Global interpretations of LHC data using the Standard Model Effective Field Theory

The Standard Model Effective Field Theory (SMEFT) provides a powerful theoretical framework for interpreting subtle deviations from the Standard Model and searching for heavy new physics at the LHC.  It benefits from a global approach, and I will give an overview of results from a global fit to the SMEFT combining data from the top, Higgs, diboson and electroweak sectors.  I will discuss two recent developments which may impact the sensitivity of future global SMEFT fits to new physics.  Firstly, I will present an application of machine learning techniques to the construction of unbinned multivariate observables optimised for global SMEFT fits.  Secondly, it is crucial that we are confident in our theoretical inputs to such global analyses: in particular, that the use of parton distribution functions, which are fit under the assumption of the SM, does not introduce a bias into the fit.  I will discuss the issue of PDF-SMEFT interplay in global SMEFT fits, focusing on an example of their interplay in high-mass Drell-Yan tails.