Parton Physics from Large-Momentum Effective Field Theory

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.

• The paper introduces LaMET to bypass traditional light-front quantization, enabling lattice QCD to access parton distributions.
• It employs a 1/P^2 expansion to systematically match lattice-computed quasi-distributions with physical light-front parton densities.
• The framework promises enhanced precision in high-energy experiments, advancing our understanding of hadronic structure.

Large-Momentum Effective Field Theory for Parton Physics

The paper "Parton Physics from Large-Momentum Effective Field Theory" by Xiangdong Ji introduces a novel framework to study parton distributions within lattice Quantum Chromodynamics (QCD) by leveraging the concept of Large-Momentum Effective Field Theory (LaMET). This theoretical approach revisits the original Feynman picture and aims to simplify the non-perturbative characterization of hadrons at high energies.

The core motivation for this work stems from the limitation of previous methods used to calculate parton distributions, particularly in the light-front formalism that, despite theoretical conveniences, encounters significant practical difficulties. The paper proposes an alternative approach which bypasses the need for light-cone quantization, instead utilizing effective field theories to handle the complexities of hadrons at large momenta in a systematic expansion in terms of $1/P$, where $P$ represents the momentum of the hadron.

Key Concepts and Methodology

1. Parton Model Paradigm: Originating from Feynman, the parton model simplifies high-energy hadron behavior as a collection of non-interacting quarks and gluons. This abstraction is underpinned by factorization theorems in QCD, providing a theoretical justification for separating perturbative scattering cross sections from non-perturbative parton densities.
2. LaMET Framework: Ji develops LaMET as an effective field theory framework where calculations are performed using finite, but large, hadron momenta on a Euclidean lattice. This circumvents the inherent difficulties of an infinite-momentum frame, by employing an expansion in $1/P^2$, analogous to expansions in the Heavy Quark Effective Theory (HQET).
3. Computation of Parton Densities: In LaMET, the computation of parton observables begins with lattice-accessible quantities, defined in terms of quasi-distributions, which are subsequently extrapolated to the infinite momentum limit. The transition involves a rigorous matching procedure, ensuring that lattice results converge to their light-front counterparts.

Numerical and Theoretical Implications

The paper discusses, in detail, the mechanism of LaMET which involves matching quasi-observables to their infinite momentum limits through perturbatively calculable corrections. This approach provides a tractable pathway to obtaining light-front parton densities from lattice QCD simulations. LaMET's methodology holds significant promise for extracting physical predictions in the context of high-energy experiments, e.g., deep inelastic scattering at accelerators, thereby enhancing our understanding of hadronic structure.

Moreover, Ji outlines potential realization techniques exploiting LaMET, enabling more precise simulations at realistic computational scales. The formulation stresses the significance of choosing appropriate operators whose lattice-extracted quasi-distributions will converge efficiently to their parton counterparts.

Future Prospects and Challenges

While the approach delineated in this paper represents a substantial theoretical advancement, the practical implementation and numerical validations remain areas of active exploration. Future research must address the refinement of matching procedures and the extent of computational feasibility at extreme fermionic retained dimensions. As the technique matures, it is expected that LaMET will play an instrumental role in the precise characterization of partonic dynamics, with implications extending to the detailed exploration of nucleon structure at unprecedented small-x values.

In summary, this paper establishes a novel and systematic channel for addressing parton physics through lattice QCD, poised to significantly enhance the precision of theoretical predictions relevant to a broad range of high-energy physics phenomena. The LaMET approach is likely to become a pivotal component in future lattice-based explorations of QCD.