Speaker
Description
Disconnected quark-loop diagrams contribute to many key hadronic observables, from flavor-singlet spectroscopy to nucleon structure and the muon anomalous magnetic moment, but require traces of the inverse Dirac operator, which can only be estimated stochastically. Probing methods reduce the variance of such estimates by exploiting the exponential decay of the quark propagator: noise vectors built from a distance-$d$ coloring of the lattice cancel all short-range off-diagonal contributions exactly. A widely used construction, hierarchical probing, achieves reusability of previous computations through nested colorings, but offers valid colorings only at power-of-two distances, with an exponentially increasing number of colors. We present an alternative coloring strategy that assigns colors through integer linear forms on the lattice coordinates, yielding valid distance-$d$ colorings at arbitrary distances, not only powers of two, and with fewer colors than hierarchical probing at equal distance. Numerical studies on Wilson-Dirac configurations, for disconnected loops Tr$[\Gamma(t)D^{-1}(t,t)]$ evaluated on single time slices, show that the new construction matches hierarchical probing at its complete levels while providing valid colorings at several intermediate budgets, allowing the accuracy to be improved continuously with the available computational cost.