# Nuclear axial current operators to fourth order in chiral effective field theory

## Abstract

We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of the continuity equation.

- Authors:

- Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum (Germany)
- (United States)
- Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn (Germany)
- (Germany)

- Publication Date:

- OSTI Identifier:
- 22617486

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 378; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHIRALITY; CONTINUITY EQUATIONS; FIELD THEORIES; MATHEMATICAL OPERATORS; NUCLEAR FORCES; PSEUDOSCALARS; RELATIVISTIC RANGE; RENORMALIZATION

### Citation Formats

```
Krebs, H., E-mail: hermann.krebs@rub.de, Epelbaum, E., E-mail: evgeny.epelbaum@rub.de, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93016, Meißner, U.-G., E-mail: meissner@hiskp.uni-bonn.de, Institut für Kernphysik, Institute for Advanced Simulation, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, and JARA - High Performance Computing, Forschungszentrum Jülich, D-52425 Jülich.
```*Nuclear axial current operators to fourth order in chiral effective field theory*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.01.021.

```
Krebs, H., E-mail: hermann.krebs@rub.de, Epelbaum, E., E-mail: evgeny.epelbaum@rub.de, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93016, Meißner, U.-G., E-mail: meissner@hiskp.uni-bonn.de, Institut für Kernphysik, Institute for Advanced Simulation, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, & JARA - High Performance Computing, Forschungszentrum Jülich, D-52425 Jülich.
```*Nuclear axial current operators to fourth order in chiral effective field theory*. United States. doi:10.1016/J.AOP.2017.01.021.

```
Krebs, H., E-mail: hermann.krebs@rub.de, Epelbaum, E., E-mail: evgeny.epelbaum@rub.de, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93016, Meißner, U.-G., E-mail: meissner@hiskp.uni-bonn.de, Institut für Kernphysik, Institute for Advanced Simulation, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, and JARA - High Performance Computing, Forschungszentrum Jülich, D-52425 Jülich. Wed .
"Nuclear axial current operators to fourth order in chiral effective field theory". United States.
doi:10.1016/J.AOP.2017.01.021.
```

```
@article{osti_22617486,
```

title = {Nuclear axial current operators to fourth order in chiral effective field theory},

author = {Krebs, H., E-mail: hermann.krebs@rub.de and Epelbaum, E., E-mail: evgeny.epelbaum@rub.de and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93016 and Meißner, U.-G., E-mail: meissner@hiskp.uni-bonn.de and Institut für Kernphysik, Institute for Advanced Simulation, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich and JARA - High Performance Computing, Forschungszentrum Jülich, D-52425 Jülich},

abstractNote = {We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of the continuity equation.},

doi = {10.1016/J.AOP.2017.01.021},

journal = {Annals of Physics},

number = ,

volume = 378,

place = {United States},

year = {Wed Mar 15 00:00:00 EDT 2017},

month = {Wed Mar 15 00:00:00 EDT 2017}

}

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