\subsection{Physics Summary}
\label{sec:physics-summary}

Neutrino oscillations and the associated large leptonic family mixing
are arguably the first clear-cut discovery of physics beyond the
Standard Model that is not obtained from cosmology. Large mixing
angles came as a surprise and, while we have been able to formulate a
plethora of theories which can accommodate these results, we are far
from an actual understanding of mixing in particular and flavour in
general. This lack of understanding is also exemplified by the
non-observation of new physics in B-factories.  In some models
of neutrino mass generation, there is a connection between neutrinos
and Grand Unification. In this class, called see-saw models, neutrinos
can be ultimately responsible for the observed matter-antimatter
asymmetry of the Universe. In the first place, this requires neutrinos
themselves to violate matter-antimatter symmetry. The origin of flavour
is one of the profound open questions in particle physics and neutrino
oscillation studies will play a crucial part in providing the data,
which is necessary to make progress towards an answer.


The Neutrino Factory will be the ultimate neutrino physics facility
and provides a superior performance for CP violation, the mass
hierarchy and $\theta_{13}$, see figure~\ref{fig:euronu2009}. At the
same time, it provides the necessary precision to rigorously test the
three-flavour oscillation framework and thus, also has the potential
to discover new physics.  The baseline configuration of a Neutrino
Factory consists of one 100\,kTon MIND at a baseline of 4000\,km, to
determine the CP phase, and one 50\,kTon MIND at a baseline of 7500\,km,
to determine $\theta_{13}$ and the mass hierarchy. 
The stored muon energy is 25\,GeV and
$10^{21}$ useful muon decays per year are available. This baseline
configuration has been derived under the assumption that
$\stheta<0.01$, i.e., $\theta_{13}\neq0$ has not been discovered
prior to the start of the Neutrino Factory project. In this case, the
second, longer baseline is necessary to ensure a robust physics
performance throughout the parameter space, see
figure~\ref{fig:robustness}, and to provide the best possible
sensitivity to new physics.  On the other hand, if $\stheta>0.01$,
then it is very likely that $\stheta$ will be measured before we
embark onto the Neutrino Factory project and hence we would use this
information to optimise the design of the facility. 
Thus, in this case, we would use a
single baseline between 1\,500---2\,500\,km and a stored muon energy
around 10\,GeV, see top left panel of figure~\ref{fig:elopt}.  
The detector
can still be a 100\,kTon MIND, since recent updates of the MIND
performance, in particular the inclusion of quasi-elastic events, have
improved the low-energy performance significantly as explained in
detail in section~\ref{sec:MIND}.

In terms of new physics sensitivities, we have studied sterile
neutrinos and non-standard interactions as generic examples and find
the Neutrino Factory, in its baseline configuration, provides good
sensitivity to physics that cannot be studied at the LHC or
elsewhere. In addition, a Neutrino Factory, in most cases, would be
able to disentangle a new physics contribution from the usual
oscillations. 

We, as a community, have been searching for new physics for many
decades in vain. The discovery of neutrino mass is the first tangible
sign for physics beyond the Standard Model. It seems therefore, natural
and compelling to follow up to this initial discovery by a dedicated,
long term science program with the goal to establish the flavour
physics of neutrinos at a level of precision comparable to which we
tested the CKM theory of quark flavour. The results presented
in this section are supported by a large body of literature and
demonstrate clearly that a Neutrino Factory is \emph{the} ultimate
tool to study neutrinos and their flavour transitions with the highest
achievable precision.

