High-momentum tails from low-momentum effective theories

TL;DR

This paper extends the understanding of high-momentum tails in nuclear and many-body systems by demonstrating their factorization into universal and state-dependent parts using RG and OPE-inspired methods.

Contribution

It introduces a generalized factorization framework for high-momentum tails applicable to arbitrary low-energy many-body states, building on previous two-nucleon system results.

Findings

High-momentum tails factorize into universal functions and state-dependent matrix elements.

The framework applies to systems like the unitary Fermi gas and electron gas.

Reproduces known high-momentum tail expressions for these systems.

Abstract

In a recent work \cite{Anderson:2010aq}, Anderson \emph{et al.} 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 Ref. \cite{Anderson:2010aq} 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.