A precise measurement of the top quark mass, a fundamental parameter of the Standard Model, is among the most important goals of top quark studies at the Large Hadron Collider. Apart from the standard methods, numerous new observables and reconstruction techniques are employed to improve the overall precision and to provide different sensitivities to various systematic uncertainties. Recently, the normalised inverse invariant mass distribution of the $tbar{t}$ system and the leading extra jet not coming from the top quark decays has been proposed for the $pp to tbar{t}j$ production process, denoted as ${cal R}(m_t^{pole},rho_s)$. In this paper, a thorough study of different theoretical predictions for this observable, however, with top quark decays included, is carried out. We focus on fixed order NLO QCD calculations for the di-lepton top quark decay channel at the LHC with $sqrt{s}=13$ TeV. First, the impact on the extraction of $m_t$ is investigated and afterwards the associated uncertainties are quantified. In one approach we include all interferences, off-shell effects and non-resonant backgrounds. This is contrasted with a different approach with top quark decays in the narrow width approximation. In the latter case, two cases are employed: NLO QCD corrections to the $ppto tbar{t}j$ production process with leading order decays and the more sophisticated case with QCD corrections and jet radiation present also in top quark decays. The top quark mass sensitivity of ${cal R}(m_t^{pole},rho_s)$ is investigated and compared to other observables: the invariant mass of the top anti-top pair, the minimal invariant mass of the $b$-jet and a charged lepton as well as the total transverse momentum of the $tbar{t}j$ system.
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