Speaker
Description
Integrated time-slice correlation functions $C(t)$ with weights $K(t)$ appear e.g. in
the moments method to determine $\alpha_s$ from heavy quark correlators,
in the muon g-2 determination or in the determination of smoothed spectral
functions. We show that the short distance part of the integral may lead to $\log(a)$-enhanced
discretization errors when $C(t)K(t) \sim t $ for small $t$. Starting from the Symanzik expansion
of the integrand we derive the asymptotic convergence of the integral at small lattice spacing.
For the (tree-level-) normalized moment $R_4$ of the heavy-heavy pseudo-scalar correlator $R_4$
we have non-perturbative results down to $a=10^{-2}$ fm and for masses, $m$, of the order of the charm
mass. A bending of the curve as a function of $a^2 m^2$ is observed at small lattice
spacings. We try to understand the behavior and extract an improved continuum limit.
