Effective Field Theories of Axion, ALP and Dark Photon

TL;DR

This paper systematically enumerates effective operators up to dimension-8 for axion, ALP, and dark photon models using Young tensor techniques, providing a comprehensive basis for phenomenological studies.

Contribution

It introduces a complete set of effective operators for axion, ALP, and dark photon theories up to dimension-8, extending previous work with a novel tensor method and symmetry constraints.

Findings

Enumerated operators for axion/majoron at various dimensions

Extended dark photon operators with a new chiral Lagrangian approach

Provided explicit operator counts for different fermion generations

Abstract

With the help of Young tensor technique, we enumerate the complete and independent set of effective operators up to $dim$-8 for the extension of the standard model with a Goldsonte boson by further imposing the Adler's zero condition in the soft momentum limit. Such basis can be reduced to describe the axion or majoron effective Lagrangian if further (symmetry) constraints are imposed. Then reformulating dark photon as combination of Goldstone boson and transverse gauge boson, the effective operators of the Goldstone boson can be extended to effective chiral Lagrangian description of the dark photon. For the first time we obtain 0 (0), 6 (44), 1 (1), 44 (356), 32 (520) operators in Goldstone effective field theory, and 9 (49), 0 (0), 108 (676), 10 (426), 1904 (40783) operators in dark photon effective field theory at the dimension 4, 5, 6, 7, 8 for one (three) generation of fermions.