  We construct the most general low-energy effective lagrangian including local
parity violating terms parametrized by an axial chemical potential or chiral
imbalance $\mu_5$, up to ${\cal O}(p^4)$ order in the chiral expansion for two
light flavours. For that purpose, we work within the Chiral Perturbation Theory
framework where only pseudo-NGB fields are included, following the external
source method. The $\cal{O}(p^2)$ lagrangian is only modified by constant
terms, while the $\cal{O}(p^4)$ one includes new terms proportional to
$\mu_5^2$ and new low-energy constants (LEC), which are renormalized and
related to particular observables. In particular, we analyze the corrections to
the pion dispersion relation and observables related to the vacuum energy
density, namely the light quark condensate, the chiral and topological
susceptibilities and the chiral charge density, providing numerical
determinations of the new LEC when possible. In particular, we explore the
dependence of the chiral restoration temperature $T_c$ with $\mu_5$. An
increasing $T_c(\mu_5)$ is consistent with our fits to lattice data of the
ChPT-based expressions. Although lattice uncertainties are still large and
translate into the new LEC determination, a consistent physical description of
those observables emerges from our present work, providing a theoretically
robust model-independent framework for further study of physical systems where
parity-breaking effects may be relevant, such as heavy-ion collisions.
