Nuclear currents in chiral effective field theory

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 give all available expressions for vector, axial-vector currents. Vector and axial-vector currents are discussed up to order Q with leading-order contribution starting at order $$Q^{-3}$$ Q - 3 . Pseudoscalar and scalar currents will be discussed up to order $$Q^0$$ Q 0 with leading-order contribution starting at order $$Q^{-4}$$ Q - 4 . This is a complete set of expressions in next-to-next-to-next-to-leading-order (N$$^3$$ 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 a consistent regularization is an additional point which is emphasized: lack of a 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, the 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.

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“…[25,26,27,28] for a related work on electroweak currents by the JLab-Pisa group and Ref. [29] for a review article. Furthermore, selected N 4 LO contributions to the 3NF have been worked out in Refs.…”

Pion photoproduction in chiral perturbation theory with explicit treatment of the $Δ(1232)$ resonance

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Nuclear Structure at the Crossroads

“…The latter contributions are typically missing in model calculations but emerge naturally in an EFT based on the most general effective Lagrangian. Significant progress has been made on consistently regulated currents [36] (that is, consistent with chiral symmetry), although these are not yet universally adopted. The critical role of two-body currents has been shown for precision calculations of electromagnetic transitions and magnetic moments [37] and for neutrino reactions [38].…”