As discussed in Sect.~\ref{sec:datatheory}, the LHC experiments have provided
a large number of experimental measurements with important
PDF sensitivity, most of which are now part of the toolbox
of global PDF fits.
%
In addition to presenting the results of such measurements, the ATLAS 
and CMS collaborations have developed themselves an active
program of PDF interpretation studies, aimed at quantifying the constrains of their
data on the proton structure.

In most cases, these studies have been performed using the {\tt HERAfitter/xFitter} frameworks,
described in Sect~\ref{sec:pdfgroups.xfitter}.
%
Thus the PDFs are parameterised at $Q_0^2=1.9\,{\rm GeV}^2$ in terms of relatively
simple polynomials in $x$.
%
Fits are then performed with an increasing number of free parameters introduced up to the point when no further improvement in $\chi^2$ is observed. This generally leads to $\sim 15$ free parameters in the fit, with the precise number depending on the particular analysis. Experimental uncertainties are calculated using the standard `$\Delta\chi^2=1$' criteria, and as in the HERAPDF approach, with
additional model and parameterisation uncertainties are determined to estimate the total
PDF uncertainty.
%
In all cases, either the HERA I DIS~\cite{Aaron:2009aa}, or in later studies the I + II combination~\cite{Abramowicz:2015mha} are included in a baseline fit,
before assessing the impact of the corresponding LHC measurements, which
are then fit in addition.

Such studies represent an important contribution to the PDF fitting community,
not only because they demonstrate the PDF impact of specific measurements,
but also because they provide an internal cross-checks that the information
required for PDF fits, in particular the full experimental covariance matrix,
is ready to be used.
%
In the following, we describe the individual efforts from ATLAS and CMS,
highlighting a representative sample of their PDF studies.

\subsubsection{ATLAS}\label{sec:pdfgroups.LHC.ATLAS}

A representative selection of ATLAS PDF interpretation studies is given below:

\begin{itemize}

\item The ATLAS measurements of $W^+$, $W^-$ and $Z$ rapidity distributions
at 7 TeV from the 2010 dataset were used in Ref.~\cite{Aad:2012sb}, in combination with HERA DIS data, to determine
the strange content of the proton.
%
The full cross-correlations between the three
rapidity distributions were accounted for, and while $W^+$ and $W^-$ measurements constrained
the up and down quarks and antiquarks, the $Z$ measurement constrained the strangeness.
%
This analysis found that the strange sea was not suppressed as compared to the up and down
quark sea.

\item The recent study~\cite{Aaboud:2016btc},
based on the updated $W^+$, $W^-$ and $Z$ rapidity distributions
at 7 TeV  from the 2011 dataset, corresponding to a greatly improved precision in comparison to 2010.
%
An analysis of this data, combined with HERA DIS data, was found to prefer a strange quark sea that is symmetric with respect
to the light quark sea, consistent with the previous findings
of~\cite{Aad:2012sb}.
%
The PDF uncertainties in the strangeness
determination were significantly reduced in comparison to the PDFs determined from the
analysis of the 2010 data.
%
The issue of the strange content of the proton will be
discussed in more detail in Sect.~\ref{sec:structure.strange}.

\item PDF fits based on jet production measurements have also been performed
by ATLAS.
%
For instance, in~\cite{Aad:2013lpa} an analysis of the HERA DIS data
supplemented with inclusive jet cross sections at
$\sqrt{s}=2.76$ TeV and $\sqrt{s}=7$ TeV (from the 2010 run) was performed.
%
It was shown that an improved constraint could be achieved by considering
the ratio $R_{7/2.76}$ of jet cross-sections is used, given that many
experimental and theoretical uncertainties cancel when taking
such ratios between different centre-of-mass energies~\cite{Mangano:2012mh}.

\end{itemize}

In Fig.~\ref{fig:atlaspdffits} we show some representative results
of PDF interpretation studies performed within the ATLAS collaboration.
%
In the left plot, we show the results of a
PDF fit quantifying the effect on the gluon 
   of the ATLAS inclusive jet measurements at $\sqrt{s}=2.76$ TeV
   and 7 TeV, in comparison to a HERA--only fit.
   %
   In the right plot we show the
   determination of the strangeness ratio $R_s(x=0.023,Q^2=1.9\,{\rm GeV}^2)$
   for a HERA--only fit and including the 2011 ATLAS measurements of the $W^{\pm}$ and $Z$
   rapidity distributions at 7 TeV. The results of the {\tt xFitter} analysis,
   denoted by ATLAS-epWZ16, are compared with the predictions from various PDF fits.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.45]{5-pdfgroups/plots/atlaspdffits.pdf}
   \caption{\small Two representative results of the PDF fitting efforts
   performed within the ATLAS collaboration.
   %
   Left plot: a PDF fit quantifying the effect on the gluon from the HERA-only fit
   of the ATLAS inclusive jet measurements at $\sqrt{s}=2.76$ TeV
   and 7 TeV, from Ref.~\cite{Aad:2013lpa}.
   %
   Right plot: the determination of the strangeness ratio $R_s(x=0.023,Q^2=1.9\,{\rm GeV}^2)$
   for a fit to HERA data and the 2011 ATLAS measurements of the $W^{\pm}$ and $Z$
   rapidity distributions at 7 TeV, where the results of the {\tt xFitter} analysis,
   denoted by ATLAS-epWZ16, are compared with the predictions from various PDF fits. Taken from~\cite{Aaboud:2016btc}.
    \label{fig:atlaspdffits}
  }
\end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsubsection{CMS}\label{sec:pdfgroups.LHC.CMS}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.65]{5-pdfgroups/plots/CMSfig1.pdf}\qquad
  \includegraphics[scale=0.25]{5-pdfgroups/plots/CMSfig2.pdf}
   \caption{\small 
    \label{fig:cmspdffits}
    Left: the gluon distribution at $\mu^2= 30000\,{\rm GeV}^2$, as obtained from a PDF fit to HERA DIS data and CMS $W^\pm$ boson charge asymmetry measurements~\cite{Khachatryan:2016pev}, the CMS inclusive jet production cross sections~\cite{Khachatryan:2016mlc}, and the $W^{\pm}$ boson charge asymmetry plus the double-differential $t\overline{t}$ cross section~\cite{Sirunyan:2017azo}, in all cases at 8 TeV. All presented PDFs are normalized to the results from the fit using the DIS and $W^{\pm}$ boson charge asymmetry measurements, and the total uncertainty band in each fit is shown. Taken from~\cite{Sirunyan:2017azo}.
    %
    Right: the down valence distribution at $\mu^2=M_W^2$ as obtained from a PDF fit to the HERA DIS data and CMS $W^\pm$ boson charge asymmetry measurement at 8 TeV, with the total PDF uncertainties shown. In the lower panel the distributions are normalized to 1. Taken from~\cite{Khachatryan:2016pev}.
  }
\end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


A representative selection of PDF interpretation studies from CMS is given below:

\begin{itemize}

\item In~\cite{Chatrchyan:2013mza} the 7 TeV measurement of the $W$ charge asymmetry, as well as $W+c$ production~\cite{Chatrchyan:2013uja}, is fit at NLO, and improvements in the determination of the up and down valence quark PDFs due to the $W$ asymmetry, and the strange quark PDFs due to the $W+c$ data, are demonstrated. 

\item In~\cite{Khachatryan:2016pev} a fit to the the 8 TeV differential $W$ boson production data~\cite{Khachatryan:2016pev} is performed at NNLO, again showing improvements in the 
determination of the up and down valence quark PDFs.

\item In~\cite{Khachatryan:2014waa} the 7 TeV inclusive jet measurement is fit at NLO, and the significant impact of these data on the gluon PDF in particular is demonstrated. A study is also performed here using the MC method for PDF determination, allowing for a more flexible PDF parameterisation, and consistent results are found but with larger PDF uncertainties.

\item A NLO fit to the 8 TeV jet data is performed in~\cite{Khachatryan:2016mlc}, and a direct comparison to the 7 TeV case is shown, with the impact found to be very similar.

\item In~\cite{Sirunyan:2017azo} a NLO fit to the 8 TeV double differential top pair production data is compared to a baseline fit that includes the 8 TeV $W$ boson production data~\cite{Khachatryan:2016pev}. The impact of including the data differential in different kinematic variables is assessed, and a sizeable reduction in the uncertainty on the gluon PDF in particular is found for $x>0.01$, with the largest constraint coming from the rapidity, $y_{t\overline{t}}$, and invariant mass, $M_{t\overline{t}}$ of the top pair.

\item More recent preliminary results including PDF fits to triple differential dijet production at 8 TeV~\cite{CMS:2016wpr} and the top pair production cross section at 5.02 TeV~\cite{CMS:2017olb} have been presented.

\end{itemize}

To illustrate these CMS PDF studies,
in Fig.~\ref{fig:cmspdffits}  we show the impact on the gluon PDF of the CMS $W^\pm$ data~\cite{Khachatryan:2016pev}, the double differential top pair production data~\cite{Sirunyan:2017azo} and the inclusive jet production data~\cite{Khachatryan:2016mlc}, in all cases at 8 TeV. This is seen to lead to a sizeable reduction in the uncertainty at higher $x$, in a way that is consistent between the data sets in the probed $x$ region.
%
The $t\overline{t}$ differential data are competitive with the the measurement. In Fig.~\ref{fig:cmspdffits} (Right) we show the impact of the  CMS $W^\pm$ boson charge asymmetry measurement at 8 TeV on the down valence distribution, in comparison to a HERA--only fit. The impact on the shape, and reduction in uncertainties, achieved by the asymmetry data is clear.






