Nucleon Structure from Stochastic Estimators

The structure of the proton and neutron, parameterized by moments of generalized parton distribution functions (GPDs), can be accessed from first principle through the computation of baryon three-point functions with lattice QCD. The numerical effort involved in such computations is quite high and thus an efficient algorithm that extracts most information at given cost is highly desirable. In this work we demonstrate that stochastic estimation techniques can efficiently increase the information/cost ratio. We examine the available results at $N_f=2$ for the nucleon axial coupling $g_A$ and iso-vector quark momentum fraction $\langle x \rangle _{u-d}$ from various collaborations and compare them to the experimental values. The tension between them is attributed to excited state contributions (ESC). We furthermore study the impact of this ESC in moments of GPDs through a model fit. This model also deals with the effects of the choice of parameters used in the computation, like the source-sink separation $t_{\mathrm{sink}}$. We demonstrate that the choice of $t_{\mathrm{sink}}$ by the Regensburg group in previous studies was reasonable and cannot account for discrepancies with the experiment. To reduce the excited state contributions in two-point functions, and consequently three-point functions, we suggest a non-Gaussian quark smearing. This is a linear combination of two Gaussian smearings with one free parameter, which can be tuned to an optimal choice with a fit.