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We present an analysis of two key sets of data constraining the high $x$gluon at up to approximate N${}^3$LO in QCD within the MSHT global PDF fittingframework. We begin with LHC 7 and 8 TeV inclusive jet and dijet production atboth NNLO and aN${}^3$LO. This makes use of the formalism established in theprevious global MSHT20aN${}^3$LO PDF fit, but now considers the role of dijetproduction for the first time at this order. We present a detailed comparisonof the fit quality and PDF impact for both cases, and consider the role thatelectroweak corrections, and the scale choice for inclusive jet production has.Some mild tension between these data sets in the impact on the high $x$ gluonis seen at NNLO, but this is largely eliminated at aN${}^3$LO. While a good fitquality to the dijet data is achieved at both orders, the fit quality to theinclusive jet data is relatively poor. We examine the impact of including fullcolour corrections in a global PDF fit for the first time, finding this to berelatively mild. We also revisit the fit to the ATLAS 8 TeV $Z$ $p_T$ data,considering the role that the $p_T$ cuts, data selection and different aspectsof the aN${}^3$LO treatment have on the fit quality and PDF impact. We observethat in all cases the aN${}^3$LO fit quality is consistently improved relativeto the NNLO, indicating a clear preference for higher order theory for thesedata.

The Impact of LHC Jet and $Z$ $p_T$ Data at up to Approximate N${}^3$LO Order in the MSHT Global PDF Fit