Euclidean Effective Theory for Partons in the Spirit of Steven Weinberg

TL;DR

This paper proposes a Euclidean effective field theory approach to calculate parton distributions using lattice QCD, avoiding light-cone complications and enabling direct computation of $x$-distributions.

Contribution

It introduces an alternative Euclidean formulation of partons that allows direct lattice QCD calculations of parton $x$-distributions, inspired by Weinberg's effective field theory and Wilson's renormalization group.

Findings

Enables direct computation of parton $x$-distributions on the lattice.

Circumvents light-cone divergence issues in traditional formulations.

Aligns with effective field theory and renormalization group principles.

Abstract

The standard formulation of parton physics involves light-cone correlations of quark and gluon fields in a hadron, which leads to a widespread impression that it can only be studied through real-time Hamiltonian dynamics or light-front quantization, which are challenged by non-perturbative computations with a pertinent regulator for light-cone/rapidity divergences (or zero modes). As such, standard lattice QCD studies have been limited to indirect parton observables such as first few moments and short-distance correlations, which do not provide the $x$-distributions without solving the model-dependent inverse problem. Here I describe an alternative formulation of partons in terms of equal-time (or Euclidean) correlators, which allows to compute precision-controlled $x$-distribution through lattice QCD simulations. This approach is in accord with Weinberg's pioneering idea of effective field theory as well as Wilson's renormalization group, in which the large hadron momentum serves as a natural cut-off for light-cone/rapidity divergences and can ultimately be eliminated through a method like the ``perfect action'' program in lattice QCD.