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.

72 pages, 21 figures, 3 tables

References in corpus (21)

• Chiral effective field theory and nuclear forces
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Three-body forces: From cold atoms to nuclei
• Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory
• Subleading contributions to the chiral three-nucleon force I: long-range terms
• Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
• Electromagnetic Currents and Magnetic Moments in $\chi$EFT
• Two-pion exchange electromagnetic current in chiral effective field theory using the method of unitary transformation
• Analysis strategies for general spin-independent WIMP-nucleus scattering
• Axial, induced pseudoscalar, and pion-nucleon form factors in manifestly Lorentz-invariant chiral perturbation theory
• Two-pion exchange three-nucleon potential: O(q^4) chiral expansion
• Four-nucleon force using the method of unitary transformation
• Effects of three-nucleon forces and two-body currents on Gamow-Teller strengths
• Tritium $\beta$-decay in chiral effective field theory
• Statistical uncertainties of a chiral interaction at next-to-next-to leading order
• Three-nucleon force at large distances: Insights from chiral effective field theory and the large-N_c expansion
• Signatures of the chiral two-pion exchange electromagnetic currents in the 2H and 3He photodisintegration reactions
• Testing semi-local chiral two-nucleon interaction in selected electroweak processes
• Neutron-neutron scattering length from the reaction gamma d --> pi^+ nn employing chiral perturbation theory
• Bridging over p-wave pi-production and weak processes in few-nucleon systems with chiral perturbation theory
• Unification of the physics of nucleons and nuclei

Cited by in corpus (64)

• Discrepancy between experimental and theoretical $\beta$-decay rates resolved from first principles
• Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
• Toward the discovery of matter creation with neutrinoless double-beta decay
• 50 Years of Quantum Chromodynamics
• Light-nuclei spectra from chiral dynamics
• Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Quantum Monte Carlo Methods in Nuclear Physics: Recent Advances
• Local chiral interactions, the tritium Gamow-Teller matrix element, and the three-nucleon contact term
• Quantum Monte Carlo calculations of weak transitions in $A$=6--10 nuclei
• Neutrinoless double beta decay matrix elements in light nuclei
• Towards high-order calculations of three-nucleon scattering in chiral effective field theory
• Chiral Effective Field Theory Calculations of Weak Transitions in Light Nuclei
• Towards grounding nuclear physics in QCD
• Ab initio calculation of the potential bubble nucleus ${}^{34}$Si
• Few- and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon-nucleon forces
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (II) Single-Baryon $\beta$-Decay in Real Time
• Benchmark calculations of pure neutron matter with realistic nucleon-nucleon interactions
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• The Role of Lattice QCD in Searches for Violations of Fundamental Symmetries and Signals for New Physics
• Lattice QCD and Neutrino-Nucleus Scattering
• Nuclear Currents in Chiral Effective Field Theory
• Nuclear modification of scalar, axial and tensor charges from lattice QCD
• First-principle calculations of Dark Matter scattering off light nuclei
• Quenching of nuclear matrix elements for $0\nu \beta \beta$ decay by chiral two-body currents
• Nuclear electromagnetic currents to fourth order in chiral effective field theory
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Extraction of nucleon axial charge and radius from lattice QCD results using baryon chiral perturbation theory
• Parity- and time-reversal-violating nuclear forces
• Three-nucleon force in chiral EFT with explicit $\Delta (1232)$ degrees of freedom: Longest-range contributions at fourth order
• Neutrino-deuteron scattering: Uncertainty quantification and new $L_{1,A}$ constraints
• Ab initio structure factors for spin-dependent dark matter direct detection
• Lattice QCD Inputs for Nuclear Double Beta Decay
• Ab initio calculation of the $\beta$ decay spectrum of ${}^6$He
• Uncertainties in constraining low-energy constants from ${}^3$H $\beta$ decay
• Unitary ambiguity of NN contact interactions and the 3N force
• Momentum space treatment of inclusive neutrino scattering off the deuteron and trinucleons
• Muon capture in nuclei: an ab initio approach based on quantum Monte Carlo methods
• Effective-field-theory predictions of the muon-deuteron capture rate
• Three-body forces and Efimov physics in nuclei and atoms
• Theoretical tools for neutrino scattering: interplay between lattice QCD, EFTs, nuclear physics, phenomenology, and neutrino event generators
• Recent progress in the electroweak structure of light nuclei using quantum Monte Carlo methods
• Present Status of Nuclear Shell-Model Calculations of Neutrinoless Double-Beta Decay Matrix Elements
• Beta Decay in Medium-Mass Nuclei with the In-Medium Similarity Renormalization Group
• Subleading contributions to the nuclear scalar isoscalar currents
• Quantum Monte Carlo calculations of magnetic form factors in light nuclei
• Inclusive neutrino scattering off deuteron at low energies in chiral effective field theory
• Box diagram contribution to the axial two-nucleon current
• Electroweak Currents from Chiral Effective Field Theory
• Magnetic structure of $A\le 10$ nuclei using the Norfolk nuclear models with quantum Monte Carlo methods
• Can the strong interactions between hadrons be determined using femtoscopy?
• Two-body weak currents in heavy nuclei
• Magnetic moments of $A=3$ nuclei with chiral effective field theory operators
• Applications of the chiral potential with the semi-local regularization in momentum space to the disintegration processes
• Renormalization of proton-proton fusion in chiral effective field theory
• Investigating nuclear beta decay using lattice quantum Monte Carlo approach
• Longitudinal form factors of $A\le 10$ nuclei in a chiral effective field theory approach
• Muon capture on the deuteron in chiral effective field theory
• The Role of Ab Initio Beta-Decay Calculations in Light Nuclei for Probes of Physics Beyond the Standard Model
• The "Folk Theorem" on Effective Field Theory: How Does It Fare in Nuclear Physics?
• Ab initio calculations of beta-decay half-lives for $N=50$ neutron-rich nuclei
• Investigation of interaction of circularly and linearly polarized photon beams with polarized 3He target
• Pion absorption from the lowest atomic orbital in 2H, 3H and 3He
• Fundamental Physics with Electroweak Probes of Nuclei