We summarize the quantitative results of our analysis [1] of top-pair photoproduction in semileptonic mode in pe collisions at the LHeC and FCC-he. We define three photoproduction regions, based on the rapidity acceptance range of the electron tagger, that provide different degrees of sensitivity to top-quark effective couplings. We focus on the ttγ dipole couplings and the left-handed vector tbW coupling, for which we determine limits at both energies in the different photoproduction regions. Furthermore, we find that the LHeC and FCC-he will yield tight direct bounds on top dipole moments, greatly improving on current direct limits from hadron colliders, and direct limits on the tbW coupling as restrictive as those expected from the HL-LHC. We also consider indirect limits from b → sγ branching ratio and CP asymmetry, that are well known to be very sensitive probes of top electromagnetic dipole moments.
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