Uncertainties on the theoretical input for $t\bar{t}j$ experimental analyses at the LHC

The precise measurement of the top-quark mass constitutes one of the main goals of the LHC top-quark physics program. One possibility to extract this parameter uses the $\rho_{\mathrm{s}}$ distribution, which depends on the invariant mass of the $t\bar{t}j$ system. To fully take advantage of the experimental accuracy achievable in measuring top quark production cross sections at the LHC, the theory uncertainties need to be well under control. We present a study of the effect of varying the input parameters of the theoretical calculation on the predicted $\rho_{\mathrm{s}}$ distribution. Thereby we studied the influence of the $R$ parameter in the jet reconstruction procedure, as well as the effect of various renormalization and factorization scale definitions and different PDF sets. A behaviour similar to the one presented here for the $\rho_{\mathrm{s}}$-distribution was also found for other differential distributions.