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incorporate Patricks comments

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Justus Kuhlmann 2024-07-25 14:37:52 +02:00
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talk.tex
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@ -50,19 +50,15 @@
% differences at sym point? % differences at sym point?
% improvement at the symmetric point % improvement at the symmetric point
% example % example
\begin{frame}
\frametitle{What is this all about?}
\begin{itemize}
\item working with exp. Wilson-clover fermions
\item massive $\Rightarrow$ at $N_{\rm f}=3$ symmetric point
\end{itemize}
\end{frame}
\begin{frame} \begin{frame}
\frametitle{Relevance for further improvement and physics} \frametitle{Relevance for further improvement and physics}
\begin{itemize} \begin{itemize}
\item needed for improv. determination of the PCAC quark-mass \item exp. Wilson-clover fermion framework
\item decay constants \item massive $\Rightarrow$ at $N_{\rm f}=3$ symmetric point
\item masses of mesons (e.g. $\chi_\mathrm{c1}$ or $D_\mathrm{1}^\ast$) \vspace{.5cm}
\item needed for improv. quark current mass
\item decay constants & matrix elements
% \item masses of mesons (e.g. $\chi_\mathrm{c1}$ or $D_\mathrm{1}^\ast$)
\pause \pause
\vspace{.5cm} \vspace{.5cm}
\item improvement and renormalisation: \item improvement and renormalisation:
@ -77,9 +73,9 @@
\begin{frame} \begin{frame}
\frametitle{Determination of $\ca$} \frametitle{Determination of $\ca$}
\begin{itemize} \begin{itemize}
\item in Schrödinger functional boundary conditions \item Schrödinger functional boundary conditions
\item similar in quenched \arxivtag{hep-lat/9609035}, $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999} \item similar to quenched \arxivtag{hep-lat/9609035}, $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999}
\item from PCAC mass \item derive from PCAC mass
\end{itemize} \end{itemize}
\vspace{.5cm} \vspace{.5cm}
$$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$$ $$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$$
@ -89,7 +85,7 @@
\begin{frame} \begin{frame}
\frametitle{The wavefunction method} \frametitle{The wavefunction method}
\begin{itemize} \begin{itemize}
\item mimic pionic sources on boundaries $\pi^{(0)}, \pi^{(1)}$ and require PCAC to hold \item mimic pionic sources on boundaries $\pi^{(0)}, \pi^{(1)}$ and require PCAC relation to hold for both
\begin{itemize} \begin{itemize}
\item basis wavefunctions: \item basis wavefunctions:
$\omega_{\rm b1} = e^{-r/a_0}\;,\quad\omega_{\rm b2} = r~e^{-r/a_0}\;,\quad\omega_{\rm b3} = e^{-r/(2a_0)}$ $\omega_{\rm b1} = e^{-r/a_0}\;,\quad\omega_{\rm b2} = r~e^{-r/a_0}\;,\quad\omega_{\rm b3} = e^{-r/(2a_0)}$
@ -113,7 +109,7 @@
\begin{frame} \begin{frame}
\frametitle{Ensembles} \frametitle{Ensembles}
\framesubtitle{$L\approx 3\,{\rm fm}$ Schrödinger-Functional ensembles, exp. Wilson-Clover fermions} \framesubtitle{$T=L\approx 3\,{\rm fm}$ Schrödinger-Functional ensembles, exp. Wilson-Clover fermions}
\begin{center} \begin{center}
\begin{tabular}{cc|c|c|c|c} \begin{tabular}{cc|c|c|c|c}
\toprule \toprule
@ -124,6 +120,7 @@
40&3.90&0.1388562&0.1386148&0.1386030&0.080\\ 40&3.90&0.1388562&0.1386148&0.1386030&0.080\\
48&4.00&0.1384942&0.1384880&0.1382720&0.064\\ 48&4.00&0.1384942&0.1384880&0.1382720&0.064\\
56&4.10&0.1381410&0.1380000&0.1379450&0.055\\ 56&4.10&0.1381410&0.1380000&0.1379450&0.055\\
96&4.37&---&---&---&0.035\\
\bottomrule \bottomrule
\end{tabular} \end{tabular}
\end{center} \end{center}
@ -147,7 +144,7 @@
% interpolations % interpolations
\begin{frame} \begin{frame}
\frametitle{Interpolation} \frametitle{Interpolation}
\framesubtitle{Hit symmetric and critical point exactly} \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 two or three values per $\beta$