From 76fb1ec0a6d11c49359758d71a86732f69d0281c Mon Sep 17 00:00:00 2001 From: Justus Kuhlmann Date: Thu, 25 Jul 2024 15:34:30 +0200 Subject: [PATCH] better, more compact wording --- talk.tex | 17 ++++++++++------- 1 file changed, 10 insertions(+), 7 deletions(-) diff --git a/talk.tex b/talk.tex index b482558..ce12aa7 100644 --- a/talk.tex +++ b/talk.tex @@ -25,7 +25,7 @@ \newcommand{\openlat}{OpenLat} -\title[$A_\mu^a$ impr. msl. \& mass. quarks]{Non-singlet axial current improvement for massless and massive sea quarks} +\title[$A_\mu^a$ impr. for msl. \& mass. quarks]{Non-singlet axial current improvement for massless and massive sea quarks} \author[Justus Kuhlmann]{\textbf{Justus Kuhlmann}\\ Patrick Fritzsch, Jochen Heitger} % \institute wird von der Vorlage nicht direkt verwendet @@ -55,6 +55,7 @@ \begin{itemize} \item exp. Wilson-clover fermion framework \item massive $\widehat{=}$ at $N_{\rm f}=3$ symmetric point + \pause \vspace{.5cm} \item needed for improv. quark current mass \item decay constants \& matrix elements @@ -78,7 +79,7 @@ \item derive from PCAC mass \end{itemize} \vspace{.5cm} - $$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$$ + $$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca~a\frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca~as$$ $$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$ \end{frame} @@ -90,11 +91,13 @@ \item basis wavefunctions: $\omega_{\rm b1} = e^{-r/a_0}\;,\quad\omega_{\rm b2} = r~e^{-r/a_0}\;,\quad\omega_{\rm b3} = e^{-r/(2a_0)}$ \item also include $\omega_{\rm b4} = {\rm cons.}\;,\quad\omega_{\rm b5} = -r^2~e^{-r/a_0}$ + \quad with $r=|\vec{y}-\vec{x}|$ \end{itemize} - \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 $\pi^{(0)}, \pi^{(1)}$ + \pause + \item eigenvectors of boundary-to-boundary corr. func. $(F_1)_{i,j} = -\langle O(\omega_{{\rm b}i}) O'(\omega_{{\rm b}j})\rangle$ \vspace{.5cm} \pause - \item project $f_{\rm A}$ and $f_{\rm P}$ onto the eigenstates of $F_1$ + \item diagonalise $(F_1)_{i,j}$ \& project $f_{\rm A}(x_0)$ and $f_{\rm P}(x_0)$ onto the eigenstates % Question: do we include all wavefunctions or just some? % How does this interplay with the states that we achieve? % Which is the optimal wf combination? @@ -125,7 +128,7 @@ \end{tabular} \end{center} \begin{itemize} - \item interested in 2 LCPs: chiral and at $N_{\rm f}=3$ symmetric point + \item interested in 2 LCPs: chiral and $N_{\rm f}=3$ sym. point \item matching sym. point of \openlat~\arxivtag{2201.03874} \end{itemize} \end{frame} @@ -134,7 +137,7 @@ \frametitle{Improvement of the axial-vector current} \framesubtitle{$\ca$ estimators} \begin{tabular}{cc} - Close to chiral ensembles&Symmetric ensembles\\ + Critical point ensembles&Symmetric point ensembles\\ \includegraphics[width=\halflinewidth]{plots/plateaus_chi_0.2_0.3_0124_ee_ee_total_quad.pdf}& \includegraphics[width=\halflinewidth]{plots/plateaus_sym_0.2_0.3_0124_ee_ee_total_quad.pdf} \end{tabular} @@ -147,7 +150,7 @@ \framesubtitle{... to the symmetric and critical point} \begin{itemize} \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 2 or 3 ensembles per $\beta$ \item determine points of interest as in \openlat~ensembles \arxivtag{2201.03874} \item define: $$\Phi^{\rm SF}_4 = \frac{3}{2}\,8t_0\,|m_{\rm eff}|\,m_{\rm eff} \quad \Rightarrow \quad \Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm cr}}} = 0\,,\;\Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm sym}}} = 1.115$$