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.datalad/config
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[datalad "dataset"]
id = 56aad42b-b483-4f65-9c63-d24ef3cac2c2
[datalad "containers.TeX"]
image = .images/texlive
cmdexec = docker run {img} {cmd}

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cA_analysis

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Subproject commit 6fd3a4938973adfa7b6444e8caf5d6282072c0ba
Subproject commit af344f1f55496eb05232ac7bc497a2100682d792

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justfile
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_default:
@just --list
compile MESSAGE: update-plots
datalad save -m "{{MESSAGE}}" talk.tex
datalad run -o talk.pdf -i talk.tex -m "build pdf" "lualatex talk.tex && lualatex talk.tex"
update-plots:
datalad run -o plots -m "update plots" "bash plt_update.sh"

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justfile Symbolic link
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.git/annex/objects/ZZ/ZQ/MD5E-s312--c7c1fdc72cdf960f7ad7299d761074d1/MD5E-s312--c7c1fdc72cdf960f7ad7299d761074d1

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plots/T48L48_b4.00_k0.1384942/plot_dr_ds10-0124projection-wgcorr.pdf
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../../.git/annex/objects/KZ/VK/MD5E-s15402--1c37f44962b8c3ae17584a237ea24d53.pdf/MD5E-s15402--1c37f44962b8c3ae17584a237ea24d53.pdf

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plots/T48L48_b4.00_k0.1384942/plot_m_eff_P-0124projection-wgcorr.pdf
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../../.git/annex/objects/v6/9G/MD5E-s19583--53aa1c2167f4f91a219cae041f4d2c29.pdf/MD5E-s19583--53aa1c2167f4f91a219cae041f4d2c29.pdf

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plots/T56L56_b4.10_k0.1381410/plot_dr_ds10-0124projection-wgcorr.pdf
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../../.git/annex/objects/fF/xf/MD5E-s16516--07e54acdcb61b8a95684bfb4afe9abfa.pdf/MD5E-s16516--07e54acdcb61b8a95684bfb4afe9abfa.pdf

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plots/T56L56_b4.10_k0.1381410/plot_m_eff_P-0124projection-wgcorr.pdf
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../../.git/annex/objects/F6/g9/MD5E-s20786--5588f21cefc0aa7d831ba5df5d565c35.pdf/MD5E-s20786--5588f21cefc0aa7d831ba5df5d565c35.pdf

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plots/ca2sym_b3.9.pdf
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../.git/annex/objects/3W/xG/MD5E-s15046--24f1eabf567a36fd075c012b14461706.9.pdf/MD5E-s15046--24f1eabf567a36fd075c012b14461706.9.pdf
../.git/annex/objects/1g/K1/MD5E-s15046--bf0ab1e4bb9433d0cd294bdcb37528f4.9.pdf/MD5E-s15046--bf0ab1e4bb9433d0cd294bdcb37528f4.9.pdf

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plots/ca2sym_b4.1.pdf Symbolic link
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../.git/annex/objects/6z/V6/MD5E-s15345--35daf76fc2bf3f2456596dada3d73214.1.pdf/MD5E-s15345--35daf76fc2bf3f2456596dada3d73214.1.pdf

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plots/ca2sym_b4.pdf
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../.git/annex/objects/j8/2p/MD5E-s15404--105a9b2fb44c4312cb5bc8b342093125.pdf/MD5E-s15404--105a9b2fb44c4312cb5bc8b342093125.pdf
../.git/annex/objects/Kw/1V/MD5E-s15404--b75157f027d9e94d5e681c6a0c89229b.pdf/MD5E-s15404--b75157f027d9e94d5e681c6a0c89229b.pdf

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plots/fix_sym_b3.9.pdf
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../.git/annex/objects/zV/87/MD5E-s21143--f35d0804e7f94ed2ded33739cca4d926.9.pdf/MD5E-s21143--f35d0804e7f94ed2ded33739cca4d926.9.pdf
../.git/annex/objects/P5/3V/MD5E-s21143--4a699d1536673f8706ad02885689edc8.9.pdf/MD5E-s21143--4a699d1536673f8706ad02885689edc8.9.pdf

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plots/fix_sym_b4.1.pdf Symbolic link
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../.git/annex/objects/mf/KQ/MD5E-s21018--d579caf997fcc0f45b1b9ae51261fda1.1.pdf/MD5E-s21018--d579caf997fcc0f45b1b9ae51261fda1.1.pdf

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plots/fix_sym_b4.pdf
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../.git/annex/objects/Gj/z9/MD5E-s21036--4409bd5d72b3d7d678b913288d652f3e.pdf/MD5E-s21036--4409bd5d72b3d7d678b913288d652f3e.pdf
../.git/annex/objects/zq/Fp/MD5E-s21036--57382f1fc56bd304ae27c2f135bb0960.pdf/MD5E-s21036--57382f1fc56bd304ae27c2f135bb0960.pdf

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plots/g0sq_chi.pdf
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../.git/annex/objects/Kx/F1/MD5E-s20086--bac2b7f5102e68b001f01b14f0a73c62.pdf/MD5E-s20086--bac2b7f5102e68b001f01b14f0a73c62.pdf
../.git/annex/objects/kz/mZ/MD5E-s20071--63797fdd400035849b1bd06ea3b76f81.pdf/MD5E-s20071--63797fdd400035849b1bd06ea3b76f81.pdf

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plots/g0sq_sym.pdf
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../.git/annex/objects/04/f4/MD5E-s20401--6a13a0a0544ed1542f580b8e9ebad42c.pdf/MD5E-s20401--6a13a0a0544ed1542f580b8e9ebad42c.pdf
../.git/annex/objects/pV/2m/MD5E-s20432--9e1ca9bcf2606c369e33342243db08bd.pdf/MD5E-s20432--9e1ca9bcf2606c369e33342243db08bd.pdf

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plots/test_f_part_ZA_chi_imp.pdf
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../.git/annex/objects/vX/35/MD5E-s27909--5d40d50f3aff4fd9aca6002702e6a833.pdf/MD5E-s27909--5d40d50f3aff4fd9aca6002702e6a833.pdf

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plt_update.sh
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#! /bin/bash
rm -rf plots/*
mkdir plots/{T48L48_b4.00_k0.1384942,T56L56_b4.10_k0.1381410}
datalad update -d cA_analysis --how=merge
datalad get cA_analysis/plot_vault/{overview,interpolations,T48L48_b4.00_k0.1384942,T56L56_b4.10_k0.1381410}
cp ./cA_analysis/plot_vault/overview/plateaus_{chi,sym}_0.2_0.3_0124_ee_ee_total_quad.pdf plots
cp ./cA_analysis/plot_vault/interpolations/fix_sym_b{3.9,4}.pdf plots
cp ./cA_analysis/plot_vault/interpolations/ca2sym_b{3.9,4}.pdf plots
cp ./cA_analysis/plot_vault/interpolations/g0sq_{chi,sym}.pdf plots
cp ../../research_env2/charmonium_analysis/plot_vault/decay_constants/test_f_part_ZA_chi_imp.pdf plots
cp ./cA_analysis/plot_vault/T48L48_b4.00_k0.1384942/plot_{dr_ds10,m_eff_P}-0124projection-wgcorr.pdf plots/T48L48_b4.00_k0.1384942
cp ./cA_analysis/plot_vault/T56L56_b4.10_k0.1381410/plot_{dr_ds10,m_eff_P}-0124projection-wgcorr.pdf plots/T56L56_b4.10_k0.1381410
rm plots/*
cp ../../research_env2/cA_analysis/plot_vault/overview/plateaus_{chi,sym}_0.2_0.3_0124_ee_ee_total_quad.pdf plots
cp ../../research_env2/cA_analysis/plot_vault/interpolations/fix_sym_b{3.9,4}.pdf plots
cp ../../research_env2/cA_analysis/plot_vault/interpolations/ca2sym_b{3.9,4}.pdf plots
cp ../../research_env2/cA_analysis/plot_vault/interpolations/g0sq_{chi,sym}.pdf plots

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talk.pdf
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.git/annex/objects/7V/7P/MD5E-s446841--cdc44d630eb943ea5cb4bc1f4d1a00c2.pdf/MD5E-s446841--cdc44d630eb943ea5cb4bc1f4d1a00c2.pdf
.git/annex/objects/zK/3g/MD5E-s367460--c68ea62437ece7020a749496a366b2ba.pdf/MD5E-s367460--c68ea62437ece7020a749496a366b2ba.pdf

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talk.tex
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\frametitle{Determination of $\ca$}
\begin{itemize}
\item Schrödinger functional boundary conditions
\item similar to quenched \arxivtag{hep-lat/9609035}, $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999, hep-lat/0703006}
\item similar to quenched \arxivtag{hep-lat/9609035}, $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999}
\item derive from PCAC mass
\end{itemize}
\vspace{.5cm}
$$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca~a\frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca~as$$
$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
\begin{itemize}
\item states (0) and (1) are the PS ground and first excited state in our setup
\item PCAC relation holds for both
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{The wavefunction method}
\begin{itemize}
\item construct pseudoscalar states
\item mimic pionic sources on boundaries $\pi^{(0)}, \pi^{(1)}$ and require PCAC relation to hold for both
\begin{itemize}
\item H-like basis wavefunctions:
$\omega_{1} = e^{-r/a_0}\;,\quad\omega_{2} = r~e^{-r/a_0}\;,\quad\omega_{3} = e^{-r/(2a_0)}$
\item also include $\omega_{4} = {\rm cons.}\;,\quad\omega_{5} = -r^2~e^{-r/a_0}$
\item basis wavefunctions:
$\omega_{\rm b1} = e^{-r/a_0}\;,\quad\omega_{\rm b2} = r~e^{-r/a_0}\;,\quad\omega_{\rm b3} = e^{-r/(2a_0)}$
\item also include $\omega_{\rm b4} = {\rm cons.}\;,\quad\omega_{\rm b5} = -r^2~e^{-r/a_0}$
\quad with $r=|\vec{y}-\vec{x}|$
\end{itemize}
\pause
\item diagonalise boundary-to-boundary corr. func. $(F_1)_{i,j} = -\langle O(\omega_{i}) O'(\omega_{j})\rangle$
\item eigenvectors of boundary-to-boundary corr. func. $(F_1)_{i,j} = -\langle O(\omega_{{\rm b}i}) O'(\omega_{{\rm b}j})\rangle$
\vspace{.5cm}
\pause
\item employ eigenvectors of $(F_1)_{i,j}$ to project $f_{\rm A}(x_0)$ and $f_{\rm P}(x_0)$ onto the eigenstates
\item diagonalise $(F_1)_{i,j}$ \& project $f_{\rm A}(x_0)$ and $f_{\rm P}(x_0)$ onto the eigenstates
% Question: do we include all wavefunctions or just some?
% How does this interplay with the states that we achieve?
% Which is the optimal wf combination?
% \item also: where on the lattice do we define $c_{\rm A}$?
\vspace{.5cm}
\pause
\item evaluate $c_{\rm A}(x_0)$ with projected correlation functions
\item evaluate $c_{\rm A}(x_0)$ with these source terms
\item later: choice of $x_0$ and wavefunction basis is part of the improvement condition
\end{itemize}
\end{frame}
@ -120,7 +116,7 @@
\begin{center}
\begin{tabular}{cc|c|c|c|c}
\toprule
$L/a$ & $\beta$ & $\kappa_{1}\approx\kappa_{\rm cr}$ & $\kappa_{2}$ & $\kappa_{3}\approx\kappa_{\rm sym}$&$\approx a\;{\rm [fm]}$\\
$L/a$ & $\beta$ & $\kappa_{1}\approx\kappa_{\rm cr}$ & $\kappa_{2}$ & $\kappa_{3}\approx\kappa_{\rm sym}$&$\approx a$\\
\midrule
24&3.685&0.1396980&0.1395500&0.1394400&0.120\\
32&3.80&0.1392500&---&0.1389630&0.095\\
@ -182,7 +178,7 @@
\begin{frame}
\frametitle{Improvement of the axial-vector current}
\framesubtitle{Interpolations in $g_0^2$}
\framesubtitle{Final interpolations in $g_0^2$}
\begin{tabular}{cc}
\includegraphics[width=\halflinewidth]{plots/g0sq_chi.pdf}&
\includegraphics[width=\halflinewidth]{plots/g0sq_sym.pdf}
@ -193,27 +189,24 @@
\begin{frame}
\frametitle{First scaling test of improvement}
\begin{itemize}
\item Example: Calculate $f_{\pi K}$ with stabilised Wilson fermions
\item Example: Calculate $f_\pi/K$ with stabilised Wilson fermions
\item symmetric point \openlat~ensembles
\item improve with $\ca = 0$ vs $\ca(g_0^2)|_{\rm chi}$ vs $\ca(g_0^2)|_{\rm sym}$
$$f_{\pi K}^{\rm RI} = Z_{\rm A} (1+b_{\rm A} am_{\rm q}+\bar{b}_{\rm A} a\Tr[M_{\rm q}])\frac{\sqrt{2} \mathcal{A}_{\rm A_0P}}{\sqrt{\mathcal{A}_{\rm PP} m_\pi}}$$
with $C_{XX} \propto \mathcal{A}_{XX}{\rm e}^{-mx_0}$
$$f_{\rm A}^{RI} = Z_{\rm A} (1+b_{\rm A} m_{\rm q})(1+\bar{b}_{\rm A} \Tr[M_{\rm q}])f\frac{\sqrt{2} \mathcal{A}_{\rm A_0P}}{\sqrt{\mathcal{A}_{\rm PP} m_\pi}}$$
\item renormalisation: $Z_{\rm A}$ preliminary, $b_{\rm A}$ from pert. theory, $\bar{b}_{\rm A}$ neglected
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{First scaling test of improvement}
\frametitle{First study of improvement}
\framesubtitle{Results}
\vspace{-.3cm}
\centering
\includegraphics[width=.6\linewidth]{plots/test_f_part_ZA_chi_imp.pdf}
%\includegraphics{plots/test_f.pdf}
\end{frame}
\begin{frame}
\frametitle{Outlook}
\begin{itemize}
\item finish $\za$, $\zv$, $\bV$ and $\bar{b}_{\rm V}$ through SF
\item finish $\zv$, $\bV$ and $\bar{b}_{\rm V}$ through SF
\item further improvement and renormalisation currently in the works:
\begin{itemize}
\item vector and tensor current improvement ($c_{\rm V}$, $c_{\rm T}$)
@ -222,22 +215,4 @@
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Backup}
\framesubtitle{$\Delta r$ and $\Delta s$ behaviour}
\begin{tabular}{cc}
\includegraphics[width=\halflinewidth]{plots/T48L48_b4.00_k0.1384942/plot_dr_ds10-0124projection-wgcorr.pdf}&
\includegraphics[width=\halflinewidth]{plots/T56L56_b4.10_k0.1381410/plot_dr_ds10-0124projection-wgcorr.pdf}
\end{tabular}
\end{frame}
\begin{frame}
\frametitle{Backup}
\framesubtitle{Behaviour of $\fp$ projected}
\begin{tabular}{cc}
\includegraphics[width=\halflinewidth]{plots/T48L48_b4.00_k0.1384942/plot_m_eff_P-0124projection-wgcorr.pdf}&
\includegraphics[width=\halflinewidth]{plots/T56L56_b4.10_k0.1381410/plot_m_eff_P-0124projection-wgcorr.pdf}
\end{tabular}
\end{frame}
\end{document}