incorporate changes discussed on 23.7.
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1 changed files with 22 additions and 13 deletions
35
talk.tex
35
talk.tex
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@ -35,7 +35,6 @@
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\keywords{Münster}
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\newcommand{\customcite}[1]{{\color{fu-blue}\citename{#1}{author}}, \citefield{#1}{journaltitle}, {\color{pantone315}\citeyear{#1}}}
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\addbibresource{"./My Library.bib"}
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\begin{document}
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\begin{frame}[plain]
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@ -51,7 +50,13 @@
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% differences at sym point?
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% improvement at the symmetric point
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% example
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\begin{frame}
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\frametitle{What is this all about?}
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\begin{itemize}
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\item working with exp. Wilson-clover fermions
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\item massive $\Rightarrow$ at $N_{\rm f}=3$ symmetric point
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\end{itemize}
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\end{frame}
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\begin{frame}
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\frametitle{Relevance for further improvement and physics}
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\begin{itemize}
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@ -72,13 +77,13 @@
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\begin{frame}
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\frametitle{Determination of $\ca$}
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\begin{itemize}
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\item Schrödinger functional
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\item used already \arxivtag{hep-lat/9609035} for $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999}
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\item from PCAC mass $m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$
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\item in Schrödinger functional boundary conditions
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\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}
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\item from PCAC mass
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\end{itemize}
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\vspace{.5cm}
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$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}$$
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$$\Leftrightarrow \ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
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$$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$$
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$$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$
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\end{frame}
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\begin{frame}
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@ -91,6 +96,9 @@
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\item also include $\omega_{\rm b4} = {\rm cons.}\;,\quad\omega_{\rm b5} = -r^2~e^{-r/a_0}$
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\end{itemize}
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\item eigenvectors of boundary-to-boundary corr. func. $(F_1)_{i,j} = -\langle O(\omega_{{\rm b}i}) O'(\omega_{{\rm b}j})\rangle$ lead to eigenstates $\pi^{(0)}, \pi^{(1)}$
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\vspace{.5cm}
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\pause
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\item project $f_{\rm A}$ and $f_{\rm P}$ onto the eigenstates of $F_1$
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% Question: do we include all wavefunctions or just some?
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% How does this interplay with the states that we achieve?
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% Which is the optimal wf combination?
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@ -112,10 +120,10 @@
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$L/a$ & $\beta$ & $\kappa_{1}\approx\kappa_{\rm cr}$ & $\kappa_{2}$ & $\kappa_{3}\approx\kappa_{\rm sym}$&$a$\\
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\midrule
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24&3.685&0.1396980&0.1395500&0.1394400&0.120\\
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32&3.80&0.1392500&---&0.1389630&\\
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40&3.90&0.1388562&0.1386148&0.1386030&\\
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48&4.00&0.1384942&0.1384880&0.1382720&\\
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56&4.10&0.1381410&0.1380000&0.1379450&\\
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32&3.80&0.1392500&---&0.1389630&0.095\\
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40&3.90&0.1388562&0.1386148&0.1386030&0.080\\
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48&4.00&0.1384942&0.1384880&0.1382720&0.064\\
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56&4.10&0.1381410&0.1380000&0.1379450&0.055\\
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\bottomrule
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\end{tabular}
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\end{center}
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\framesubtitle{Hit symmetric and critical point exactly}
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\begin{itemize}
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\item ensembles not exactly tuned
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\item determine points of interest as in \openlat~ensembles
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\item able to interpolate to the desired points due to two or three values per $\beta$
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\item determine points of interest as in \openlat~ensembles \arxivtag{2201.03874}
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\item define: $$\Phi^{\rm SF}_4 = \frac{3}{2}\,8t_0\,|m_{\rm eff}|\,m_{\rm eff}
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\quad \Rightarrow \quad \Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm cr}}} = 0\,,\;\Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm sym}}} = 1.115$$
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\item interpolate to the desired points
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\end{itemize}
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\end{frame}
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