  We show that the interplay of chiral effective field theory and lattice QCD
can be used in the evaluation of so-called disconnected diagrams, which appear
in the study of the isoscalar and isovector channels of pion-pion scattering
and have long been a major challenge for the lattice community. By means of
partially-quenched chiral perturbation theory, we distinguish and analyze the
effects from different types of contraction diagrams to the pion-pion
scattering amplitude, including its scattering lengths and the
energy-dependence of its imaginary part. Our results may be used to test the
current degree of accuracy of lattice calculation in the handling of
disconnected diagrams, as well as to set criteria for the future improvement of
relevant lattice computational techniques that may play a critical role in the
study of other interesting QCD matrix elements.
