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\section{Motivation and status (Dominik St\"ockinger, TU Dresden)}

Magnetic moments in general and the muon anomalous magnetic moment
$a_\mu=(g_\mu-2)/2$ in particular are clean and sensitive probes of
fundamental particles and interactions. After the Brookhaven
measurement, $a_\mu$ is sensitive to all interactions of the Standard
Model of particle physics. The observed deviation from the Standard
Model theory prediction might be due to physics beyond the
Standard Model (BSM), but at the same time it constrains
BSM scenarios. A new generation of $a_\mu$ measurements will further
increase the experimental accuracy and the sensitivity to SM and BSM
physics. The goal of the workshop is to initiate and contribute to
progress on the SM theory prediction of $a_\mu$, and in the following
paragraphs we will give a reminder of the current status and the
motivation for further improvement.

Huge
progress has been achieved on the SM theory prediction of $a_\mu$ in the past years. We highlight the 5-loop
QED computation \cite{Kinoshita2012}, the inclusion of high-precision
$e^+e^-$-data into the hadronic vacuum polarization contributions
\cite{Davier,HMNT,Benayoun:2012wc}, the resolution of the
$\tau$-vs.-$e^+e^-$-puzzle \cite{Benayoun:2012wc,JegerlehnerSzafron},
and the exact evaluation of the electroweak contributions after the
Higgs boson mass measurement \cite{Gnendiger:2013pva}.
As a result of this progress, the SM theory prediction has a smaller
uncertainty than the Brookhaven measurement, but the precision of the
hadronic 
contributions needs to be further improved to match the new
experiments.

One new $a_\mu$ measurement will be carried out at Fermilab \cite{Carey:2009zzb}. It
combines the technique of the Brookhaven experiment with specific
advantages present at Fermilab. Datataking is
expected to start in 2017. A second promising experiment is planned at
J-PARC. It would make use of an entirely complementary strategy and
therefore provide important cross-checks.
Both experiments promise to reduce the uncertainty
by a factor four, down to a level less than half as large as the
current SM theory uncertainties coming from the hadronic vacuum
polarization and hadronic light-by-light contributions. 

Measuring and computing the SM prediction for $a_\mu$ as precisely as
possible is very important also to study hypothetical new physics
scenarios. This statement is independent of whether the current
deviation will increase or decrease.
The importance of $a_\mu$ as a constraint on BSM physics 
is due to two facts. First, different types of BSM physics can
contribute to $a_\mu$ in very different amounts, so $a_\mu$
constitutes a meaningful benchmark  and discriminator between BSM
models. Second, the 
constraints from $a_\mu$ on BSM models are different and
complementary to constraints from other observables from the
low-energy and high-energy frontier.

Both aspects can be illustrated within the framework of supersymmetric
models, as shown in Figure \ref{fig:susyplots}. The red points in the
Figure show that the $a_\mu$-predictions of various benchmark
scenarios proposed in the literature scatter widely. Any future
measurement of $a_\mu$ will rule out many of these points,
illustrating the discriminating power of $a_\mu$. The green points in
the Figure illustrate the complementarity of $a_\mu$. In the
hypothetical scenario considered in \cite{Adam:2010uz}, the LHC can
find most supersymmetric particles and measure their masses, and yet
there are several very different choices of supersymmetric parameters
which give an equally good fit to LHC data. The $a_\mu$-predictions of
these ``degenerate solutions'' however, differ, hence allowing to lift
the LHC degeneracies by taking into account $a_\mu$.

\begin{figure}
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\caption{\label{fig:susyplots} SUSY contributions to $a_\mu$ for
the SPS and other benchmark points (red), and for the ``degenerate solutions''
from Ref.\ \cite{Adam:2010uz}. The yellow and blue bands are the $\pm 1~\sigma$ errors
from the Brookhaven and the planned Fermilab measurements. } 
\end{figure} 
%%%%%%%%%%%%%%%%% DS references %%%%%%%%%%%%%
\begin{thebibliography}{99}

  % \cite{Aoyama:2012wk}
\bibitem{Kinoshita2012}
  T.~Aoyama, M.~Hayakawa, T.~Kinoshita and M.~Nio,
  % ``Complete Tenth-Order QED Contribution to the Muon g-2,''
  Phys.\ Rev.\ Lett.\  {\bf 109} (2012) 111808
  [arXiv:1205.5370 [hep-ph]].
  %% CITATION = ARXIV:1205.5370;%%
  
  % \cite{Davier:2010nc}
\bibitem{Davier}
  M.~Davier, A.~Hoecker, B.~Malaescu and Z.~Zhang,
  % ``Reevaluation of the Hadronic Contributions to the Muon g-2 and to alpha(MZ),''
  Eur.\ Phys.\ J.\ C {\bf 71} (2011) 1515
  [Erratum-ibid.\ C {\bf 72} (2012) 1874]
  [arXiv:1010.4180 [hep-ph]].
  
  % \cite{Hagiwara:2011af}
\bibitem{HMNT}
  K.~Hagiwara, R.~Liao, A.~D.~Martin, D.~Nomura and T.~Teubner,
  % ``(g-2)_mu and alpha(M_Z^2) re-evaluated using new precise data,''
  J.\ Phys.\ G G {\bf 38} (2011) 085003
  [arXiv:1105.3149 [hep-ph]].
  %% CITATION = ARXIV:1105.3149;%%

  % \cite{Benayoun:2012wc}
\bibitem{Benayoun:2012wc}
  M.~Benayoun, P.~David, L.~DelBuono and F.~Jegerlehner,
  % ``An Update of the HLS Estimate of the Muon g-2,''
  Eur.\ Phys.\ J.\ C {\bf 73} (2013) 2453
  [arXiv:1210.7184 [hep-ph]].
  %% CITATION = ARXIV:1210.7184;%%
  % \cite{Jegerlehner:2011ti}
\bibitem{JegerlehnerSzafron}
  F.~Jegerlehner and R.~Szafron,
  % ``$\rho^0 - \gamma$ mixing in the neutral channel pion form factor $F_{\pi}^{e}$ and its role in comparing $e^+ e^-$ with $\tau$ spectral functions,''
  Eur.\ Phys.\ J.\ C {\bf 71} (2011) 1632
  [arXiv:1101.2872 [hep-ph]].
  % \cite{Gnendiger:2013pva}
\bibitem{Gnendiger:2013pva}
  C.~Gnendiger, D.~St{\"o}ckinger and H.~St{\"o}ckinger-Kim,
  % ``The electroweak contributions to (g-2)_\mu\ after the Higgs boson mass measurement,''
  Phys.\ Rev.\ D {\bf 88} (2013) 053005
  [arXiv:1306.5546 [hep-ph]].
  %% CITATION = ARXIV:1306.5546;%%  

  % \cite{Carey:2009zzb}
\bibitem{Carey:2009zzb}
  R.~M.~Carey, K.~R.~Lynch, J.~P.~Miller, B.~L.~Roberts, W.~M.~Morse, Y.~K.~Semertzides, V.~P.~Druzhinin and B.~I.~Khazin {\it et al.},
  % ``The New (g-2) Experiment: A proposal to measure the muon anomalous magnetic moment to +-0.14 ppm precision,''
  FERMILAB-PROPOSAL-0989.
  %% CITATION = FERMILAB-PROPOSAL-0989;%%

\bibitem{Adam:2010uz}
  C.~Adam, J.~-L.~Kneur, R.~Lafaye, T.~Plehn, M.~Rauch and D.~Zerwas,
  %``Measuring Unification,''
  Eur.\ Phys.\ J.\ C {\bf 71} (2011) 1520
  [arXiv:1007.2190 [hep-ph]].
  %%CITATION = ARXIV:1007.2190;%%
\end{thebibliography}
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