Chiral Effective Field Theories for Strong and Weak Dynamics

The chiral effective field theory (ChEFT) is an extension of the chiral perturbation theory that includes the nuclear forces and weak currents at the hadronic and nuclear scales. We propose a systematic framework of parametrising the pion-nucleon and nucleon-nucleon Lagrangian via the Weinberg power counting rules. We enumerate the operator bases of ChEFT by extending the Hilbert series of the pure meson sector to the nucleon sector with the CP symmetries. The Young tensor method is utilized to obtain the complete sets of the nucleon-nucleon, three-nucleon operators with/without pions ($\not\pi$-EFT). Then we use the spurion technique to reconstruct the ChEFT Lagrangian by taking the adjoint spurion and leptonic fields as the building blocks, without the need of external sources. These operators can be applied to both the strong dynamics, and the nucleon/nuclear weak current processes.