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