better, more compact wording
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17
talk.tex
17
talk.tex
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@ -25,7 +25,7 @@
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\newcommand{\openlat}{OpenLat}
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\newcommand{\openlat}{OpenLat}
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\title[$A_\mu^a$ impr. msl. \& mass. quarks]{Non-singlet axial current improvement for massless and massive sea quarks}
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\title[$A_\mu^a$ impr. for msl. \& mass. quarks]{Non-singlet axial current improvement for massless and massive sea quarks}
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\author[Justus Kuhlmann]{\textbf{Justus Kuhlmann}\\ Patrick Fritzsch, Jochen Heitger}
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\author[Justus Kuhlmann]{\textbf{Justus Kuhlmann}\\ Patrick Fritzsch, Jochen Heitger}
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% \institute wird von der Vorlage nicht direkt verwendet
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% \institute wird von der Vorlage nicht direkt verwendet
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@ -55,6 +55,7 @@
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\begin{itemize}
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\begin{itemize}
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\item exp. Wilson-clover fermion framework
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\item exp. Wilson-clover fermion framework
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\item massive $\widehat{=}$ at $N_{\rm f}=3$ symmetric point
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\item massive $\widehat{=}$ at $N_{\rm f}=3$ symmetric point
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\pause
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\vspace{.5cm}
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\vspace{.5cm}
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\item needed for improv. quark current mass
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\item needed for improv. quark current mass
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\item decay constants \& matrix elements
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\item decay constants \& matrix elements
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@ -78,7 +79,7 @@
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\item derive from PCAC mass
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\item derive from PCAC mass
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\end{itemize}
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\end{itemize}
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\vspace{.5cm}
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\vspace{.5cm}
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$$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$$
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$$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca~a\frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca~as$$
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$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
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$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
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\end{frame}
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\end{frame}
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@ -90,11 +91,13 @@
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\item basis wavefunctions:
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\item basis wavefunctions:
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$\omega_{\rm b1} = e^{-r/a_0}\;,\quad\omega_{\rm b2} = r~e^{-r/a_0}\;,\quad\omega_{\rm b3} = e^{-r/(2a_0)}$
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$\omega_{\rm b1} = e^{-r/a_0}\;,\quad\omega_{\rm b2} = r~e^{-r/a_0}\;,\quad\omega_{\rm b3} = e^{-r/(2a_0)}$
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\item also include $\omega_{\rm b4} = {\rm cons.}\;,\quad\omega_{\rm b5} = -r^2~e^{-r/a_0}$
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\item also include $\omega_{\rm b4} = {\rm cons.}\;,\quad\omega_{\rm b5} = -r^2~e^{-r/a_0}$
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\quad with $r=|\vec{y}-\vec{x}|$
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\end{itemize}
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\end{itemize}
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\item eigenvectors of boundary-to-boundary corr. func. $(F_1)_{i,j} = -\langle O(\omega_{{\rm b}i}) O'(\omega_{{\rm b}j})\rangle$ lead to eigenstates $\pi^{(0)}, \pi^{(1)}$
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\pause
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\item eigenvectors of boundary-to-boundary corr. func. $(F_1)_{i,j} = -\langle O(\omega_{{\rm b}i}) O'(\omega_{{\rm b}j})\rangle$
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\vspace{.5cm}
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\vspace{.5cm}
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\pause
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\pause
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\item project $f_{\rm A}$ and $f_{\rm P}$ onto the eigenstates of $F_1$
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\item diagonalise $(F_1)_{i,j}$ \& project $f_{\rm A}(x_0)$ and $f_{\rm P}(x_0)$ onto the eigenstates
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% Question: do we include all wavefunctions or just some?
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% Question: do we include all wavefunctions or just some?
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% How does this interplay with the states that we achieve?
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% How does this interplay with the states that we achieve?
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% Which is the optimal wf combination?
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% Which is the optimal wf combination?
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@ -125,7 +128,7 @@
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\end{tabular}
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\end{tabular}
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\end{center}
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\end{center}
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\begin{itemize}
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\begin{itemize}
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\item interested in 2 LCPs: chiral and at $N_{\rm f}=3$ symmetric point
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\item interested in 2 LCPs: chiral and $N_{\rm f}=3$ sym. point
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\item matching sym. point of \openlat~\arxivtag{2201.03874}
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\item matching sym. point of \openlat~\arxivtag{2201.03874}
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\end{itemize}
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\end{itemize}
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\end{frame}
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\end{frame}
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@ -134,7 +137,7 @@
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\frametitle{Improvement of the axial-vector current}
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\frametitle{Improvement of the axial-vector current}
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\framesubtitle{$\ca$ estimators}
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\framesubtitle{$\ca$ estimators}
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\begin{tabular}{cc}
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\begin{tabular}{cc}
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Close to chiral ensembles&Symmetric ensembles\\
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Critical point ensembles&Symmetric point ensembles\\
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\includegraphics[width=\halflinewidth]{plots/plateaus_chi_0.2_0.3_0124_ee_ee_total_quad.pdf}&
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\includegraphics[width=\halflinewidth]{plots/plateaus_chi_0.2_0.3_0124_ee_ee_total_quad.pdf}&
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\includegraphics[width=\halflinewidth]{plots/plateaus_sym_0.2_0.3_0124_ee_ee_total_quad.pdf}
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\includegraphics[width=\halflinewidth]{plots/plateaus_sym_0.2_0.3_0124_ee_ee_total_quad.pdf}
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\end{tabular}
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\end{tabular}
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\framesubtitle{... to the symmetric and critical point}
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\framesubtitle{... to the symmetric and critical point}
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\begin{itemize}
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\begin{itemize}
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\item ensembles not exactly tuned
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\item ensembles not exactly tuned
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\item able to interpolate to the desired points due to two or three values per $\beta$
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\item able to interpolate to the desired points due to 2 or 3 ensembles per $\beta$
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\item determine points of interest as in \openlat~ensembles \arxivtag{2201.03874}
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\item determine points of interest as in \openlat~ensembles \arxivtag{2201.03874}
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\item define: $$\Phi^{\rm SF}_4 = \frac{3}{2}\,8t_0\,|m_{\rm eff}|\,m_{\rm eff}
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\item define: $$\Phi^{\rm SF}_4 = \frac{3}{2}\,8t_0\,|m_{\rm eff}|\,m_{\rm eff}
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\quad \Rightarrow \quad \Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm cr}}} = 0\,,\;\Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm sym}}} = 1.115$$
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\quad \Rightarrow \quad \Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm cr}}} = 0\,,\;\Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm sym}}} = 1.115$$
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