  We study effects of beyond the Standard Model physics coupling third
generation quarks to leptons of the first two generations. We parametrize these
effects by dimension-six effective operators, and we also consider related
simplified UV completions: scalar leptoquark and $W'$ models. We derive new
constraints on these scenarios by using recent ATLAS measurements of
differential cross sections of single top production in association with a $W$
boson, and also show how these limits will evolve with future data. We also
describe how the limits can be significantly improved by using ratios of
differential distributions with different flavors of leptons.
