This search, a type not previously performed at ATLAS, uses a comparison of the production cross sections for e+μ− and e−μ+ pairs to constrain physics processes beyond the Standard Model. It uses 139fb−1 of proton–proton collision data recorded at s=13TeV at the LHC. Targeting sources of new physics which prefer final states containing e+μ− to e−μ+, the search contains two broad signal regions which are used to provide model-independent constraints on the ratio of cross sections at the 2% level. The search also has two special selections targeting supersymmetric models and leptoquark signatures. Observations using one of these selections are able to exclude, at 95% confidence level, singly produced smuons with masses up to 640GeV in a model in which the only other light sparticle is a neutralino when the R-parity-violating coupling λ231′ is close to unity. Observations using the other selection exclude scalar leptoquarks with masses below 1880GeV when g1Reu=g1Rμc=1, at 95% confidence level. The limit on the coupling reduces to g1Reu=g1Rμc=0.46 for a mass of 1420GeV.