From 76fb1ec0a6d11c49359758d71a86732f69d0281c Mon Sep 17 00:00:00 2001
From: Justus Kuhlmann <j_kuhl19@uni-muenster.de>
Date: Thu, 25 Jul 2024 15:34:30 +0200
Subject: [PATCH] better, more compact wording

---
 talk.tex | 17 ++++++++++-------
 1 file changed, 10 insertions(+), 7 deletions(-)

diff --git a/talk.tex b/talk.tex
index b482558..ce12aa7 100644
--- a/talk.tex
+++ b/talk.tex
@@ -25,7 +25,7 @@
 \newcommand{\openlat}{OpenLat}
 
 
-\title[$A_\mu^a$ impr. msl. \& mass. quarks]{Non-singlet axial current improvement for massless and massive sea quarks}
+\title[$A_\mu^a$ impr. for msl. \& mass. quarks]{Non-singlet axial current improvement for massless and massive sea quarks}
 \author[Justus Kuhlmann]{\textbf{Justus Kuhlmann}\\ Patrick Fritzsch, Jochen Heitger}
 
 % \institute wird von der Vorlage nicht direkt verwendet
@@ -55,6 +55,7 @@
 	\begin{itemize}
 		\item exp. Wilson-clover fermion framework
 		\item massive $\widehat{=}$ at $N_{\rm f}=3$ symmetric point
+		\pause
 		\vspace{.5cm}
 		\item needed for improv. quark current mass
 		\item decay constants \& matrix elements
@@ -78,7 +79,7 @@
 		\item derive from PCAC mass 
 	\end{itemize}
 	\vspace{.5cm}
-	$$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$$
+	$$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca~a\frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca~as$$
 	$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca =  - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
 \end{frame}
 
@@ -90,11 +91,13 @@
 			\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}
-		\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 $\pi^{(0)}, \pi^{(1)}$
+		\pause
+		\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 project $f_{\rm A}$ and $f_{\rm P}$ onto the eigenstates of $F_1$
+		\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?
@@ -125,7 +128,7 @@
 		\end{tabular}
 	\end{center}
 	\begin{itemize}
-		\item interested in 2 LCPs: chiral and at $N_{\rm f}=3$ symmetric point
+		\item interested in 2 LCPs: chiral and $N_{\rm f}=3$ sym. point
 		\item matching sym. point of \openlat~\arxivtag{2201.03874}
 	\end{itemize}
 \end{frame}
@@ -134,7 +137,7 @@
 	\frametitle{Improvement of the axial-vector current}
 	\framesubtitle{$\ca$ estimators}
 	\begin{tabular}{cc}
-		Close to chiral ensembles&Symmetric ensembles\\
+		Critical point ensembles&Symmetric point ensembles\\
 		\includegraphics[width=\halflinewidth]{plots/plateaus_chi_0.2_0.3_0124_ee_ee_total_quad.pdf}&
 		\includegraphics[width=\halflinewidth]{plots/plateaus_sym_0.2_0.3_0124_ee_ee_total_quad.pdf}	
 	\end{tabular}
@@ -147,7 +150,7 @@
 	\framesubtitle{... to the symmetric and critical point}
 	\begin{itemize}
 		\item ensembles not exactly tuned
-		\item able to interpolate to the desired points due to two or three values per $\beta$
+		\item able to interpolate to the desired points due to 2 or 3 ensembles per $\beta$
 		\item determine points of interest as in \openlat~ensembles \arxivtag{2201.03874}
 		\item define: $$\Phi^{\rm SF}_4 = \frac{3}{2}\,8t_0\,|m_{\rm eff}|\,m_{\rm eff}
 		\quad \Rightarrow \quad \Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm cr}}} = 0\,,\;\Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm sym}}} = 1.115$$