Introduction to LaMET

Large Momentum Effective Theory (LaMET) is a powerful framework that enables the calculation of parton physics from lattice QCD. Traditionally, parton distribution functions (PDFs) and other light-cone observables are defined in Minkowski space and are not directly accessible in Euclidean lattice QCD. LaMET overcomes this challenge by relating Euclidean matrix elements of boosted hadrons to their light-cone counterparts through factorization and matching procedures.

Motivation

Understanding the internal structure of hadrons, such as protons and neutrons, is a central goal in nuclear and particle physics. PDFs encode the momentum distributions of quarks and gluons inside hadrons and are essential for interpreting high-energy scattering experiments. However, direct calculation of PDFs from first principles was long considered impossible due to the limitations of Euclidean lattice QCD.

The LaMET Approach

LaMET proposes to compute so-called quasi-distributions, which are spatial correlations in a hadron moving at large momentum. These quasi-distributions can be calculated on the lattice and are related to the physical PDFs via perturbative matching and power corrections suppressed by the hadron momentum.

Key Steps in LaMET Calculations

1. Boost the hadron to a large momentum on the lattice.
2. Compute Euclidean matrix elements of nonlocal operators (e.g., Wilson line operators).
3. Extract quasi-distributions from the lattice data.
4. Apply matching and factorization to relate quasi-distributions to light-cone PDFs.

Impact and Applications

LaMET has opened a new avenue for first-principles calculations of parton physics, enabling lattice QCD to make direct contact with experimental observables. It has been successfully applied to PDFs, generalized parton distributions (GPDs), and transverse momentum dependent distributions (TMDs).

For further reading, see the LaMET review paper.