Factorization theorem relating Euclidean and light-cone parton distributions

In a large-momentum nucleon state, the matrix element of a gauge-invariant Euclidean Wilson line operator accessible from lattice QCD can be related to the standard light-cone parton distribution function through the large-momentum effective theory (LaMET) expansion. This relation is given by a factorization formula with a nontrivial matching coefficient. Using the operator product expansion we derive the large-momentum factorization of the quasiparton distribution function in LaMET, and show that the more recently discussed pseudoparton distribution approach also obeys an equivalent factorization formula. Explicit results for the coefficients are obtained and compared at one loop. We also prove that the matching coefficients in the $\overline{\mathrm{MS}}$ scheme depend on the large partonic momentum rather than the nucleon momentum.