Distillation at high momentum

Extraction of hadronic observables at finite momenta from lattice QCD (LQCD) is constrained by the well-known signal-to-noise problems afflicting all such LQCD calculations. Traditional quark smearing algorithms are commonly used tools to improve the statistical quality of hadronic $n$-point functions, provided operator momenta are small. The momentum smearing algorithm of Bali et al. extends the range of momenta that are cleanly accessible and has facilitated countless novel lattice calculations. Momentum smearing has, however, not been explicitly demonstrated within the framework of distillation. In this work we extend the momentum-smearing idea by exploring a few modifications to the distillation framework. Together with enhanced time slice sampling and expanded operator bases engendered by distillation, we find ground-state nucleon energies can be extracted reliably for $|\stackrel{\ensuremath{\rightarrow}}{p}|\ensuremath{\lesssim}3\text{ }\text{ }\mathrm{GeV}$ and matrix elements featuring a large momentum dependence can be resolved.