We show how quark-disconnected and quark-connected contributions to hadronic
n-point functions can be written as independent correlators for which one can
derive expressions in partially quenched chiral effective theory. As an example
we apply the idea to the case of the hadronic vacuum polarisation. In
particular, we consider the cases of the Nf = 2 theory without and with a
partially quenched strange quark and also the Nf = 2 + 1 theory. In the latter
two cases a parameter-free prediction for the disconnected contribution at NLO
in the effective theory is given. Finally we show how twisted boundary
conditions can then be used in lattice QCD to improve the q^2 resolution in the
connected contributions even when flavour singlet operators are considered.Comment: 19 pages, 4 figures; results unchanged; typos corrected, references
added and discussion extended; accepted for publication in JHE
