Calculations for Double Parton Distributions and Highly Boosted Hadrons

This thesis covers two main topics, a first-principles investigation of double parton distributions (DPDs) and improvements to the calculation of highly boosted nucleon matrix elements. Double parton distributions (DPDs) are non-perturbative objects that contain information about the correlation of partons within a hadron. They are essential for a first-principles computation of double parton scattering (DPS) cross sections, which contribute to the Standard Model (SM) background. Combining lattice Quantum Chromodynamics (lattice QCD) and operator product expansion (OPE), their first Mellin moment can be reconstructed from Euclidean two-current correlation functions calculated on the lattice. We present the first systematic study of leading-twist invariant functions of DPDs at zero hadron momentum, using six gauge ensembles provided by the Coordinated Lattice Simulations (CLS) collaboration with lattice spacings ranging from 0.085 fm to 0.064 fm and pion masses between 422 MeV and 214 MeV. Our analysis indicates the dominant source of systematic uncertainties to be finite volume effects, which are found to be consistent with sufficient suppression for Lmπ ≥ 5. We further discuss the skewness ζ dependence of the non-zero momentum hadronic two-current correlation functions. We find that a polynomial model used in earlier works does not predict vanishing results at |ζ| → 1, failing this physical boundary condition. Additionally, we find that the analyticity around ζ = 0 assumed in this model is not physically justified and leads to artificially narrow error bands. We introduce and compare the impact of different model ansätze to this dependence on the extracted Mellin moment. The average of ζ² is determined consistently across all considered models to be ⟨ζ²⟩ ≈ 0.07, while the Mellin moment at ζ = 0 cannot be extracted reliably without significantly improved signal at higher hadron momenta. We address this limitation in our study of recently proposed kinematically enhanced nucleon interpolators. As highly boosted hadronic matrix elements are of broader interest, e.g. to LaMET studies, we use the nucleon quasi-PDF matrix element at a boost momentum P_z ≈ 2.5 GeV as a benchmark quantity. We compare conventional to kinematically enhanced interpolators and investigate the results for potentially increased excited state contributions, discretization and cutoff effects. To this end, we compute the nucleon quark isovector quasi-PDF matrix element on three different CLS gauge ensembles at similar pion mass mπ ≈ 350 MeV and lattice spacings ranging from 0.085 fm to 0.064 fm. We observe a reduction in variance by an order of magnitude without increasing excited state contributions. We further detail an additional improvement in computation time by a factor of two based on a reduction in inversions of the Dirac operator.