A Novel Regularization Scheme for Nucleon-Nucleon Lattice Simulations with Effective Field Theory

TL;DR

This paper introduces a new exponential regularization scheme for lattice effective field theory of nucleon-nucleon interactions, improving the accuracy of low-energy parameters and observables across various lattice spacings.

Contribution

The paper develops and tests a novel exponential regularization method for lattice EFT, enhancing the extraction of physical parameters and predictions for nucleon-nucleon systems.

Findings

Regularization improves agreement with experimental data for lattice spacings > 2 fm.

Effective range expansion parameters are accurately extracted up to order p^2.

The scheme's impact varies with regulator power and lattice spacing.

Abstract

We propose a new regularization scheme to study the bound state of two-nucleon systems in Lattice Effective Field Theory. Inspired by continuum EFT calculation, we study an exponential regulator acting on the leading-order (LO) and next-to-leading order (NLO) interactions, consisting of local contact terms. By fitting the low-energy coefficients (LECs) to deuteron binding energy and the asymptotic normalization coefficient (ANC) on a lattice simulation, we extract the effective range expansion (ERE) parameters in the $^3S_1$ channel to order $p^2$. We explore the impact of different powers of the regulator on the extracted ERE parameters for the lattice spacing $a=1.97$ fm. Moreover, we investigate how the implementation of the regularization scheme improves the predicted ERE parameters on the lattice spacing in the range of $1.4 \le a \le 2.6$ fm. Our numerical analysis indicates that for lattice spacing greater than $2$ fm, the predicted observables are very close to the experimental data.