  We show how a scheme of rewriting a divergent momentum integral can
conciliate results obtained with the Nambu--Jona-Lasinio model and recent
lattice results for the chiral transition in the presence of a chiral imbalance
in quark matter. Purely vacuum contributions are separated from
medium-dependent regularized momentum integrals in such a way that one is left
with ultraviolet divergent momentum integrals that depend on vacuum quantities
only. The scheme is applicable to other commonly used effective models to study
quark matter with a chiral imbalance, it allows us to identify the source of
their difficulties in reproducing the qualitative features of lattice results,
and enhances their predictability and uses in other applications.
