  We present a novel framework for carrying out global analyses of the Standard
Model Effective Field Theory (SMEFT) at dimension-six: SMEFiT. This approach is
based on the Monte Carlo replica method for deriving a faithful estimate of the
experimental and theoretical uncertainties and enables one to construct the
probability distribution in the space of the SMEFT degrees of freedom. As a
proof of concept of the SMEFiT methodology, we present a first study of the
constraints on the SMEFT provided by top quark production measurements from the
LHC. Our analysis includes more than 30 independent measurements from 10
different processes at 8 and 13 TeV such as inclusive top-quark pair and
single-top production and the associated production of top quarks with weak
vector bosons and the Higgs boson. State-of-the-art theoretical calculations
are adopted both for the Standard Model and for the SMEFT contributions, where
in the latter case NLO QCD corrections are included for the majority of
processes. We derive bounds for the 34 degrees of freedom relevant for the
interpretation of the LHC top quark data and compare these bounds with
previously reported constraints. Our study illustrates the significant
potential of LHC precision measurements to constrain physics beyond the
Standard Model in a model-independent way, and paves the way towards a global
analysis of the SMEFT.
