Numerical study of renormalization group flows of nuclear effective field theory without pions on a lattice

TL;DR

This paper numerically investigates the nonperturbative renormalization group flows of a pionless nuclear effective field theory on a lattice, identifying fixed points and flow lines relevant to two-nucleon systems.

Contribution

It formulates a lattice-based, next-to-leading order pionless EFT and determines the nontrivial fixed point and relevant operators through numerical diagonalization.

Findings

Fixed point location closely matches analytic predictions

Identified the relevant operator at the fixed point

Mapped the physical flow line for the deuteron

Abstract

We formulate the next-to-leading order nuclear effective field theory without pions in the two-nucleon sector on a spatial lattice, and investigate nonperturbative renormalization group flows in the strong coupling region by diagonalizing the Hamiltonian numerically. The cutoff (proportional to the inverse of the lattice constant) dependence of the coupling constants is obtained by changing the lattice constant with the binding energy and the asymptotic normalization constant for the groundstate being fixed. We argue that the critical line can be obtained by looking at the finite-size dependence of the groundstate energy. We determine the relevant operator and locate the nontrivial fixed point, as well as the physical flow line corresponding to the deuteron in the two-dimensional plane of dimensionless coupling constants. It turns out that the location of the nontrivial fixed point is very close to the one obtained by the corresponding analytic calculation, but the relevant operator is quite different.