  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.
