Search for charged-lepton-flavour violating $\mu\tau qt$ interactions in top-quark production and decay with the ATLAS detector at the LHC

A search for charged-lepton-flavour violating $\mu\tau qt$ interaction is presented, considering both in top-quark production and decay. The data analysed corresponds to $139~\textrm{fb}^{-1}$ of proton--proton collisions at a centre-of-mass energy of $\sqrt{s}= 13$ TeV recorded by the ATLAS detector at the Large Hadronic Collider. The analysis targets events containing two muons, a hadronically decaying tau lepton and at least one jet, with exactly one $b$-tagged jet, produced by a $\mu\tau qt$ interaction in top-quark production or decay. No excess above the Standard Model background is observed and limits are set on the charged-lepton-flavour violation branching ratio of $\text{BR}(t \to \mu\tau q) < 11 \times 10^{-7}$. Wilson coefficient limits, dependent on the flavour of the associated light quark and the Lorentz structure of the coupling, are set ranging from $c_{\ell equ}^{3(2313)} / \Lambda^{2} < 0.11~\textrm{TeV}^{-2}$ for $\mu\tau ut$ to $c_{\ell equ}^{1(2323)} / \Lambda^{2} < 1.9~\textrm{TeV}^{-2}$ for $\mu\tau ct$.