Forward top quark pair production is studied in $pp$ collisions in the $mu eb$ final state using a data sample corresponding to an integrated luminosity of 1.93 fb$^{-1}$ collected with the LHCb experiment at a centre-of-mass energy of 13 TeV. The cross-section is measured in a fiducial region where both leptons have a transverse momentum greater than 20 GeV and a pseudorapidity between 2.0 and 4.5. The quadrature sum of the azimuthal separation and the difference in pseudorapidities, denoted $Delta R$, between the two leptons must be larger than 0.1. The $b$-jet axis is required to be separated from both leptons by a $Delta R$ of 0.5, and to have a transverse momentum in excess of 20 GeV and a pseudorapidity between 2.2 and 4.2. The cross-section is measured to be $$sigma_{tbar{t}}= 126pm19,(mathrm{stat})pm16,(mathrm{syst})pm5,(mathrm{lumi}),,mathrm{ fb}$$ where the first uncertainty is statistical, the second is systematic, and the third is due to the luminosity determination. The measurement is compatible with the Standard Model prediction.
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