Analyzing momentum distributions in light nuclei with the operator product expansion
We analyze the high-momentum tails of nucleon distributions in nuclei using the operator product expansion (OPE) and Pionless effective field theory. The OPE factorizes the distributions into Wilson coefficients, determined from two-nucleon scattering, and local-operator matrix elements (LOMEs). Because the leading ${{}^1S_0}$ and ${{}^3S_1}$ Wilson coefficients are nearly degenerate in the single-nucleon distribution, we construct the OPE of the two-nucleon momentum distribution, which separates the two contributions into distinct spin-isospin channels. From variational Monte Carlo two-nucleon distributions of \isotope[3]{He}, \isotope[4]{He}, \isotope[6]{Li}, and \isotope[12]{C}, we extract the LOMEs and accurately reconstruct the single-nucleon distributions at large momenta. In potentials without explicit non-nucleon degrees of freedom such as AV18, the Wilson coefficients of the single- and two-nucleon OPEs are proportional, yielding approximate relations between the two distributions.