\sigma_{ij} = \int f_i\qty(x_1;Q^2) f_j\qty(x_2;Q^2) \hat{\sigma}_{ij}\qty(x_1,
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x_2, Q^2)\dd{x_1}\dd{x_2}
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\end{equation}
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\item have to be obtained experimentally (or through lattice QCD\cite{Bhat:2020ktg})
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\item have to be obtained experimentally (or through lattice
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QCD\cite{Bhat:2020ktg}) at given \(Q^2\) and evolved with the
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\emph{DGLAP} equations
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\end{itemize}
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\end{block}
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\end{frame}
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@ -646,7 +649,7 @@ labelformat=brace, position=top]{subcaption}
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{\huge\result{xs/python/pdf/my_sigma}}
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\end{center}
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\begin{itemize}
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\item compatible with \sherpa\
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\item compatible with \sherpa: \result{xs/python/pdf/sherpa_sigma}
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\item achieved \result{xs/python/pdf/samp_eff}
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\item using \result{xs/python/pdf/num_increments} hypercubes
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(\(N=10^7\) samples)
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@ -654,7 +657,7 @@ labelformat=brace, position=top]{subcaption}
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\end{frame}
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\begin{frame}[allowframebreaks]{Observables}
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\pnone{effect of the pt cuts}
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\pnote{effect of the pt cuts}
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\begin{figure}[hp]
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\centering
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\begin{subfigure}{.49\textwidth}
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@ -687,9 +690,9 @@ labelformat=brace, position=top]{subcaption}
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\item multiple interactions
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\end{itemize}
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\end{column}
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\begin{column}{.5\textwidth}
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\begin{column}{.5\textwidth}<+->
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\begin{center}
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\pause {\Huge \sherpa\ can model those effects}
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{\Huge \sherpa\ can model those effects}
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\end{center}
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\end{column}
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\end{columns}
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@ -721,7 +724,7 @@ labelformat=brace, position=top]{subcaption}
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\end{frame}
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\subsection{Results}
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\begin{frame}{Cross Sections}
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\begin{frame}{Fiducial Cross Sections}
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\pnote{
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- effects of the cuts
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}
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@ -746,10 +749,45 @@ labelformat=brace, position=top]{subcaption}
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\end{figure}
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\end{column}
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\begin{column}{.5\textwidth}
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\begin{minipage}[c][.6\textheight][c]{\linewidth}
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\begin{itemize}
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\item photon system acquires recoil momentum
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\item primordial \(\pt\) enhances xs in low momentum regions
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\end{itemize}
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\end{minipage}
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\begin{onlyenv}<-+>
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\begin{figure}
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\centering
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\begin{tikzpicture}[remember picture,overlay]
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\tikzset{yshift=1.2cm}
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\coordinate (origin) at (0,0);
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\draw[Latex-] (origin) -- (-2,0) node[left] {\(p_1\)};
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\draw[Latex-] (origin) -- (2,0) coordinate (p4) node[right] {\(p_2\)};
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\draw[-Latex] (origin) -- (1.32,1.5) coordinate (p2) node[right] {\(p_3\)};
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\draw[-Latex] (origin) -- (-1.32,-1.5) node[left] {\(p_4\)};
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\draw[fill=black] (origin) circle (.03);
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\end{tikzpicture}
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\end{figure}
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\end{onlyenv}
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\begin{onlyenv}<+>
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\begin{figure}
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\centering
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\begin{tikzpicture}[remember picture,overlay]
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\tikzset{yshift=1.2cm}
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\coordinate (origin) at (0,.1);
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\coordinate (right) at (2,0);
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\coordinate (left) at (-2,0);
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\draw[Latex-] (origin) -- (left) node[left] {\(p_1\)};
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\draw[Latex-] (origin) -- (right) coordinate (p4) node[right] {\(p_2\)};
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\draw[-Latex] (origin) -- (1.32,1.7) coordinate (p2) node[right] {\(p_3\)};
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\draw[-Latex] (origin) -- (-1.32,-1.3) node[left] {\(p_4\)};
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\draw[fill=black] (origin) circle (.03);
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\draw[dashed] (left) -- (right);
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\end{tikzpicture}
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\end{figure}
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\end{onlyenv}
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\end{column}
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\end{columns}
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\pnote{
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@ -768,6 +806,9 @@ labelformat=brace, position=top]{subcaption}
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\begin{column}{.5\textwidth}
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\begin{itemize}
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\item boost to higher \(\pt\)
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\item low \(\pt\lesssim \SI{40}{\giga\electronvolt}\) shape
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known and expected from QCD resummation of multiple emissions
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(parton shower)
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\item all but \stone\ stage largely compatible
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\end{itemize}
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\end{column}
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@ -783,7 +824,8 @@ labelformat=brace, position=top]{subcaption}
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\end{column}
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\begin{column}{.5\textwidth}
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\begin{itemize}
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\item events can be recoiled past the cuts (very rare)
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\item some events recoiled so both photons acquire
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\(\pt > \gev{20}\) (very rare)
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\item otherwise shape similar to the \stone\ stage
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\begin{itemize}
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\item largely governed by the PDF
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