Box diagram contribution to the axial two-nucleon current

Abstract

Recently, we have worked out the axial two-nucleon current operator to leading one-loop order in chiral effective field theory using the method of unitary transformation. Our final expressions, however, differ from the ones derived by the JLab-Pisa group using time-ordered perturbation theory (Phys. Rev. C 93, no. 1, 015501 (2016) Erratum: [Phys. Rev. C 93, no. 4, 049902 (2016)] Erratum: [Phys. Rev. C 95, no. 5, 059901 (2017)]). In this paper we consider the box diagram contribution to the axial current and demonstrate that the results obtained using the two methods are unitary equivalent at the Fock-space level. We adjust the unitary phases by matching the corresponding two-pion exchange nucleon-nucleon potentials and rederive the box diagram contribution to the axial current operator following the approach of the JLab-Pisa group, thereby reproducing our original result. We provide a detailed information on the calculation including the relevant intermediate steps in order to facilitate a clarification of this disagreement.

arXiv comment13 pages, 1 figure

References in corpus (11)

• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Chiral Dynamics and Heavy-Fermion Formalism in Nuclei: I. Exchange Axial Currents
• The two-nucleon electromagnetic charge operator in chiral effective field theory ($\chi$EFT) up to one loop
• Nuclear axial current operators to fourth order in chiral effective field theory
• Local chiral interactions, the tritium Gamow-Teller matrix element, and the three-nucleon contact term
• Four-nucleon force using the method of unitary transformation
• Nuclear Axial Currents in Chiral Effective Field Theory
• Tritium $\beta$-decay in chiral effective field theory
• Equivalence of Nonstatic Two-Pion-Exchange Nucleon-Nucleon Potentials
• Nuclear electromagnetic currents to fourth order in chiral effective field theory
• Orthonormalization procedure for chiral effective nuclear field theory

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