Off-shell ttj production and top-quark mass studies at the LHC.

Precision studies of the properties of the top quark represent a cornerstone of the LHC physics program. In this contribution, we focus on the production of tt pairs in association with one hard jet and, in particular, on its connection with precision measurements of the top-quark mass at the LHC. We report a summary of a full calculation of the process pp → e+νeμ−νμbbj at NLO QCD accuracy, which describes ttj production with leptonic decays beyond the Narrow Width Approximation (NWA), and discuss the impact of the off-shell effects through comparisons with NWA. Finally, we explore the sensitivity of ttj in the context of top-quark mass extraction with the template method, considering two benchmark observables as the case studies