A class of models of dark sectors consider new very weak interaction between the ordinary and dark matter transmitted by U(1) gauge bosons A (dark photons) mixing with our photons. If such As exist, they could be searched for in a light-shining-through-a-wall experiment with a high energy electron beam from the CERN SPS. The proposed search scheme suggests detection of the e+e- pairs produced in the A -> e+e- decay with a very small opening angle. Coordinate chambers based on the thin-wall drift tubes with a minimal material budget and a two-hit resolution for e+ and e- tracks separated by more than 0.5 mm are considered as an option for detecting such pairs.
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