Chiral Perturbation for Large Momentum Effective Field Theory

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.