We present the results of a PDF fit to differential top quark production within the MMHT framework. We in particular consider ATLAS data in the lepton + jet and dilepton channels and CMS data in the lepton + jet channel, at 8 TeV. While the fit quality to the ATLAS dilepton data is good, for the CMS case we see some issues in achieving a good fit quality for certain distributions. However, we focus on the ATLAS lepton + jet data, for which correlations of the statistical and systematic errors are provided across the four relevant distributions for PDF determination, namely p t T , M tt , y t and y tt . We find severe difficulties in fitting these distributions simultaneously, with particular sensitivity to the precise degree of correlation taken between the dominant two-point MC uncertainties in the data. We investigate the effect of some reasonable decorrelation of these uncertainties, finding the impact on the fit quality to be significant and the resultant gluon not negligible. This is in particular found to be larger than the effect of including NNLO QCD and NLO EW corrections in the top quark pair production cross section on the fit, motivating a closer understanding of the physics underlying these errors sources and in particular the uncertainty on the degree of correlation in them.The determination of proton structure via the parton distribution functions (PDFs) is an integral part of the LHC physics programme [1,2]. In particular, as we enter the high precision LHC era, in terms of both theory and experiment, a detailed control over all uncertainties associated with the PDFs is essential. An area of particular phenomenological relevance is the determination of the gluon PDF at high x, which can for example play an important role in predictions for new heavy BSM states via gluon-initiated production, but until more recently has suffered from a relative lack of direct constraints, resulting in rather large PDF uncertainties. However, with the advent of high precision LHC data at higher masses and transverse momenta this situation has in principle changed rather dramatically. As discussed in [3][4][5], the inclusion of inclusive jet, Z boson transverse momentum, and differential top quark pair production in PDF fits places important constraints on the high x gluon that were lacking in earlier PDF fits. In all cases, these benefit from cutting edge high precision theory calculations at NNLO in QCD [6][7][8][9].On the other hand, the inclusion of such processes in PDF fits is not without issues. In the case of jet production, it is well known [3, 10, 11] that the ATLAS jet production data at 7 and 8 TeV cannot be well fit across all rapidity bins. For the Z boson transverse momentum distribution, issues with fitting the 7 TeV (normalized) data [12], and the CMS 8 TeV data [13] in the highest rapidity bin have been reported [5], while more generally in this study an additional source of uncorrelated error, assumed to be due to residual theoretical uncertainties and possible underestimated experimental errors, h...