
\section*{Comparison between Super$B$ and the KEKB upgrade}
\label{sec:B:UKEKB}

% {\bf  TIM IT IS FOR YOU... MARCO CAN ADD A PLOT IN SUSY FOR delta 1-3} \\

First of all, we must emphasize that the KEKB upgrade plan (to a peak
instantaneous luminosity of $2 \times 10^{35}$) cannot be called a Super
Flavour Factory. That title must be reserved for a machine 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 Super$B$
provide a significant enhancement for many analyses (especially recoil
analyses) that are crucial to the physics case of Super$B$.

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 a kind of maximum for KEKB, whereas
$10^{36}$ is a kind of baseline for Super$B$.

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

Table~\ref{tab:ukekb-comp} shows a quantitative comparison of the two
proposals.
This table contains only a small subset of the observables that will be
measured at Super$B$, including all the so-called ``golden processes'' of
Table~\ref{tab:golden}.
Here we make some additional comments on the entries of
Table~\ref{tab:ukekb-comp}
\begin{itemize}
\item
  The measurements of BR$(B \to X_s \gamma)$ and BR$(B^+ \to \ell^+ \nu)$
  are particularly important in the MFV scenarios described in
  Section~\ref{sec:B:pheno}.
  It is crucial to be able to search for small deviations from the SM value.
  Therefore the improvement is sensitivity provided by Super$B$ 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 LHCb,
  but will be limited by hadronic uncertainties.
  Super$B$ can provide a much more precise and theoretically clean measurement.
\item
  Several interesting rare decay modes, such as $B \to K \nu \bar{\nu}$,
  cannot be observed with the statistics of the upgraded KEKB
  (unless dramatic and unexpected NP enhancements are present).
  Preliminary studies are just starting on several other channels that fall
  into this category.  Examples are $B \to \gamma\gamma$ and $B \to$ invisible
  type decays, which are sensitive to NP models with extra-dimensions.
\item
  Another playground for comparison is the phenomenological analysis
  within the MSSM with generic mass insertion discussed in the CDR.
  Fig. ~\ref{fig:d13} shows how well the $(\delta_{13})_{LL}$ can be
  reconstructed at Super$B$ and with the KEK-$B$ upgrade. Lattice QCD
  performances as discussed in the Appendix of the CDR are assumed in both
  cases. The remarkable difference mainly stems from the different performances
  in measuring the CKM parameters $\bar\rho$ and $\bar\eta$.

\begin{figure}[!htb]
  \begin{center}
    \hspace{-0.7cm}\includegraphics[width=0.22\textwidth]{d13_ll_all_kek.eps}
    \hspace{-0.5cm}\includegraphics[width=0.22\textwidth]
{d13_ll_all_superb.eps}
    \caption{
     Determination of the SUSY mass-insertion parameter $(\delta_{13})_{LL}$
     at the upgraded KEKB (left) and SuperB (right).
    }
    \label{fig:d13}
  \end{center}
\end{figure}


\end{itemize}

% 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.
