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better Notation on slide 11

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Justus Kuhlmann 2024-07-25 14:58:13 +02:00
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10
talk.tex
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@ -188,10 +188,11 @@
\framesubtitle{Construction}
\begin{itemize}
\item Example: construct a non-trivial observable, for which renormalisation drops out
$$\frac{A^R_{\pm}}{A^R_{ll}} = \frac{Z_{\rm A}}{Z_{\rm A}} \frac{(1+ b_{\rm A} (m_{q+} + m_{q-})/2}{(1+ b_{\rm A} m_{ql})} \frac{(1+\bar{b}_{\rm A}Tr[M_q])}{(1+ \bar{b}_{\rm A}Tr[M_q])} \frac{A_{\pm}}{A_{ll}}$$
with $$(m_{q+} + m_{q-})/2=m_{ql}$$
$$\frac{A_{\rm R}^{+-}}{A_{\rm R}^{ll}} = \frac{Z_{\rm A}}{Z_{\rm A}} \frac{(1+ b_{\rm A} (m_{{\rm q},+-}}{(1+ b_{\rm A} m_{{\rm q},ll})} \frac{(1+\bar{b}_{\rm A}Tr[M_{\rm q}])}{(1+ \bar{b}_{\rm A}Tr[M_{\rm q}])} \frac{A^{+-}}{A^{ll}}$$
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 unimproved vs improved chi vs improves sym
\item $\ca = 0$ vs $\ca(g_0^2)|_{\rm chi}$ vs $\ca(g_0^2)|_{\rm sym}$
\end{itemize}
\end{frame}
@ -205,8 +206,7 @@ $$\frac{A^R_{\pm}}{A^R_{ll}} = \frac{Z_{\rm A}}{Z_{\rm A}} \frac{(1+ b_{\rm A} (
\begin{frame}
\frametitle{Outlook}
\begin{itemize}
\item finish $\zv$ via SF determination
\item $\bV$ through similar methods
\item finish $\zv$, $\bV$ and $\bar{b}_{\rm V}$ through SF
\item further improvement and renormalisation currently in the works:
\begin{itemize}
\item vector and tensor current improvement ($c_{\rm V}$, $c_{\rm T}$)