  We analize the most general low-energy effective lagrangian including local
parity violating terms parametrized by an axial chemical potential $\mu_5$.
This result is obtained following the external source method, up to
$\mathcal{O}(p^4)$ order in the chiral expansion for two light flavours. We
show that the $\mathcal{O}(p^4)$ lagrangian includes new terms proportional to
$\mu_5^2$ and new low-energy constants. Finally, the $\mu_5$ and temperature
dependences of several observables related to the vacuum energy density are
studied.
