Next we turn to discuss the light quark content of the proton,
and in particular quantify the degree with which current fits
achieve quark flavour separation, {\it i.e.}, the ability
to separate $u$ from $d$ quarks, and  quarks from
antiquarks.
%
First of all, in Fig.~\ref{fig:pdfcomp-quarkseparation} we show
the up, down, anti-up, and anti-down quark
PDFs at $Q=100$ GeV.
%
The up quark, $u(x,Q)$ is one of the better constrained
PDFs, in particular at large-$x$, due to fixed--target DIS data.
%
For this PDF, we find good agreement within uncertainties in the entire range of $x$,
with the only exception being ABMP16, which overshoots the other
three sets in the large-$x$ region.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.39]{6-structure/plots/xu-pdfcomp-highQ.pdf}
  \includegraphics[scale=0.39]{6-structure/plots/xd-pdfcomp-highQ.pdf}
  \includegraphics[scale=0.39]{6-structure/plots/xubar-pdfcomp-highQ.pdf}
  \includegraphics[scale=0.39]{6-structure/plots/xdbar-pdfcomp-highQ.pdf}
   \caption{\small 
     Same as Fig.~\ref{fig:pdfcomp-xg} (right), now comparing the
     up, down, anti-up, and anti-down quark PDFs.
    \label{fig:pdfcomp-quarkseparation}
  }
\end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

For the down quark, $d(x,Q)$, the spread between the central values
is larger, and the PDF uncertainties are also
comparatively increased.
%
Here we find good agreement between CT14, MMHT14, and NNPDF3.1 within uncertainties
for the entire range of $x$, while ABMP16 is around 5\% lower than the central
NNPDF3.1 value at intermediate values of $x$.
%
The PDF uncertainties are the largest at high-$x$, with CT14, MMHT14 
and ABMP16 on the other hand pointing in different directions, with
the NNPDF3.1 central value lying somewhere in the middle.
%
One of the possible sources of difference between the groups
is the treatment of deuteron nuclear
corrections in the fitting of the
deuteron
structure functions~\cite{Harland-Lang:2014zoa},
though this effect is known to be localized in the region around $x\simeq 0.1$~\cite{Ball:2013gsa}.

For the light antiquark PDFs, $\bar{u}$ and $\bar{d}$, 
there is reasonable agreement between the various sets within uncertainties
for $\bar{u}$, while this agreement is only marginal for $\bar{d}$.
%
In the latter case, the ABMP16 result is again around $\simeq 5\%$ smaller
than the NNPDF3.1 central value.
%
As in the case of the quark PDFs, we see significant differences
at large $x$; in this region there are limited experimental constraints, and thus
the methodological differences in each PDF fit
can have a rather more marked impact.
%
Similarly to the gluon, these large PDF uncertainties 
at high-$x$ have phenomenological consequences,
for instance for the production
of a heavy $W'$ or $Z'$ boson, or the pair production of
a squark-antisquark
pair $\tilde{q}\tilde{q}^*$, both processes being driven
by the quark-antiquark
luminosity (see also Sect.~\ref{sec:LHCpheno.BSM}).

Another useful way to compare the quark flavour separation between the various
PDF group is to plot flavour combinations that can be more
directly related to physical cross-sections.
%
In Fig.~\ref{fig:pdfcomp-quarkseparation-2} we compare the
sea quark asymmetry $\Delta_S=\bar{d}-\bar{u}$ and
the quark
isotriplet $T_3=u+\bar{u}-d-\bar{d}$ at $Q=1.7$ GeV for
CT14, MMHT14, and NNPDF3.1.
%
The former quark
flavour combination is closely related to the $W$ asymmetries in
collider Drell-Yan production (see Sect.~\ref{sec:datatheory.gauge}),
while the latter is directly
sensitive to the difference between the proton and deuteron
DIS structure functions, the non-singlet structure
function
$F_2^{\rm NS}\equiv F_2^p-F_2^d$.

From this comparison, we see that for the sea quark
asymmetry $\Delta_S$
the general shape is similar between the three groups, although there are large
differences in the estimate of the PDF uncertainties, both at small
and large $x$, which in some cases can be traced
back to the PDF parametrization assumptions.
%
The agreement is also
reasonably good both in terms of central values
and of uncertainties for the quark
non-singlet combination $T_3$, although here again the
small-$x$ behaviour does differ among the three groups, driven
by different parametrization choices.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.39]{6-structure/plots/xDeltaS-abs-pdfcomp-lowQ.pdf}
  \includegraphics[scale=0.39]{6-structure/plots/xtriplet-abs-pdfcomp-lowQ.pdf}
    \caption{\small 
     Same as Fig.~\ref{fig:pdfcomp-xg} (left), now comparing the
     sea quark asymmetry $\Delta_S=\bar{d}-\bar{u}$ (left) and the quark
     isotriplet $T_3=u+\bar{u}-d-\bar{d}$ (right plot).
    \label{fig:pdfcomp-quarkseparation-2}
  }
\end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

From these comparisons, we can see that the differences in the quark
flavour separation between the various groups are mostly localised in the
large-$x$ region.
%
With this in mind, in Fig.~\ref{fig:pdfcomp-quarkseparation-largex} we again show
the up and down quark PDFs,
focusing now on the large-$x$
region and adopting a linear scale in the $x$ axis.
%
From this comparison we can see that PDF uncertainties are the largest
in NNPDF3.1.
%
In terms of central values, there is reasonable agreement for the
up quark, less
so for the down one.
%
Note that as discussed in Sect.~\ref{sec:fitmeth.PDFpara},
in the NNPDF framework,
the PDFs themselves are not forced to be positive
(although the physical cross-sections are indeed positive-definite)
and therefore the down PDF can become negative at large-$x$, although
its central value remains always positive.
%
An alternative approach to compare the behaviour
of PDF sets at large-$x$, and in doing so comparing with
non-perturbative models such as the quark counting rules,
is the effective exponent method discussed in Ref.~\cite{Ball:2016spl}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.39]{6-structure/plots/xu-abs-pdfcomp-highQ.pdf}
  \includegraphics[scale=0.39]{6-structure/plots/xd-abs-pdfcomp-highQ.pdf}
    \caption{\small 
      Same as Fig.~\ref{fig:pdfcomp-quarkseparation}, now focusing
      on the large-$x$ region of the up quark (left) and down quark
      (right plot) PDFs.
    \label{fig:pdfcomp-quarkseparation-largex}
  }
\end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
