MSHT20 PDFs - Review and Updates

I will first review the MSHT20 parton distribution functions (PDFs) [1], the post Run 1 PDF set developed for precision LHC physics and wider applications. I will then focus on subsequent developments and recent progress. This will cover notable experimental, methodological and theoretical advances. I will therefore describe several further studies including amongst others: (1) The study of the strong coupling constant and heavy quark masses in our PDFs [2], resulting in a competitive determination of the S(MZ). (2) QED evolved PDFs and the photon, and impacts on cross-sections. (3) Approximate N3LO PDFs [3] and the inclusion of theoretical uncertainties into PDFs for the first time. (4) Constraining the top quark mass in the PDF fit [4]. (5) Inclusion of a variety of new data sets, from dijet data to seaquest drell-yan data to EIC pseudodata. Of particular relevance for this workshop are the aN3LO PDFs needed for precision calculations and their effects on uncertainties, including the incorporation of missing higher order uncertainties. There are also connections with small x resummation in this work. Meanwhile, separately our studies of the impacts of EIC pseudodata on PDF uncertainties will also be of particular interest