[Paper Review] Parton Physics from Large-Momentum Effective Field Theory

Xiangdong Ji|arXiv (Cornell University)|Apr 26, 2014

Particle physics theoretical and experimental studies3 references4 citations

TL;DR

This paper introduces Large-Momentum Effective Field Theory (LaMET) as a framework to extract light-front parton physics from lattice QCD simulations at finite momentum $P \sim \text{few GeV}$. By formulating parton distributions via a systematic $1/P$ expansion, LaMET enables non-perturbative computation of parton wave functions and distributions, bridging lattice QCD data with light-front formalism and allowing extraction of hadron structure with precision comparable to experimental hard-scattering data.

ABSTRACT

Parton physics, when formulated as light-front correlations, are difficult to study non-perturbatively, despite the promise of light-front quantization. Recently an alternative approach to partons have been proposed by re-visiting original Feynman picture of a hadron moving at asymptotically large momentum. Here I formulate the approach in the language of an effective field theory for a large hadron momentum $P$ in lattice QCD, LaMET for short. I show that using this new effective theory, parton properties, including light-front parton wave functions, can be extracted from lattice observables in a systematic expansion of $1/P$, much like that the parton distributions can be extracted from the hard scattering data at momentum scales of a few GeV.

Motivation & Objective

• To overcome the non-perturbative challenges in computing parton distributions using light-front quantization or Euclidean lattice QCD.
• To formulate a systematic effective field theory for hadrons with large momentum $P$ in lattice QCD, avoiding the need for infinite momentum limits.
• To enable the extraction of light-front parton wave functions and distributions from lattice observables through a $1/P$ expansion.
• To provide a practical bridge between lattice QCD simulations and the parton model used in high-energy scattering processes.
• To resolve the conflict between Lorentz contraction in the infinite-momentum frame and the divergent correlation lengths in light-front quantization by redefining the correlation structure via boosting.

Proposed method

• Formulate parton physics in the language of an effective field theory—LaMET—by taking the large momentum limit $P^z \to \infty$ in lattice QCD.
• Use light-cone correlation functions as the fundamental objects, with matrix elements defined via non-local operators involving gauge-ordered quark fields.
• Implement a systematic $1/P$ expansion to relate lattice matrix elements to light-front parton distributions, including perturbative matching coefficients.
• Construct the effective theory by boosting the hadron to high momentum, transforming the infinite-momentum frame into a finite but large $P$ limit.
• Relate the longitudinal spatial resolution in LaMET to the $x$-dependence of partons: $\Delta z \sim 1/(xP^z)$, enabling access to small-$x$ physics at high $P^z$.
• Use the $A^+ = 0$ gauge in light-front quantization to simplify the Fock state expansion and relate the wave functions to the parton momentum fractions $x_i$.

Experimental results

Research questions

• RQ1 Can parton distributions and wave functions be extracted from lattice QCD simulations at finite momentum $P \sim \text{few GeV}$ without requiring infinite momentum?
• RQ2 How can the light-cone correlation functions in the infinite-momentum frame be reformulated as a finite-$P$ effective field theory?
• RQ3 What is the systematic $1/P$ expansion that relates lattice matrix elements to light-front parton distributions?
• RQ4 How does the longitudinal spatial resolution in LaMET scale with parton momentum fraction $x$ and hadron momentum $P^z$?
• RQ5 Why does light-front quantization lead to divergent correlation lengths, and can this be resolved via the LaMET framework?

Key findings

• LaMET provides a systematic $1/P$ expansion that allows the non-perturbative extraction of light-front parton wave functions and distributions from lattice QCD data.
• The correlation length along the longitudinal direction in LaMET scales as $1/(xP^z)$, enabling high-resolution access to small-$x$ partons at sufficiently large $P^z$.
• For small-$x$ partons with $x \sim 10^{-4}$, a hadron momentum of $P^z \sim 3\,\text{TeV}$ is required to resolve the $1/\Lambda_{\text{QCD}}$ correlation length, demanding thousands of lattice sites in the $z$-direction.
• In contrast to light-front quantization, where correlation lengths grow as $\gamma \sim P^z$, LaMET maintains compact spatial resolution, making Monte Carlo simulations feasible.
• The matching coefficients between lattice matrix elements and parton distributions are perturbatively calculable, enabling precision extraction of parton properties.
• The framework allows lattice data to be used with the same interpretive power as experimental hard-scattering data, particularly for parton distributions and wave functions.