The Lagrangian density for electrons and photons is taken in the form of 11.1.1.

Introducing renormalized fields and charge and mass, the counterterms can be written as

\(\mathscr{L}_2=-\frac{1}{4}(Z_3-1)F^{\mu\nu}F_{\mu\nu}-(Z_2-1)\bar\psi [\gamma_\mu\partial^\mu+m]\psi+Z_2\delta m\bar\psi\psi\\
-ie(Z_2-1)A_\mu\bar\psi\gamma^\mu\psi\)

The book states:

It will turn out that all of the terms in \(\mathscr L_2\) are of second order and higher order in e,...

Isn't the order of e in the expression just one or zero?