  Among many possibilities, solar axion has been proposed to explain the
electronic recoil events excess observed by Xenon1T collaboration, although it
has tension with astrophysical observations. The axion couplings, to photon
$g_{a\gamma}$ and to electron $g_{ae}$ play important roles. These couplings
are related to the Peccei-Quinn (PQ) charges $X_f$ for fermions. In most of the
calculations, $g_{a\gamma}$ is obtained by normalizing to the ratio of
electromagnetic anomaly factor $E = TrX_f Q^2_f N_c$ ($N_c$ is 3 and 1 for
quarks and charged leptons respectively) and QCD anomaly factor $N = TrX_q
T(q)$ ($T(q)$ is quarks' $SU(3)_c$ index). The broken PQ symmetry generator is
used in the calculation which does not seem to extract out the components of
broken generator in the axion which are "eaten" by the $Z$ boson. However,
using the physical components of axion or the ratio of anomaly factors should
obtain the same results in the DFSZ for $g_{a\gamma}$. When going beyond the
standard DFSZ models, such as variant DFSZ models, where more Higgs doublets
and fermions have different PQ charges, one may wonder if the results are
different. We show that the two methods obtain the same results as expected,
but the axion couplings to quarks and leptons $g_{af}$ (here f indicates one of
the fermions in the SM) are more conveniently calculated in the physical axion
basis. The result depends on the values of the vacuum expectation values
leading to a wider parameter space for $g_{af}$ in beyond the standard DFSZ
axion. We also show explicitly how flavor conserving $g_{af}$ couplings can be
maintained when there are more than one Higgs doublets couple to the up and
down fermion sectors in variant DFSZ models at tree level, and how flavor
violating couplings can arise.
