Chiral Perturbation for Large Momentum Effective Field Theory

TL;DR

This paper applies chiral perturbation theory to large momentum effective field theory to derive model-independent formulas for extrapolating lattice QCD results to physical quark masses and infinite volume, showing finite volume effects diminish at high nucleon momentum.

Contribution

It introduces a novel application of chiral perturbation theory to LaMET, providing formulas to reduce finite volume effects and improve extrapolations in lattice QCD calculations.

Findings

Finite volume effects are less than 1% for nucleon momentum > 1 GeV and m_pi L ≥ 3.

Finite momentum reduces finite volume effects due to Lorentz contraction.

Quark mass dependence at finite momentum matches zero momentum results in infinite volume.

Abstract

Large momentum effective field theory (LaMET) enables the extraction of parton distribution functions (PDFs) directly on a Euclidean lattice through a factorization theorem that relates the computed quasi-PDFs to PDFs. We apply chiral perturbation theory (ChPT) to LaMET to further separate soft scales, such as light quark masses and lattice size, to obtain leading model independent extrapolation formulas for extrapolations to physical quark masses and infinite volume. We find that the finite volume effect is reduced when the nucleon carries a finite momentum. For nucleon momentum greater than $1$ GeV and the lattice size $L$ and pion mass $ m_\pi $ satisfying $m_\pi L\geq 3$, the finite volume effect is less than $1\%$ and is negligible for the current precision of lattice computations. This can be interpreted as a Lorentz contraction of the nucleon size in the $z$-direction which makes the lattice size effectively larger in that direction. We also find that the quark mass dependence in the infinite volume limit computed with non-zero nucleon momentum reproduces the previous result computed at zero momentum, as expected. Our approach can be generalized to other parton observables in LaMET straight forwardly.