lattice/talk-lattice2024
Archived
1
0
Fork 0
Code Activity

first scaling test of improvement

Browse source
This commit is contained in:
Justus Kuhlmann 2024-07-30 00:41:41 +02:00
parent e3a748c825
commit 00665ed6c3
1 changed files with 5 additions and 8 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

13
talk.tex
View file

@ -188,22 +188,19 @@
% first study for difference: % first study for difference:
\begin{frame} \begin{frame}
\frametitle{First scaling test of improvement} \frametitle{First scaling test of improvement}
\framesubtitle{Construction}
\begin{itemize} \begin{itemize}
\item Example: construct a non-trivial observable, for which renormalisation drops out \item Example: Calculate $f_\pi/K$ with stabilised WIlson fermions
$$\frac{A_{\rm R}^{+-}}{A_{\rm R}^{ll}} = \frac{Z_{\rm A}}{Z_{\rm A}} \frac{(1+ b_{\rm A} (m_{{\rm q},+-})}{(1+ b_{\rm A} m_{{\rm q},ll})} \frac{(1+\bar{b}_{\rm A}Tr[M_{\rm q}])}{(1+ \bar{b}_{\rm A}Tr[M_{\rm q}])} \frac{A^{+-}}{A^{ll}}$$
\quad with $m_{{\rm q}, ij} = (m_{{\rm q}, i} + m_{{\rm q}, j})/2$
\item fulfilled by $m_{{\rm q}, \pm}=m_{{\rm q}, l}\pm \Delta$
\item symmetric point \openlat~ensembles \item symmetric point \openlat~ensembles
\item $\ca = 0$ vs $\ca(g_0^2)|_{\rm chi}$ vs $\ca(g_0^2)|_{\rm sym}$ \item improve with $\ca = 0$ vs $\ca(g_0^2)|_{\rm chi}$ vs $\ca(g_0^2)|_{\rm sym}$
\item $f_{\rm A}^{RI} = Z_{\rm A} (1+b_{\rm A} m_{\rm q})(1+\bar{b}_{\rm A} \Tr[M_{\rm q}])f\frac{\sqrt{2} A}{\sqrt{A m_\pi}}$
\item renormalisation: $Z_{\rm A}$ preliminary, $b_{\rm A}$ from pert. theory, $\bar{b}_{\rm A}$ neglected
\end{itemize} \end{itemize}
\end{frame} \end{frame}
\begin{frame} \begin{frame}
\frametitle{First study of improvement} \frametitle{First study of improvement}
\framesubtitle{Results} \framesubtitle{Results}
\includegraphics{plots/test_f.pdf}
\end{frame} \end{frame}
\begin{frame} \begin{frame}