%
The LHeC is in a unique position to 
unravel all quark densities
in the proton with a complete quark flavour
separation for the first time and 
with unprecented precision.
The huge 
phase space covered matches the needs of the LHC
and includes the extreme values of Bjorken $x$,
lowest, $x \simeq 10^{-5}$, where saturation
may set in and largest, near to $1$,
which determine the multi-TeV BSM
cross sections at the LHC.
The detailed shape measurements of the
various parton distributions, for example
of the strange density versus $Q^2$ and $x$,
imply that the nowadays large uncertainties
due to PDF parameterisations in pQCD fits
will be drastically reduced. A complete base
of PDFs as the LHeC promises to deliver
will at many places lead to possibly sizeable 
deviations of the now canonical PDF pattern.
This is a necessary input for future LHC
measurements, as  precision $Higgs$ coupling
and cross section determinations. There are
also expectations that discoveries are
made in the conventional PDF pattern, as
by possible observations of anti-quarks 
to be different from their sea quarks
or an intrinsic heavy flavour part. Since 
the momentum is conserved, and shared
between quarks and gluons, any deviation
affects the overall pattern, which reflects
on other parts of physics~\footnote{
A recent example is the ATLAS observation of
the light sea to be flavour symmetric. Combined
with the precision HERA $F_2$ data this changes
the singlet sea by $8$\,\%, which has consequences
for the ultra high energy neutrino-nucleon
scattering cross sections.}. Moreover, 
a crucial variety of non-canonical PDFs
will be accessed: generalised, unintegrated,
diffractive, neutron, photon and nuclear 
parton distributions.
% It is a mistake to believe
%that these are known (well enough) or
%of no fundamental interest, and further
%substructure as of $W,\,Z,\,top,\,Higgs$
%may not be excluded.

The basis of LHC physics and discoveries
BSM is QCD at high orders and 
the accurate knowledge of the 
classic PDFs. In the following,
based on~\cite{AbelleiraFernandez:2012cc},
some brief remarks are made on the unique
potential of the LHeC in the determination of 
the complete set of quark densities, while the mapping
of the gluon density is described subsequently below.
%
%
\begin{itemize}
\item
{\bf Valence quarks:}
The knowledge of the valence quark distributions, both
at large and at low Bjorken $x$, as derived in the current 
world data QCD fit analyses is amazingly limited.
An impressive improvement is expected from the LHeC. 
A NLO QCD fit to simulated inclusive neutral and charged
current LHeC data (see~\cite{AbelleiraFernandez:2012cc}) 
shows that the uncertainty of the down valence quark
distribution at, for example, $x=0.7$ can be reduced from
a level of   $50 - 100$\,\%  to about $5$\,\%.
This will be crucial for searches of new physics at the LHC
at the high energy frontier, in order to verify any excess
(or deficiency) compared to the SM prediction.
Direct access to valence quarks down to low $x\sim 0.001$ can be obtained at LHeC from
the  NC, $Z$ exchange related $e^{\pm}p$ cross section difference,
which can resolve possible sea-antiquark differences.
%, which isolates
%the  $\gamma-Z$ interference term.
\item
{\bf Light sea quarks:}
The measurement of the structure functions $F_2 \propto 4U+D$, in $ep$
and $F_2 \propto U+D$, in $eD$ is
the basis for determining the light sea quark densities
in the nucleon.
LHeC will extend greatly the HERA kinematic coverage
to much lower $x$ and to higher 
scales $Q^2$.
%, reducing the range of evolution to the LHC scales.
%
From NC and CC measurements and comparing $ep$ with $eD$
data, the up and down sea quark densities will
be unfolded, which nowadays are assumed to be equal
at $x < 0.01$.
\item
{\bf Strange:} Several long-standing questions
are related to the strange quark density in the proton:
how much is it suppressed with respect to the other two light quarks?
Is there an asymmetry between the strange and anti-strange density?
The knowledge of the strange-quark density itself is important
for many processes, for instance for the  precision measurement
of the $W$ boson mass.
%~\cite{Krasny:2010vd},
%for the formation of strange
%matter~\cite{Farhi:1984qu} and
%for neutrino interactions at ultra-high
%energies~\cite{Gandhi:1998ri}.
Information on the strange quark density is available from several experiments, 
in particular from previous Neutrino DIS experiments\footnote{
The interpretation of these neutrino data is sensitive to uncertainties
from charm quark fragmentation and nuclear corrections.},
but overall there is no real
understanding of the strange quark distribution.
%
The strange quark distribution is accessible at LHeC in charged current
scattering through the subprocesses $W^+s \to c$ (for positron beams)
and $W^-\bar{s} \to \bar c$ (for electron beams),
with charm tagging in the final state.
%
The LHeC simulation studies show that for the first time
accurate measurements of the $s$ and $\bar{s}$ densities can be performed
over a large kinematical phase space in $x$ and $Q^2$.
\item
{\bf Charm:} 
Information on the charm content in the proton can 
be accessed at LHeC by measuring the inclusive
charm production cross section in neutral current DIS.
%
At low scales $Q^2 \sim m_c^2$ (with $m_c$ being the charm quark mass)
one has to treat the charm production fully massive,
i.e. the charm quarks can be only dynamically produced 
in the reaction $\gamma g \rightarrow c\bar{c}$ and thus
are themselves no active flavours in the proton.
%
However, at large scales $Q^2 \gg m_c^2$
one can treat the charm quarks as massless partons,
which are contributing to the sea.
%
The charm quark mass $m_c$ is a crucial parameter:
it regulates the ratio of charm and light quarks in the sea
and thus affects predictions
for almost any quark driven process at the LHC.
%
At LHeC one expects much more precise and kinematically
extended measurements of inclusive charm production compared to HERA.
%
This will allow to map for the first time the transition from the massive to the massless regime.
%
Simulations show that one can use 
the data for a $m_c$ determination at a precision
of two permille.
%
With very good forward charm tagging one can also test
the hypothesis of an intrinsic charm component in the
proton wave function, which could appear at high $x\simeq 0.2$.
\item
{\bf Beauty:}
%
Simulation studies show that
one expects at LHeC precise measurements
of inclusive beauty production in DIS.
%
For large squared momentum transfer $Q^2 \gg m_b^2$
(with $m_b$ being the beauty quark mass)
these measurements can be directly translated
into an effective beauty quark density in the proton.
%
There is a huge interest in these densities, since in many scenarios
of new physics the beauty quarks are the original particles.
%
For instance
%, as discussed in~\cite{Belyaev:2005nu},
in the minimal supersymmetric extension of the standard model
the production of the neutral Higgs boson $A$ is driven by $b\bar{b} \rightarrow A$.
%
While at HERA the inclusive beauty production results were statistically
limited to about $20\%$ precision, very accurate results
can be expected at the LHeC.
\item
{\bf Top:}
%
The production of top quarks can be studied at the LHeC for the first time 
in DIS experiments.
%
The dominant process is single top (or anti-top) production in $W b$ to $t$ fusion.
%
The unique top physics program that can be performed at
the LHeC includes possibly
the consideration of a quark density for the top, from NC,
%which at very high scales may be considered ``light''.
% It also
%promises 
a high precision measurement of the top
mass from its decay and cross section.
Top physics at the LHeC is a promising
subject for further study.
%
\end{itemize}
%
In summary, while the LHC data can add information to
certain aspects of the quark densities in the proton
using specific reactions (e.g. Drell Yan),
it remains reserved for the LHeC to uniquely
resolve the complete quark and antiquark structure of the
proton, for all quark flavours, over the largest
kinematic range ever and last but not least with the best theoretical understanding.
%
%summarise uv,dv,s,c,b, emphasise on dv for searches, 
%strange for new info and light sea,  and beauty for SUSY input as MSSM Higgs
%
