  Different computational methods are employed to evaluate elastic
(rotationally summed) integral and differential cross sections for low energy
(below about 10 eV) positron scattering off gas-phase C$_2$H$_2$ molecules. The
computations are carried out at the static and static-plus-polarization levels
for describing the interaction forces and the correlation-polarization
contributions are found to be an essential component for the correct
description of low-energy cross section behavior. The local model potentials
derived from density functional theory (DFT) and from the distributed positron
model (DPM) are found to produce very high-quality agreement with existing
measurements. On the other hand, the less satisfactory agreement between the
R-matrix (RM) results and measured data shows the effects of the slow
convergence rate of configuration-interaction (CI) expansion methods with
respect to the size of the CI-expansion. To contrast the positron scattering
findings, results for electron-C$_2$H$_2$ integral and differential cross
sections, calculated with both a DFT model potential and the R-matrix method,
are compared and analysed around the shape resonance energy region and found to
produce better internal agreement.
