
\subsection*{$B$ Physics}
%\section*{Comparison between Super$B$ and the KEKB upgrade}
\label{sec:B:UKEKB}
\vskip-8pt
% {\bf  TIM IT IS FOR YOU... MARCO CAN ADD A PLOT IN SUSY FOR delta 1-3} \\

%We must emphasise that the KEKB upgrade plan (to a peak
%instantaneous luminosity of $2 \times 10^{35}$) cannot properly be called a Super
%Flavour Factory. That title should be reserved for a collier that can accumulate
%the data samples necessary for a precision study of flavor in the LHC era.
%We expect that our colleagues who are the proponents of the KEKB upgrade, who
%have for many years been promoting an upgrade to a higher luminosity, will
%agree on this.

%Secondly, we recall that a comparison must take into account not only the
%available statistics (luminosity), but that the low backgrounds and improved
%hermeticity (largely due to the smaller beam energy asymmetry) of \superb\
%provide a significant enhancement for many analyses (especially recoil
%analyses) that are crucial to the physics case of \superb.

$B$ physics remains a primary objective of \superb. With \babar\ and Belle having clearly established the ability of the CKM phase to account for \CP-violating asymmetries in tree-level $b \rightarrow c {\bar c} s$ decays, the focus shifts to the study of very rare processes. With a SUSY mass scale below 1 TeV, New Physics effects in \CP-violating asymmetries, in branching fractions and kinematic distributions of penguin-dominated decays and in leptonic decays can indeed be seen, in the five-year \superb\ data sample. It is highly unlikely that these effects can be studied with the SuperKEKB sample.

\begin{table}[!htb]

\caption{\label{tab:ukekb-comp}
    Comparison of current experimental sensitivities with those expected
    at the upgraded KEKB ($10 \ {\rm ab}^{-1}$)
    and at \superb\  ($75 \ {\rm  ab}^{-1}$).
    Only a small selection of observables are shown.
    Quoted sensitivities are relative uncertainties if given as a percentage,
    and absolute uncertainties otherwise. An ``X'' means that the quantity is not measured at this integrated
    luminosity.
    For more details, see text and Refs.~\cite{Bona:2007qt,Browder:2007gg,Browder:2008em}.
    }
  \begin{tabular}{lccc}
    \hline\hline
    Mode & \multicolumn{3}{c}{Sensitivity} \\
    & Current & $10 \ {\rm ab}^{-1}$ &$75 \ {\rm
      ab}^{-1}$  \\
    \hline
    ${\cal B}(B \to X_s \gamma)$ & 7\% & 5\% & 3\% \\
    $A_{\CP}(B \to X_s \gamma)$ & 0.037 & 0.01 & 0.004--0.005 \\
    ${\cal B}(B^+ \to \tau^+ \nu)$ & 30\% & 10\% & 3--4\% \\
    ${\cal B}(B^+ \to \mu^+ \nu)$ & X & 20\% & 5--6\% \\
    ${\cal B}(B \to X_s l^+l^-)$ & 23\% & 15\% & 4--6\% \\
    $A_{{\rm FB}}(B \to X_s l^+l^-)_{s_0}$ & X & 30\% & 4--6\% \\
    ${\cal B}(B \to K \nu \overline{\nu})$ & X & X & 16--20\% \\
    $S(\KS \pi^0 \gamma)$ & 0.24 & 0.08 & 0.02--0.03 \\
    \hline\hline
  \end{tabular}
\end{table}

%Due to the high power consumption, there is a question over how many months
%per year KEKB can afford to run. However, we understand that the estimated
%total integrated luminosity should be taken to be $10 \ {\rm ab}^{-1}$.  We do
%not currently have an estimate of sensitivity with that data sample from the
%KEKB upgrade proponents, and therefore we must rely on our own estimates.  We
%also note that $2 \times 10^{35}$ is the maximum peak luminosity  specified for KEKB in the KEK Roadmap, whereas
%$10^{36}$ is the baseline luminosity for \superb.


Table~\ref{tab:ukekb-comp} shows a quantitative comparison of the two
proposals for
some of the important observables that will be
measured at \superb, including all the so-called ``golden processes'' of
Table~\ref{tab:golden} (see the following section).
We list below some additional comments on the entries of
Table~\ref{tab:ukekb-comp}

\begin{itemize}
\item
  The measurements of ${\cal B}(B \to X_s \gamma)$ and \hbox{${\cal B}(B^+ \to \ell^+ \nu)$ }
  are particularly important in minimal flavor violation scenarios.
  It is crucial to be able to search for small deviations from the Standard Model value.
  Therefore the improvement is sensitivity provided by \superb is highly
  significant (see Figure~\ref{fig:btaunu}).
\item
The statistics of the upgraded KEKB is not sufficient to take advantage of
  the theoretical cleanliness of several inclusive observables, such as
  the zero-crossing of the forward-backward asymmetry in $b \to s\ell^+\ell^-$.
  Results with $10 \ {\rm ab}^{-1}$ would not match the precision from the
  exclusive mode $B \to K^* \mu^+\mu^-$, which will be measured by LHC$b$.
  Furthermore, these exclusive channel measurements will be limited by hadronic uncertainties.
  \superb\  can provide a much more precise and theoretically clean measurement using inclusive modes.
\item
  Several interesting rare decay modes, such as \hbox{$B \to K \nu \bar{\nu}$,}
  cannot be observed with the statistics of the upgraded KEKB,
  unless dramatic and unexpected New Physics enhancements are present.
  Preliminary studies are underway on several other channels in this category, such as $B \to \gamma\gamma$ and $B \to$ invisible
  decays which are sensitive to New Physics models with extra-dimensions.
\item
  Another area for comparison is the phenomenological analysis
  within the MSSM with generic mass insertion discussed in the \superb\ CDR.
  Fig. ~\ref{fig:d13} shows how well the $(\delta_{13})_{LL}$ can be
  reconstructed at \superb\ and with the KEKB upgrade. Improvements in lattice QCD
  performance, as discussed in the Appendix of the CDR, are assumed in both
  cases. The remarkable difference in sensitivity stems mainly from the different performance
  in measuring the CKM parameters $\bar\rho$ and $\bar\eta$.

\end{itemize}

\begin{figure}[!htb]
  \begin{center}
    \hspace{-0.1cm}\includegraphics[width=0.25\textwidth]{d13_ll_all_kek.eps}
    \hspace{-0.4cm}\includegraphics[width=0.25\textwidth]
{d13_ll_all_superb.eps}
    \caption{\label{fig:d13}
     Determination of the SUSY mass-insertion parameter $(\delta_{13})_{LL}$
     at the upgraded KEKB (left) and \superb\  (right).
    }
  \end{center}
\end{figure}

% The figure below shows a comparison of the exclusion plot in the
% $m(H^+)$--$\tan\beta$ plane coming from a measurement of ${\cal B}(B \to \tau
% \nu)$ with the different data samples (assuming that the result is consistent
% with the SM).  Note that this plot was specifically requested by the IRC
% during the meeting in November.  Another plot that will be prepared is the
% MSSM exclusion plot for various different luminosities (but with naive scaling
% of sensitivities).  A comparison of the sensitivities to NP at the (``worst
% case'') mSUGRA snowmass point (see below) may also be interesting.  However,
% we believe that a qualitative comparison of the physics reach may be more
% useful.

% The most obvious channel to demonstrate a dramatic improvement in the physics
% reach of Super$B$ compared to the KEKB upgrade is for lepton flavor violating
% $\tau$ decays ({\it e.g.} $\tau \to \mu \gamma$), but there are also several in
% $B$ physics.

% In the following we discuss very briefly few example of channels Super Flavour
% Factory luminosity are necessary  and could possibly be observed with data
% samples in excess of $10 \ {\rm ab}^{-1}$. Preliminary studies are just
% started.

% \begin{itemize}

% \item $B \to K \nu \bar{\nu}$ \\



% \item $B \to$ invisible \\
%   \indent in the SM, $B \to \nu \bar{\nu} \gamma$ has a branching fraction of
%   ${\cal O}(10^{-9})$ (${\cal B}(B \to \nu \bar{\nu})$ being negligibly
%   small); NP from {\it e.g.} models with extra-dimensions and light dark matter
%   permit ${\cal B}$ up to $10^{-5}$; the current limit is ${\cal O}(10^{-4})$
%   -- we will ask groups working on models with extra-dimensions to take look
%   at this channel

% \item $B \to l \nu$ \\


%   \indent discussed in the talks of A.~Bevan and S.~Robertson.  Note that $B
%   \to \mu \nu$ is experimentally cleaner and will eventually overtake $B \to
%   \tau \nu$ (which will become systematics limited) in terms of sensitivity to
%   small NP effects.  Furthermore, this channel allows a NP-sensitive
%   universality check from the ratio ${\cal B}(B \to \tau \nu)/{\cal B}(B \to
%   \mu \nu)$.

% \item ${\cal B}(b \to s \gamma)$ \\
%   \indent though this is likely systematics and/or theory limited

% \item ${\cal B}(b \to s l^+l^-)$ \\
%   \indent possibly theory limited

% \item zero crossing in the inclusive $b \to s l^+l^-$ forward-backward asymmetry

% \item we are also alert to other possibilities, including other rare channels
%   which are not necessarily discussed in the CDR.  We do not want to make an
%   excessively long list, but there are plenty of things to think about, {\it
%     e.g.} $B \to \gamma \gamma$, $B \to 4$leptons, ... Even $B_d \to \mu\mu$
%   could possibly be observed with data samples in excess of $100 \ {\rm
%     ab}^{-1}$.
% \end{itemize}

% % To conclude on this discussion, we recall that with a very high luminosity
% % Super Flavour Factory, such as Super$B$, there is a ``no lose theorem.''
% % For this to be the case, all observables must be measured as precisely as
% % possible.  We do not believe that this is true for the KEKB upgrade.
