  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.
