\section{Introduction}\label{sec:intro}

Considerations of the stability of the electroweak scale lead to the
general belief that there is new physics with particle masses below 1
TeV. While the high-$p_T$ experiments at the LHC should
produce these new particles directly, one can study their dynamics also
indirectly, through their impact on precision measurements at lower
energies. To this end flavour-changing neutral current (FCNC)
processes are extremely useful. On one hand they are highly
suppressed in the Standard Model and are therefore very sensitive to new
physics. On the other hand FCNC processes of $K$, $B_d$ and $B_s$ mesons
are still large enough to be studied with high statistics in dedicated
experiments. Here meson--antimeson mixing plays an outstanding
role. First, meson--antimeson oscillations occur at time scales which
are sufficiently close to the meson lifetimes to permit their
experimental investigation. Second, the Standard Model contribution to
meson--antimeson mixing is loop-suppressed and comes with two or more
small elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix \cite{ckm}.
Third, the decays of oscillating mesons give access to many
mixing-induced \CP asymmetries through the time-dependent study of
decays into CP-eigenstates, which in some cases one can relate to the
parameters of the underlying theory with negligible hadronic uncertainties.

The $B$-factories have revealed that the dominant $b\to d$ and $b\to u$ 
transitions fit into the pattern of the CKM mechanism and are in agreement 
with the information on $s\to d$ transitions gained in more than fourty 
years of kaon physics. The success of the CKM picture is evident from 
the many different measurements combining into a consistent and precise
determination of the apex $(\rhobar,\etabar)$ of the $B$-meson
unitarity triangle (in terms of the Wolfenstein parameterization of the
CKM matrix \cite{Wolfenstein,BurasLautenbacherOstermaier}).  As a
consequence, any contribution from the expected new TeV-scale physics to
the measured flavour-changing processes must be suppressed
compared to the established CKM mechanism.

Models with only CKM-like flavour violation are said to respect the principle 
of \emph{minimal flavour violation (MFV)} \cite{dgis}. The overall picture 
of experimental data does not require sizable corrections to MFV. Still it is
difficult to probe the CKM picture with a better accuracy than, say, 30\%, 
because most quantities entering the global fit of the unitarity triangle 
suffer from sizable hadronic uncertainties. It should also be stressed that 
the accuracy of the determination of the CKM parameters decreases notably 
when one assumes that one or several crucial input(s) could be affected by
New Physics contributions. Interestingly, several authors have detected 
possible hints of new physics in the data. For example it has been argued 
in the literature that one starts to see a discrepancy between the measurement 
of $\sin2\beta$ and the region preferred by $|V_{ub}|$ from semileptonic 
decays on  one hand, and $|\varepsilon_K|$ on the other hand~\cite{smtensions,bg}. 
Also the recently improved measurement of the $B\to\tau\nu$ branching
ratio deviates from its indirect CKM fit prediction~\cite{CKMfitter08}.
In addition there are anomalies in the data on  $b\to s$ transitions. 
The latter processes do not involve $\rhobar$ and $ \etabar$ (to a good
accuracy) and therefore directly probe the CKM mechanism. An ongoing debate 
addresses an extra contribution to $b\to s \ov{q} q$, $q=u,d,s$, decay 
amplitudes with a \CP phase different from $\arg(V_{ts}^* V_{tb}^{\phantom{*}})$ 
that can alleviate the pattern of shifts between the measured \CP asymmetries
in these $b\to s$ penguin modes and the Standard Model predictions 
(see e.g. \cite{cppeng}).    

However, the first place to look for new physics in $b\to s$
transitions is \bbms, where new physics can be parameterised in terms
of just two parameters in a model-independent way, as we will discuss
in great detail below.  A combined analysis of several observables has
pointed at the end of 2006 at the possibility of a new-physics
contribution with a \CP phase different from that of the
Standard-Model box diagram \cite{ln}.  Models of supersymmetric grand
unification can naturally accommodate new contributions to $b \to s$
transitions \cite{cmm}: right-handed quarks reside in the same
quintuplets of SU(5) as left-handed neutrinos, so that the large
atmospheric neutrino mixing angle could well affect squark-gluino
mediated $b\to s$ transitions.  At the same time the GUT models of
Refs.~\cite{cmm} do not induce too dangerous contributions to the
well-measured rare decay $B\to X_s \gamma$.  \bbms\ has been further
investigated in other supersymmetric scenarios with \cite{othergut}
and without \cite{SUSY,bsltb} GUT boundary conditions, in unparticle
physics scenarios in Ref.~\cite{unparticle}, in multi-Higgs-doublet
models \cite{MoreHiggsDoubletts}, in models with extra gauge bosons
$Z'$ \cite{Zprime}, warped extra dimensions
\cite{WarpedExtraDimensions}, left-right symmetry \cite{LRmodels},
anomalous tWb-couplings \cite{AnomaloustWbcouplings}, additional quark
families \cite{fourthfamily} or an additional singlet quark
\cite{AdditionalsingletQuark}, and in a little-Higgs model
\cite{dmphenburas}.  On the experimental side, the understanding of
$b\to s$ transitions has made a tremendous progress in the past
years. The \TeVatron experiments have discovered and precisely
quantified \bbms\ oscillations \cite{dmsexp,dmsexpvalue} whose
frequency is in good agreement with the SM prediction, and presented
first determinations of the associated \CP-violating phase from tagged
analyses of $B_s\to \jpsi \phi$
decays~\cite{taggedphaseCDF,taggedphaseD0,taggedphaseCDF_2,taggedphaseCDF_3,taggedphaseD0_2}.
Recently, possible new physics in the \CP\ phase of the
\bbms\ amplitude has received new attention: The D\O\ collaboration
has reported a measurement of the dimuon charge asymmetry which
disagrees with the SM prediction by 3.2 standard deviations
\cite{dimuon_evidence_d0}. The CP asymmetry in semileptonic or, more
generally, any flavour-specific decays, involves the \bbms\ phase just
as $B_s\to \jpsi \phi$, so that both pieces of experimental
information can be combined to constrain this phase.  The new
measurement of the dimuon charge asymmetry has already triggerd
considerable theoretical interest.  Besides predictions for the
\CP\ phase of \bbms\ in specific models, as quoted above, also
model-independent analyses of new physics effects have appeared
\cite{paperafterD0}. Due to the large size of the dimuon asymmetry it
was also investigated whether sizeable new physics contributions to
the decay of $B_s$ mesons are possible. This alternative is however
strongly constrained by the lifetime ratios of $B$-mesons (see
e.g. \cite{lifetimes}) as well as the semileptonic branching ratios
and the the average number of charm quarks per b-decays (see
e.g. \cite{nc}).  \\ In this paper we analyse generic scenarios of New
Physics which are compatible (at different levels) with the
experimental picture sketched above. We set up our notation and define
our theoretical framework in Sect.~\ref{sec:scene}, the relevant
updated experimental and theoretical inputs to our global analysis are
presented in Sect.~\ref{ssec:inputs}.  In Sect.~\ref{ssec:SMfit} we
first present the current status of the Standard Model fit. In
Sect.~\ref{ssec:bdbs} we perform a fit in which we allow for New Physics
in the \bbmd\ and the \bbms\ system and we project the results onto
the New Physics parameters that describe the \bbmd\ and the
\bbms\ system. Sects.~\ref{ssec:mfv1} and \ref{ssec:mfv2} are
dedicated to two MFV scenarios with correlated effects in all
meson--antimeson mixing amplitudes. Finally we conclude and list a few
perspectives {\rd for} the close future.
