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talk.tex
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@ -25,7 +25,7 @@
\newcommand{\openlat}{OpenLat} \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} \author[Justus Kuhlmann]{\textbf{Justus Kuhlmann}\\ Patrick Fritzsch, Jochen Heitger}
% \institute wird von der Vorlage nicht direkt verwendet % \institute wird von der Vorlage nicht direkt verwendet
@ -55,6 +55,7 @@
\begin{itemize} \begin{itemize}
\item exp. Wilson-clover fermion framework \item exp. Wilson-clover fermion framework
\item massive $\widehat{=}$ at $N_{\rm f}=3$ symmetric point \item massive $\widehat{=}$ at $N_{\rm f}=3$ symmetric point
\pause
\vspace{.5cm} \vspace{.5cm}
\item needed for improv. quark current mass \item needed for improv. quark current mass
\item decay constants \& matrix elements \item decay constants \& matrix elements
@ -78,7 +79,7 @@
\item derive from PCAC mass \item derive from PCAC mass
\end{itemize} \end{itemize}
\vspace{.5cm} \vspace{.5cm}
$$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$$ $$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca~a\frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca~as$$
$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$ $$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
\end{frame} \end{frame}
@ -90,11 +91,13 @@
\item basis wavefunctions: \item basis wavefunctions:
$\omega_{\rm b1} = e^{-r/a_0}\;,\quad\omega_{\rm b2} = r~e^{-r/a_0}\;,\quad\omega_{\rm b3} = e^{-r/(2a_0)}$ $\omega_{\rm b1} = e^{-r/a_0}\;,\quad\omega_{\rm b2} = r~e^{-r/a_0}\;,\quad\omega_{\rm b3} = e^{-r/(2a_0)}$
\item also include $\omega_{\rm b4} = {\rm cons.}\;,\quad\omega_{\rm b5} = -r^2~e^{-r/a_0}$ \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} \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} \vspace{.5cm}
\pause \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? % Question: do we include all wavefunctions or just some?
% How does this interplay with the states that we achieve? % How does this interplay with the states that we achieve?
% Which is the optimal wf combination? % Which is the optimal wf combination?
@ -125,7 +128,7 @@
\end{tabular} \end{tabular}
\end{center} \end{center}
\begin{itemize} \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} \item matching sym. point of \openlat~\arxivtag{2201.03874}
\end{itemize} \end{itemize}
\end{frame} \end{frame}
@ -134,7 +137,7 @@
\frametitle{Improvement of the axial-vector current} \frametitle{Improvement of the axial-vector current}
\framesubtitle{$\ca$ estimators} \framesubtitle{$\ca$ estimators}
\begin{tabular}{cc} \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_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} \includegraphics[width=\halflinewidth]{plots/plateaus_sym_0.2_0.3_0124_ee_ee_total_quad.pdf}
\end{tabular} \end{tabular}
@ -147,7 +150,7 @@
\framesubtitle{... to the symmetric and critical point} \framesubtitle{... to the symmetric and critical point}
\begin{itemize} \begin{itemize}
\item ensembles not exactly tuned \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 determine points of interest as in \openlat~ensembles \arxivtag{2201.03874}
\item define: $$\Phi^{\rm SF}_4 = \frac{3}{2}\,8t_0\,|m_{\rm eff}|\,m_{\rm eff} \item define: $$\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$$ \quad \Rightarrow \quad \Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm cr}}} = 0\,,\;\Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm sym}}} = 1.115$$