Nuclear currents in chiral effective field theory
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Review
Nuclear currents in chiral effective field theory Hermann Krebsa Faculty of Physics and Astronomy, Institute for Theoretical Physics II, Ruhr-Universität Bochum, 44780 Bochum, Germany
Received: 11 August 2020 / Accepted: 19 August 2020 / Published online: 17 September 2020 © The Author(s) 2020 Communicated by Ulf Meissner
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 . 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-nextto-leading-order (N3 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.
1 Introduction The internal structure of nucleons and nuclei can be studied by probing them with electromagnetic, weak, or even scalar a e-mail:
[email protected] (corresponding author)
probes. Scalar probes play an important role in beyond the standard model searches of dark matter. The interactions of hadrons with the external probes are well approximated by one photon, W ± , Z 0 . In this case, the full scattering amplitude factorizes in a leptonic and a hadronic part. In case of the electroweak interaction, the amplitude can be written as a multiplication of leptonic and hadronic four-current operators. Leptonic four-current can be well approximated by perturbative calculations within the standard model. Hadronic four-current is less known. Electroweak nuclear currents have been extensively studied in the last century within bosonexchange (pions and heavier mesons) and soliton models, see [1,2] for recent and [3,4] for earlier reviews on this topic. Electromagnetic nuclear currents have
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