High-momentum tails from low-momentum effective theories

In a recent work, Anderson et al. [Phys. Rev. C 82, 054001 (2010)] used the renormalization group (RG) evolution of the momentum distribution to show that, under appropriate conditions, operator expectation values exhibit factorization in the two-nucleon system. Factorization is useful because it provides a clean separation of long-and short-distance physics, and suggests a possible interpretation of the universal high-momentum dependence and scaling behavior found in nuclear momentum distributions. In the present work, we use simple decoupling and scale-separation arguments to extend the results of Anderson et al. to arbitrary low-energy A-body states. Using methods that are reminiscent of the operator product expansion (OPE) in quantum field theory, we find that the high-momentum tails of momentum distributions and static structure factors factorize into the product of a universal function of momentum that is fixed by two-body physics, and a state-dependent matrix element that is the same for both and is sensitive only to low-momentum structure of the many-body state. As a check, we apply our factorization relations to two well studied systems, the unitary Fermi gas and the electron gas, and reproduce known expressions for the high-momentum tails of each. DOI: 10.1103/PhysRevC.86.064304