This paper tests a practical trick to make lattice quantum chromodynamics (QCD) calculations of fast-moving protons much cleaner. The authors study “kinematically enhanced” interpolating operators. These are ways of building the simulated proton from quark fields so that the pieces that dominate at large momentum are emphasized and the noisy pieces are suppressed. The work focuses on unpolarized isovector nucleon quark matrix elements used to study parton distributions, a target of methods such as Large Momentum Effective Theory (LaMET) and of future experiments like the Electron–Ion Collider.

The team implemented and tuned these enhanced interpolators on ensembles generated by the CLS collaboration. They benchmarked results for three different lattice spacings a but the same pion mass. To reduce excited-state contamination they extracted matrix elements at large source–sink separations. They compared the conventional interpolators to the kinematically enhanced ones and tracked statistical precision and discretization effects.

At a high level the improvement comes from projecting the quark fields onto their “+” components, the parts that matter most when the hadron carries large momentum. One projector the authors use, called γ+ in the paper, removes certain “−” components of the quark propagators that add noise. Combining different projections (for example the time-like γt and the boost-direction γz) also reuses information and reduces variance. The authors report that the precision of renormalized nucleon matrix elements is typically improved by about an order of magnitude at momentum Pz ≈ 2.5 GeV. They attribute part of this gain to the γ+ projector giving an additional factor-of-four improvement in variance, with a further factor-of-two coming from combining different matrix-element components.