Nuclear Currents in Chiral Effective Field Theory

TL;DR

This paper reviews the calculation of nuclear currents within chiral effective field theory, emphasizing the importance of consistent regularization and presenting expressions up to N$^3$LO for various current operators.

Contribution

It provides a complete set of N$^3$LO expressions for nuclear scalar, pseudoscalar, vector, and axial-vector current operators, highlighting the need for consistent regularization to preserve chiral symmetry.

Findings

Consistent regularization is crucial to maintain chiral symmetry.

Presented N$^3$LO expressions for various nuclear current operators.

Demonstrated a high-accuracy calculation of the deuteron charge form factor.

Abstract

In this article, we review the status of the calculation of nuclear currents within chiral effective field theory. After formal discussion of the unitary transformation technique and its application to nuclear currents we will give all available expressions for vector, axial-vector currents. Vector and axial-vector currents will be discussed up to order $Q$ with leading-order contribution starting at order $Q^{-3}$. Pseudoscalar and scalar currents will be discussed up to order $Q^0$ with leading-order contribution starting at order $Q^{-4}$. This is a complete set of expressions in next-to-next-to-next-to-leading-order (N$^3$LO) analysis for nuclear scalar, pseudoscalar, vector and axial-vector current operators. Differences between vector and axial-vector currents calculated via transfer-matrix inversion and unitary transformation techniques are discussed. The importance of consistent regularization is an additional point which is emphasized: lack of consistent regularization of axial-vector current operators is shown to lead to a violation of the chiral symmetry in the chiral limit at order $Q$. For this reason, a hybrid approach at order $Q$, discussed in various publications, is non-applicable. To respect the chiral symmetry the same regularization procedure needs to be used in the construction of nuclear forces and current operators. Although full expressions of consistently regularized current operators are not yet available an isoscalar part of the electromagnetic charge operator up to order $Q$ has a very simple form and can be easily regularized in a consistent way. As an application, we review our recent high accuracy calculation of the deuteron charge form factor with a quantified error estimate.