# Improving the Precision of First-Principles Calculation of Parton Physics from Lattice QCD

## TL;DR

This paper discusses recent methodological advancements in lattice QCD and LaMET that improve the precision and reliability of calculating proton parton distributions from first principles, with promising future prospects.

## Contribution

It introduces improved renormalization schemes, higher-loop matching kernels, Coulomb-gauge correlator approaches, and enhanced lattice operators for accessing higher proton momenta.

## Key findings

- Enhanced perturbative and power accuracy in LaMET calculations.
- Successful extraction of key parton observables with phenomenological relevance.
- Potential for extending predictions to higher momenta with better signal-to-noise ratios.

## Abstract

Large Momentum Effective Theory (LaMET) provides a general framework for computing the multi-dimensional partonic structure of the proton from first principles using lattice quantum chromodynamics (QCD). In this effective field theory approach, LaMET predicts parton distributions through a power expansion and perturbative matching of a class of Euclidean observables -- quasi-distributions -- evaluated at large proton momenta. Recent advances in lattice renormalization, such as the hybrid scheme with leading-renormalon resummation, together with improved matching kernel that incorporates higher-loop corrections and resummations, have enhanced both the perturbative and power accuracy of LaMET, enabling a reliable quantification of theoretical uncertainties. Moreover, the Coulomb-gauge correlator approach further simplifies lattice analyses and improves the precision of transverse-momentum-dependent structures, particularly in the non-perturbative region. State-of-the-art LaMET calculations have already yielded certain parton observables with important phenomenological impact. In addition, the recently proposed kinematically enhanced lattice interpolation operators promise access to unprecedented proton momenta with greatly improved signal-to-noise ratios, which will extend the range of LaMET prediction and further suppress the power corrections. The remaining challenges, such as controlling excited-state contamination in lattice matrix elements and extracting gluonic distributions, are expected to benefit from emerging lattice techniques for ground-state isolation and noise reduction. Thus, lattice QCD studies of parton physics have entered an exciting stage of precision control and systematic improvement, which will have a broader impact for nuclear and particle experiments.