From 00665ed6c3c7497de9e6f42fd568103f97a65aeb Mon Sep 17 00:00:00 2001 From: Justus Kuhlmann Date: Tue, 30 Jul 2024 00:41:41 +0200 Subject: [PATCH] first scaling test of improvement --- talk.tex | 13 +++++-------- 1 file changed, 5 insertions(+), 8 deletions(-) diff --git a/talk.tex b/talk.tex index ce12aa7..85eaf17 100644 --- a/talk.tex +++ b/talk.tex @@ -188,22 +188,19 @@ % first study for difference: \begin{frame} \frametitle{First scaling test of improvement} - \framesubtitle{Construction} \begin{itemize} - \item Example: construct a non-trivial observable, for which renormalisation drops out - $$\frac{A_{\rm R}^{+-}}{A_{\rm R}^{ll}} = \frac{Z_{\rm A}}{Z_{\rm A}} \frac{(1+ b_{\rm A} (m_{{\rm q},+-})}{(1+ b_{\rm A} m_{{\rm q},ll})} \frac{(1+\bar{b}_{\rm A}Tr[M_{\rm q}])}{(1+ \bar{b}_{\rm A}Tr[M_{\rm q}])} \frac{A^{+-}}{A^{ll}}$$ - \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 Example: Calculate $f_\pi/K$ with stabilised WIlson fermions \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{frame} \begin{frame} \frametitle{First study of improvement} \framesubtitle{Results} - + \includegraphics{plots/test_f.pdf} \end{frame} \begin{frame}