Electroweak Structure of Light Nuclei Within Chiral Effective Field Theory

Abstract

We review the results of the most recent calculations for the electromagnetic structure of light nuclei, the weak muon capture on deuteron and 3 He and the weak proton-proton capture reaction at energies of astrophysical interest, performed within the chiral effective field theory framework.

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

“…For the current operator, diagrams (1-9), (11)(12)(13)(14), (17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) are found to yield non-vanishing contributions, from which those of graphs (1-5), (21), (23)(24)(25), (27)(28)(29)(30) depend on the unitary phases: For our standard choice, we find a vanishing result for the short-range current operator after renormalization. This is consistent with the matching condition to the nuclear forces, since the static one-pion-contact 3NF's vanish after antisymmetrization.…”

“…(5.14) which involve the loop function L(q). This is not surprising given that they originate solely from the irreducible topologies (26) and (28) in Fig. 11 and thus can be obtained by evaluating the corresponding Feynman diagrams.…”

“…For the axial charge, diagrams (3), (5), (8), (10), (15)(16)(17), (20), (25)(26)(27)(28)(29)(30) are found to give non-vanishing contributions, from which those of graphs (3), (5), (8), (10), (15)(16)(17), (20), (25)(26)(27)(28)(29)(30) For our standard choice of the unitary phases, we obtain a vanishing result for the pion-pole terms in the axial charge. All ultraviolet divergences in the loop contributions to the axial charge operator are cancelled by the corresponding counterterms upon expressing the bare LECs z i in terms of their renormalized valuesz i via…”

“…[3,26,27] and references therein. In particular, electromagnetic exchange current operators were first discussed in this framework in the seminal paper by Park et al [28], who, however only focused on the near-threshold kinematics.…”

“…For the axial current, the diagrams (1-6), (9-15), (19)(20)(21)(22) and (25)(26)(27) give non-vanishing contributions, from which those of graphs (1-5), (9-11), (13), (15) turn out to depend on the unitary phases: …”