Search for electroweak <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo accent="true">‾</mml:mo> </mml:mover> <mml:mi>W</mml:mi> <mml:mi>j</mml:mi> </mml:m

A search is presented for the electroweak production of a top quark pair in association with a <i>W</i> boson and at least one additional jet, known as the <i>tt^-Wj</i>_EW process. This process has embedded within it a <i>tW</i>-scattering vertex, which is probed directly for the first time. The collision data were collected with the ATLAS detector during Run 2 of the LHC and correspond to an integrated luminosity of 140 fb⁻¹ at √<i>s </i>= 13∼TeV. The search uses same-charge pairs of electrons and muons together with jets, of which at least one is $b$-tagged. The properties of the most forward jet relative to the rest of the event are used to discriminate the electroweak <i>tt^-Wj</i>_EW production process from its strong <i>tt^-W</i> production counterpart. A measured (expected) 95% CL upper limit on the cross section is set at σ_{<i>tt-Wj</i>EW} &lt; 251~fb (230 fb), to be compared with the expected SM cross section of 47.7 fb. Limits are set on the SM Effective Field Theory (EFT) operators <i>O_Ht</i> and <i>O</i>⁽¹⁾<i>_HQ</i>, which modify the electroweak couplings of the top quark through contributions to the <i>tW</i>-scattering vertex. The interpretation acts as a case study to emphasize the importance of energy-dependent sensitivity, multi-process and multi-operator EFT contributions.