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{\centerline{\rule[0in]{0.9\columnwidth}{2pt}}
\vspace {-0.7cm}
\part*{\centerline{Spectroscopy and the}}
\vspace {-1cm}
\part*{\centerline{Decays of Quarkonia}}
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%\part*{\centerline{Spectroscopy and the}}
%\vspace {-1cm}
%\part*{\centerline{Decays of Quarkonia}}

%\thispagestyle{fancy}

%\section*{Introduction}

\bigskip
\smallskip

Although the Standard Model is well-established,
QCD, the fundamental theory of strong interactions, provides a quantitative comprehension only of phenomena
at very high energy scales, where perturbation theory is effective due
to asymptotic freedom.
The description of hadron dynamics below the QCD dimensional transmutation scale
is therefore far from being under full theoretical control.

Systems that include heavy quark-antiquark pairs
(quarkonia) are a unique and, in fact, ideal laboratory for probing both the high
energy regimes of QCD, where an expansion in terms of the coupling
constant is possible, and the low energy regimes, where
nonperturbative effects dominate.
For this reason, quarkonia have been studied for decades in great detail.
The detailed level of understanding of the quarkonia mass spectra
is such that a particle mimicking quarkonium properties, but not fitting any quarkonium level,
is most likely to be considered to be of a different nature.

In particular, in the past few years the $B$ Factories and the Tevatron have provided evidence for states that
do not admit the conventional mesonic interpretation and that instead could be
made of a larger number of constituents (see Sec.~\ref{sec:data}). While
this possibility has been considered since the
beginning of the quark model~\cite{ GellMann:1964nj}, the actual identification of such states
would represent a major revolution in our understanding of elementary particles. It would also imply the existence
of a large number of additional states that have not yet been observed.

Finally, the study of the strong bound states could be of relevance to
understanding the Higgs boson, if it turns out to be itself
a bound state, as predicted by several technicolor models (with or without extra dimensions)~\cite{techni}.

The most likely possible states beyond the mesons and the
baryons are:
%\footnote{A comprehensive theoretical review can be found
%in Ref.~\cite{Brambilla:2004wf}}:

\begin{itemize}

\item {\bf hybrids:} bound states of a quark-antiquark pair and a number of
constituent gluons. The lowest-lying state is expected to have quantum numbers
$J^{PC}=0^{+-}$. Since a quarkonium state cannot have
these quantum numbers (see below), this a unique signature for
hybrids. An additional signature is the preference for a hybrid to
decay into quarkonium and a state that can be produced by the excited
gluons (\eg, $\pi^+\pi^-$ pairs); see \eg,~Ref.~\cite{ibridi}.
\item {\bf molecules:} bound states of two mesons, usually represented as
$[Q\bar{q}][q^{\prime}\bar{Q}]$, where $Q$ is the heavy quark. The
system would be stable if the binding energy were to set the mass of the
states below the sum of the two meson masses.
While this could be the case for when $Q=b$, this does not apply for
$Q=c$, the case for which most of the current experimental data exist. In this case,
the two mesons can be bound by pion exchange. This means that only
states decaying strongly into pions can bind with other mesons (\eg,
there could be $D^*D$ states), but
that the bound state could decay into its constituents~\cite{others}.
\item {\bf tetraquarks:} a bound quark pair, neutralizing its color with a bound
antiquark pair, usually represented as $[Qq][\bar{q^{\prime}}\bar{Q}]$. A full
nonet of states is predicted for each spin-parity, \ie, a large number
of states are expected. There is no need for these states to be close to
any threshold~\cite{mppr}.

\end{itemize}

In addition, before the panorama of states is fully clarified, there is always the
lurking possibility that some of the observed states are misinterpretations of
threshold effects: a given amplitude might be enhanced when new hadronic final
 states become energetically possible, even in the absence of resonances.
% Since the tetraquark model
%is the most robust and complete one in understanding the recent findings,
%we will show how the SuperBF data could verify or falsify it and
%distinguish it with
%respect to the other ones.
%In case the correct model proves to be a different one, we believe the
%arguments in this document
%will hold anyhow, since the modes to be explored and the required
%statistics for them cannot be significantly different.

While there are now several good experimental candidates for unconventional states,
the overall picture is not complete and needs confirmation, as well as
discrimination between the alternative explanations.
A much larger dataset than is currently available is needed, at several energies, to pursue this program; this capability is uniquely within the reach  of \superb.

Finally, bottomonium decays also allow direct searches for physics beyond the Standard Model
in regions of the parameters space that have not been reached by LEP.
% In particular running at the
%center of mass of $Y(3S)$ for a relatively little portion of the SuperBF
%program would have a large
%sensitivity to a possible light Higgs boson, expected in extensions of
%the MSSM~\cite{Dermisek:2006py}, via
%$Y(nS)\to H,A+\gamma$ decays, and to possible dark matter candidates,
%such as neutralinos, in $Y(nS)\to \chi_0\chi_0\to \rm{invisible}$ decays.



\section{Light meson spectroscopy}%


 The problem of the interpretation of the light scalar mesons, namely
$f_0, a_0,\kappa,\sigma$, is one of the oldest problems in hadronic physics
%, since the times of the paper by Gell-Mann and L\'evy on the formulation of the Linear-$\sigma$-Model
\cite{gell}.
For many years the question of the existence of the $\sigma$ meson as a resonance in $\pi\pi$ scattering has been debated~\cite{resu};  only recently has a thorough analysis of $\pi\pi$ scattering amplitudes shown that the $\sigma(500)$ and $\kappa(800)$ can be considered to be
proper resonances~\cite{Caprini}.

Reconsideration of the $\sigma$ was triggered by the E791 analysis of $D\to 3\pi$ data~\cite{e791}; a number of papers have commented on those results, \eg,~Ref.~\cite{torni}.  The role of the scalar mesons in several exclusive $B$ decays could be rather relevant: for example, in the perspective of a high precision measurement of the $\alpha$ angle at the SuperB factory, the hadronic contributions, like the one of the isoscalar $\sigma$ in $B\to rho \pi$, must be properly controlled~\cite{io}.
Also diverse studies on light and heavy scalar mesons could be
performed analyzing the Dalitz plots of exclusive decays like $B\to KKK$ and $B\to K \pi\pi$. In this respect, having sufficient statistics to clearly 
assess the presence of a scalar $\kappa (800)$ resonance, would certainly be a major result for hadron spectroscopy.
%The presence of a $\sigma$ resonance has also turned out to have a potentially serious impact on the high precision extraction of the CKM angle $\alpha$

Beyond the ``taxonomic'' interest in the classification of scalar mesons, the idea that these mesons could play a key role in our understanding of
aspects of non-perturbative QCD has been raised; see, for example, the interesting paper, Ref.~\cite{gribov}.

In what follows we would like to underscore the latter point by observing that:

\begin{itemize}%

\item Light scalar mesons are most likely the lightest particles with an {\it exotic} structure, \ie, they cannot be classified as $q\bar q$ mesons.
\item Their dynamics is tightly connected with instanton physics.  Recent discussions have shown that instanton effects facilitate the creation of a consistent model for the description of light scalar meson dynamics, under the hypothesis
that these particles are diquark-antidiquark mesons.%

\end{itemize}%


Therefore, new modes of aggregation of quark matter could be established by the experimental/theoretical investigation of these particles, further expanding the role of instantons in hadronic physics.

The idea of four-quark mesons dates back to the pioneering papers by Jaffe~\cite{jaffe}, while the discussion of exotic mesons and hadrons in terms of diquarks was introduced in Ref.~\cite{wilc} and then extended in Ref.~\cite{noim} to the scalar meson sector.

In the following, we will assume that the scalar mesons below $1$~GeV are indeed  bound states of  a spin~0 diquark and an anti-diquark (we will often call this a tetraquark).  A spin~0 diquark field can be written as:


\begin{equation}
\qq_{i\alpha}= \epsilon_{ijk}\epsilon_{\alpha\beta\gamma} \bar q^{j\beta}_C\gamma_5 q^{k\gamma},%
\label{defdq}
\end{equation}

%&&&&&&&&&&&&&&&&&
%\end{document}
%&&&&&&&&&&&&&&&&&

\par\noindent
where Latin indices label flavor and Greek letters label color.  The color is saturated, as in a standard $q\bar q$ meson: $\qq^\alpha {\bar \qq}_\alpha$. Therefore, since a spin zero diquark is in a ${\bf \bar 3}$-flavor representation,  nonets of $\qq\bar \qq$ states are allowed (crypto-exotic states). The sub-GeV scalar mesons most likely represent the lowest tetraquark nonet.

The $\qq\bar \qq$ model of light-scalars is very effective at explaining the most striking feature of these particles, namely  their inverted pattern, with respect to that of ordinary $q\bar q$ mesons, in the  mass-versus-$I_3$ diagram~\cite{jaffe}, as shown in Fig.~\ref{fig:i3}.

\begin{figure}[!htb]
%\centering
%\hspace{-2.0truecm}
\includegraphics[width=40mm]{Spectroscopy/vectors.eps}
\includegraphics[width=40mm]{Spectroscopy/lscalars.eps}
\caption{\label{fig:i3}
Vector mesons ($q\bar q$ states) and the sub-GeV scalar mesons in the $I_3-m$ plane.}
\end{figure}

Such a pattern is not explained in a $q\bar q$ model,
in which, for example, the $f_0(980)$ would be an $s\bar s$ state~\cite{torni} while the
$I=1$, $a_0(980)$, would be a $u\bar u+d\bar d$ state. If this were the case, the degeneracy of the two particles appears rather unnatural.

Besides a correct description of the mass-$I_3$ pattern, the tetraquark model offers the possibility of explaining the decay rates of scalars at a level never reached by standard $q\bar q$ descriptions.
The effective decay Lagrangian into two pseudoscalar mesons, \eg, $\sigma \to \pi\pi$, is written as:
\begin{equation}
{\cal L}_{\rm exch.}=c_f S^i_j  \epsilon^{j t u}\epsilon_{i r s}  \partial_\mu \Pi^r_t  \partial^\mu \Pi^s_u,
\label{exchange}
\end{equation}
where $i,j$ are the flavor labels of $\qq^i$ and $\bar\qq^j$, while $r,s,t,u$ are the flavor labels of the quarks $\bar q^t,\bar q^u$ and  $ q^r, q^s$. $c_f$ is the effective coupling weighting this interaction term and ${S},{\Pi}$ are the scalar and pseudoscalar matrices. This Lagrangian describes the quark exchange amplitude for  the quarks to tunnel out of their diquark shells to form ordinary mesons~\cite{noim}. Such a mechanism is an alternative to the color string breaking  $\qq\ \gluon q\bar q\gluon\ \bar \qq\to B\bar B$, {\it i.e.}, a baryon-anti-baryon decay, which is phase-space forbidden to sub-GeV scalar mesons.

The main problem with eq.~(\ref{exchange}) is that it is not able to describe the decay $f_0\to \pi\pi$, since $f_0=( \qq^2{\bar\qq}^2+\qq^1\bar \qq^1)/\sqrt{2}$, being $1,2,3$ the $u,d,s$ flavors so that, see equation~(\ref{defdq}),  $\qq^1=[ds]$ and $\qq^2=[su]$. An annihilation diagram would be needed to replace the $s$ quarks, inducing a small rate that does not match the observation.

Alternatively, one can suppose  the mixing between the two isoscalars $f_0$ and $\sigma$ is at work, the $\sigma$ component ($\qq^3{\bar\qq}^3$) providing the $\pi\pi$ decay. However, as discussed in~\cite{winprog}, such mixing is expected to be too small, $<5^\circ$, to account for
the structure of the inverted mass pattern (a precise determination of the $\kappa$ mass would be crucial to fix this point).

A solution that improves the overall  agreement with data  of all light scalar mesons decay rates  has been found~\cite{winprog}. In low energy QCD, instantons  generate a quark interaction term that can be written as:
\begin{equation}
{\cal L}_I= \det (\bar q_L^i q_R^j),
\label{six}
\end{equation}
$i,j=1,2,3$ being flavor indices. Such a left-right mixing interaction is
screened at high energies, the instanton action scaling as $S\sim
\exp(-8\pi^2/g^2)$.  In addition to  the quark-exchange diagrams, described at
the effective theory level by the Lagrangian of eq.~(\ref{exchange}), (see
Fig.~\ref{fig:qdiags}~(a)), there are also contributions such as those in
Fig.~\ref{fig:qdiags}~(b)~\cite{footnote1}.

\begin{figure}[!htb]
%\centering
%\hspace{-2.0truecm}
\includegraphics[width=80mm]{Spectroscopy/decays3.eps}
\caption{\label{fig:qdiags}
Decay of a tetraquark scalar meson $S$ in two $q \bar{q}$ mesons $M_1 M_2$: (a) quark rearrangement (b) instanton-induced process.}
\end{figure}

The quark-level instanton interaction, Fig.~\ref{fig:qdiags}(b), reflects into an effective meson interaction of the kind:
\begin{equation}
{\cal L}_I=c_I {\rm Tr} ({\bf S \times (\partial \Pi)^2} ),
\label{einst}
\end{equation}
$c_I$ being an effective coupling as $c_f$ in~(\ref{exchange}). Assuming that the low energy dynamics of light scalar mesons is described by:
\begin{equation}
{\cal L}={\cal L}_{\rm exch.}+{\cal L}_{I},
\end{equation}
one can reach a remarkably satisfying description of light meson decays~\cite{winprog}. Namely:
\begin{itemize}
\item  Such a good description of decays is possible {\it only} if the assumption is made that sub-GeV light scalars are
diquark-antidiquark mesons (see Table~\ref{tab:res}). In the $q\bar  q$ hypothesis, the agreement of $a_0\to\pi^0\eta$ with data appears very poor.
\item The inverted mass spectrum of super-GeV scalar mesons can be explained by assuming that they form
the lightest $q\bar q$ scalar multiplet, deformed in the mass-$I_3$ pattern by mixing with the lowest exotic multiplet
of sub-GeV scalar mesons (see Fig.~\ref{fig:i3h}~\cite{winprog}).
\end{itemize}

\begin{figure}[!htb]
%\centering
%\hspace{-2.0truecm}
\includegraphics[width=50mm]{Spectroscopy/hscalars.eps}
\caption{\label{fig:i3h}
Super-GeV scalar mesons in the $I_3-m$ plane.}
\end{figure}
One of the isoscalars in the decuplet in Fig.~\ref{fig:i3h} is likely to be the lowest {\it glueball}; there are arguments favoring the $f_0(1500)$ as the most probable glueball candidate.

We quote a table from~\cite{winprog} describing at what level one can fit the decays of the lightest scalar mesons in
a diquark-antidiquark picture:

\begin{table}[!htb]
\begin{center}

\caption{\label{tab:res}
\footnotesize Numerical results, amplitudes in GeV. Second and third columns: results obtained with a decay  Lagrangian including or not including instanton effects, respectively (Labels $I$ and no-$I$ mean that we add or do not add the instanton contribution.).
No $f_0-\sigma$ mixing is assumed in this table. Fourth column: best fit, see text, with instanton effects included. Fifth column: predictions for a $q\bar q$ picture of the light scalars.
The $\eta-\eta^\prime$ singlet-octet mixing angle assumed: $\phi_{_{PS}}=-22^\circ$~\cite{ginop}.
Data for $\sigma$ and $\kappa$ decays are from~\cite{Caprini}, the reported amplitudes correspond to: $\Gamma_{\rm tot}(\sigma) = 272 \pm 6$, $\Gamma_{\rm tot}(\kappa) = 557 \pm 24$.
 }
\begin{tabular}{lccccc}
\hline\hline
Proc. &   \multicolumn{3}{c}{ ${\cal A}_{\rm th}([qq][\bar q \bar q])$} &${\cal A}_{\rm th}(q\bar q)$& ${\cal A}_{\rm expt}$  \\
    & $I$ &  no-$ I$ & best fit & $I$ & \\ \hline
$ \sigma   ( \pi^+\pi^-) $ &
{\rm input}  &   {\rm input}  & 1.7 &
{\rm input}  &$2.27 (0.03)$   \\ \hline
$\kappa^+   (K^0 \pi^+)  $ &   $5.0$ &
5.5 & 3.6 & 4.4&$5.2 (0.1) $   \\  \hline
$f_0  (\pi^+\pi^-) $    &    {\rm input} &{\bf 0}&1.6 &
{\rm input}  &$1.4 (0.6)$  \\
$f_0     (K^+ K^-) $    & $4.8$  & 4.5&3.8&  4.4 &$3.8(1.1)$  \\  \hline
$a_0   (\pi^0 \eta)$    &  $4.5$ & 5.4&3.0& 8.9&$2.8 (0.1)$    \\
$a_0  (K^+ K^-)$        &   $3.4 $  & 3.7&2.4 & 3.0 &$2.16(0.04)$  \\  \hline\hline
\end{tabular}  \\ [2pt]

\end{center}
\end{table}
%One of the reasons why multiquark mesons were expected to be very broad, experimentally unaccessible states is the following.
%In the large number of colors expansion~\cite{thooft} of the
%two-point correlation function $\langle {\cal O}(x){\cal O}(0)\rangle$, four-quark states of the kind $\bar q_\alpha q^\alpha \bar q_\beta q^\beta(={\cal O}(x)) $
%are suppressed, in the sense that they appear as subleading terms.
%The leading term of such a correlation would instead be represented by a disconnected graph: two freely propagating standard mesons - fall apart decay.

%But if we replace quarks with diquarks: $q^\alpha\to\qq^\alpha$, and we treat diquarks as the fundamental building blocks, in place of quarks, there are no disconnected parts and  one evades the $1/N$ difficulty with tetraquarks operators of the form as given above~\cite{cornell}.

A relative of the lowest lying scalar mesons may have been found very
 recently by \babar: the $Y(2175)$, a particle first observed in the decay
 $Y\to \phi f_0(980)$~\cite{y2175}.  This object could be a
 radial excitation of the lowest lying scalar mesons, of the kind
 $\qq^1{\bar \qq}^1+\qq^2{\bar\qq}^2$ and could strikingly manifest all
the three tetraquark decay mechanisms: the instanton ($Y\to
\phi(1020)f_0(980)$), the quark rearrangement ($Y\to KK^*$), and the
string breaking ($Y\to KK^*$) mechanisms. It is to be noted that only the
first decay mode has been observed; there are only hints of the other two.

We tend to exclude the possibility of a $Y(2175)$ built as $\qq^3{\bar \qq}^3$ because, though it would contain four $s$ quarks as the observed final state, it would involve spin ~1 diquarks, because of Fermi statistics. Spin~1 diquarks are thought to be energetically disfavoured, but, worse, they are in the ${\bf 6_f}$ representation, thus requiring a large number of exotic particles: ${\bf 6}\otimes {\bf \bar 6}={\bf 1}\oplus{\bf 8}\oplus{\bf 27}$. The search for other decay mechanisms would be quite crucial to test this hypothesis.

Searches of radially excited partners of the scalar mesons in the high statistics data samples from a SuperB factory, would deeply improve 
the comprehension of the tetraquark picture. To give an example, consider that
predictions of lighter partners of the $Y(2175)$, to be found in ISR,
are at hand. Are the good, spin zero, diquarks the only relevant building blocks, or bad, spin one, diquarks are also 
effective degrees of freedom to describe states at higher mass than the standard scalar nonets?
It is decisive to understand to what extent the actual models for multiquark particles are predictive.


\section{Charmonium}
\label{sec:data}

In the past few years the $B$~Factories have observed several states with clear $c\bar{c}$ content,
which do not behave like standard mesons, and that are therefore an indication of new spectroscopy.

The $X(3872)$ was the first state found that did not easily fit into charmonium spectroscopy.
It was initially observed decaying into $J/\psi\pi^+\pi^-$ with a mass just beyond the open charm
threshold~\cite{Choi:2003ue}. The $\pi^+\pi^-$ invariant mass distribution, the observation of the
$X\to J/\psi\gamma$ and the full angular analysis from CDF~\cite{Abulencia:2006ma} and Belle~\cite{Abe:2005iya}
favor the assignment of $J^{PC}=1^{++}$ for this state, and of $B\to J/\psi\rho$ as its dominant decay.
There are therefore several indications that this is not a charmonium state: the mass assignment does
not match any prediction of long-verified potential models (see
Fig.~\ref{fig:summary}); the
dominant decay would be isospin-violating; and the state is relatively narrow (less than a few MeV)
despite that fact that its mass is above threshold for the production of two charmed mesons.

\begin{figure}[!htb]
\epsfig{file=Spectroscopy/summary_d.eps, height=5cm}
 \caption{\label{fig:summary}
Measured masses of the newly observed states, positioned
in the spectroscopy according
to their most likely quantum numbers. The charged state ($Z(4430)$) clearly has
no $C$ quantum number.}
\end{figure}

Another aspect of interest of the $X(3872)$ are the measurements of its
mass, the most recent of which
is Ref.~\cite{babar:2007rv}: there
is an indication that there are two different particles, one decaying into $J/\psi\pi\pi$
and one into $D^{*0}D^0$, their masses differing
by about 4.5 standard deviations.
This observation makes the $X(3872)$ a good
tetraquark candidate:
di-quarks with an heavy meson are, in fact, flavor-triplets, and therefore
pairs give rise to the same nonet structure as conventional
mesons. There should therefore be two states with $S=I_3=0$
very close in mass~\cite{mppr}.
Without this evidence, the closeness to
the $D^0D^{*0}$ threshold suggests the hypothesis that this is a molecule composed of these two mesons.


Furthermore, the  $B$~Factories investigate
a large range of masses for particles with $J^{PC}=1^{--}$ by looking for events where the initial state
radiation brings the $e^+e^-$ center-of-mass energy down to the particle's mass. While in principle
only particles already observed in $R=\sigma_{had}/\sigma_{\mu\mu}$ scans could be produced, the high luminosity has
allowed the observation of several new particles: the  $Y(4260)\to J/\psi\pi^+\pi^-$ ~\cite{Aubert:2005rm}, the
$Y(4350)$~\cite{Aubert:2006ge} and the $Y(4660)$~\cite{belle:2007ea}, both
observed in their decay to $\psi(2S)\pi\pi$.

The invariant mass of the two pions in these decays is a critical observable in discerning the nature of these particles,
which are unlikely to be charmonium, since their masses are above the
open-charm threshold, yet they are relatively narrow.  Furthermore, their
decays to two
charmed mesons have not yet been observed, the most stringent limit being~\cite{Aubert:2007pa}
$\BR(Y(4260)\to D\bar{D})/\BR(Y(4260)\to J/\psi\pi^+\pi^-)<1.0 @$ 90\%
confidence level.

\begin{figure*}[!htb]
\begin{center}
\epsfig{file=Spectroscopy/belle_invpipi.epsi,height=6cm}
 \caption{\label{fig:bellepipiinv}
 Di-pion invariant mass distribution in $Y(4260)\to\jpsi \pi^+\pi^-$ (left), $Y(4350)\to \psi(2S) \pi^+\pi^-$ (center),\newline
and $Y(4660)\to \psi(2S) \pi^+\pi^-$ (right) decays.
}

\end{center}
\end{figure*}

Figure~\ref{fig:bellepipiinv}
shows the di-pion invariant mass spectra for all
regions in which new resonances have been observed. There is some
indication that only the $Y(4660)$ has a well-defined intermediate
state (most likely an $f_0$), while others have a more complex
structure.

These observations make the $Y(4260)$ a good hybrid candidate, and the $Y(4350)$ and  $Y(4660)$ good candidates for
$[cd][\bar{c}\bar{d}]$ and $[cs][\bar{c}\bar{s}]$ tetraquarks, respectively. The latter would, in fact, prefer to decay into an
$f_0$, while the mass difference between the two states is consistent with the hypothesis that the two belong to the same nonet.

The turning point in the query for states beyond charmonium
was therefore the observation by the Belle Collaboration of a charged
state
decaying into $\psi(2S)\pi^\pm$~\cite{belle:2007wg}.
Figure~\ref{fig:belleZ4430}
shows the fit to the  $\psi(2S)\pi$ invariant mass distribution in
$B\to \psi(2S)\pi K$ decays, returning a mass $M=4433\pm4\rm{MeV/c}^2$
and a width $\Gamma=44^{+17}_{-13}$ MeV.
%Due to the relevance of such
%an observation a large number of tests has been performed, breaking the
%sample in several subsamples and finding consistent results in all
%cases. Also, the possibility of a reflection of a $B\to\psi(2S)K^**$
%decay has been falsified by explicitly vetoing windows in  the $K\pi$
%invariant mass.


\begin{figure}[!htb]
\epsfig{file=Spectroscopy/belle_psipi.epsi,height=6cm}
%\includegraphics[width=6cm]{belle_psipi.epsi}
 \caption{\label{fig:belleZ4430}
 The $\psi(2S)\pi$ invariant mass distribution in
\hbox{$B\to \psi(2S)\pi K$ decays.}}
\end{figure}

In terms of quarks, such a state must
contain a $c$ and a $\bar{c}$, but given its charge
it must also contain at least a $u$ and a $\bar{d}$. The only open
options are the tetraquark, the molecule or threshold effects. The
latter two options are viable due to the closeness of the $D_1D^*$
threshold.

Finding the corresponding neutral state, observing a decay mode of the
same state, or at least having a confirmation of its existence, are
critical before a complete picture can be drawn.

There are several reasons why a run at fifty to one hundred times the existing integrated luminosity is
critical to convert these of hints into a complete, solid picture:
\begin{itemize}
\item all the new states, apart from the $X(3872)$, have been observed in only
a single decay channel, with significance that are barely above 5$\sigma$.
a hundredfold increase in statistics would allow searches in several other
modes. It is in particular critical to observe both the decay to
charmonium and to $D$-meson pairs and/or $D_s$ meson pairs. Since the
branching fraction of observable final states for the $D$ and especially
for the $D_s$ mesons are particularly low, current experiments do not have
the sensitivity to observe all the decays.
\item the models predict several other states, such as the neutral
partners of the $Z(4430)$ and the nonet partners, for instance
 $[cd][\bar{c}\bar{s}]$ candidates decaying into a charmonium state and a kaon,
 at a significantly lower rate
(see \eg, Ref.~\cite{Maiani:2007vr}) than the observed modes. Furthermore ,
several of these states decay into particles (in particular neutral pions
and kaons) that have a low detection efficiency.
 \end{itemize}


\section{Bottomonium}

Exotic states with two bottom quarks, analogous to those with two charm quarks, could also exist.
In this respect, bottomonium spectroscopy is a
very good testbench for
speculations advanced to explain the charmonium states.
On the other side, searching for new
bottomonium states
is more challenging, since they tend to be broader and there are
more possible decay channels. This explains why there are still eight unobserved
states with masses
below open bottomonium threshold.

Among the known states, there is already one with unusual behavior: there
has been a recent
observation~\cite{Abe:2007tk} of an anomalous enhancement, by two orders
of magnitude, of
the rate of $\FiveS$ decays to the $\OneS$ or a $\TwoS$ and two pions. This
indicates that either the $\FiveS$ itself or a state very close by in
mass has a
decay mechanism that enhances the amplitudes for these processes.

In order to understand whether the exotic state coincides with the
$\FiveS)$ or not, a high luminosity
(at least 20 fb$^{-1}$ per point to have a 10\% error) scan of the
resonance region is needed.

In any case, the presence of two
decay channels to other bottomonium states excludes the possibility of
this state being a molecular aggregate, but all other models are possible, and would predict
a large variety of not yet observed states.

As an example, one can estimate possible resonant states with the tetraquark
model, by assuming that  the masses of states with two $b$ quarks can be obtained
from one with two $c$ quarks by adding the mass difference between
the $\OneS)$ and the $\jpsi$. Under this assumption, which
works approximately for the known bottomonium states, we could expect three nonets
that could be produced by the $\ThreeS$ and decaying into $\OneS$ and
pions. Assuming that the production and decay rates of these new states
are comparable to the charmonium states, and assuming
a data sample of $\ThreeS$ events comparable in size to the current $\FourS$
sample is needed to clarify the picture, we would need about $10^9\ \ThreeS$
mesons, corresponding to an integrated luminosity of \hbox{0.3 ab$^{-1}$.}

As already mentioned, searching for bottomonium-like states would require
higher statistics than the corresponding charmonium ones; this therefore
represents an even stronger case for \superb.



\section{Search for Physics Beyond the Standard Model in Bottomonium Decays}

In spite of intensive searches performed at LEP \cite{Schael:2006cr},
the possibility of
a rather light non-standard Higgs boson has not been ruled out in
several scenarios beyond the Standard Model
\cite{Dermisek:2005gg,Dermisek:2006py,SanchisLozano:2007wv},
due to the fact that a new scalar may be uncharged under the
gauge symmetries, similar to a sterile neutrino in the fermion
case.  These studies indicate that its mass could be less than twice
the $b$ mass, placing it within the reach of \superb$\!\!$.
Moreover, the
LHC might not be able to unravel a signal from a
light Higgs boson whose mass is
below $B\bar{B}$ threshold, since it will be difficult for the soft decay products
to pass the LHC triggers.  Dark matter may also be
light, evading LEP searches if it does not couple strongly to the
$Z^0$~\cite{Gunion:2005rw,McElrath:2005bp,Fayet:2007ua,Bird:2006jd}.
\superb\ will be {\it required} in most of these cases to precisely determine
its masses and couplings, and will play an important discovery role.

\subsection*{Light Higgses}

A Higgs $h$ with $M_h < M_\Upsilon$ can be
produced in $\Upsilon(nS)$ decays via the Wilczek mechanism
with a branching ratio
approximately given by the leading-order formula \cite{Wilczek:1977zn}
\[ \frac{\Gamma(\Upsilon(nS) \to \gamma h)}{\Gamma(\Upsilon(nS) \to \mu
\mu)} =
    \frac{\sqrt{2} G_F m_b^2}{\alpha \pi M_{\NS}} E_\gamma X_d^2
\]
where $X_d$ is a model-dependent quantity containing the coupling of the
Higgs
to bottom quarks, $m_b$ is the bottom quark mass, $\alpha$ and $G_F$ are
the
electroweak parameters, and $E_\gamma =
(M_{\NS}/2)(1-M_h^2/M_{\NS)}^2)$
is the photon energy.

From a theoretical viewpoint, the existence of a light
pseudoscalar Higgs is not unexpected in many
extensions of the SM. As an especially appealing example, the
Next-to-Minimal Supersymmetric Standard
Model (NMSSM) has a gauge singlet added to the
MSSM two-doublet Higgs sector (see \cite{Fullana:2007uq} and references therein for a short
summary of other scenarios leading to a light Higgs
boson) leading
to seven physical Higgs bosons, five of them neutral, including
two pseudoscalars.

In the limit of either
slightly broken $R$ or Peccei-Quinn (PQ) symmetries,
the lightest \CP-odd Higgs boson (denoted by $A_1$)
can be much lighter than the other Higgs bosons.
Interestingly, the authors of \cite{Dermisek:2005gg}
interpret the excess of $Z^0$+$b$-jet events found at LEP
as a signal, in this formalism, of a
Standard Model-like Higgs decaying partly into $b \bar{b}$, but
dominantly into $\tau$'s via two light pseudoscalars.

Let us write the physical Higgs boson $A_1$ as a mixture of
singlet ($A_{s}$)
and non-singlet ($A_{MSSM}$) fractions parametrized by the
angle $\theta_A$, according to
\[ A_1 = \cos{\theta_A} A_{MSSM}+\sin{\theta_A} A_s \]
The $A_1$ coupling to down-type fermions turns out to be proportional to
$X_d = \cos{\theta_A}$ $\tan{\beta}$, where $\tan{\beta}$ denotes
the ratio of the vevs of the up- and down-type Higgs bosons. For
$\cos{\theta_A}$ close to zero, the $A_1$ almost completely
decouples from flavor physics.
However, if $\cos{\theta_A} \sim 0.1-0.5$, present LEP and $B$ physics
bounds can be simultaneously satisfied~\cite{Domingo:2007dx}, while
a light Higgs could still show up
in $\Upsilon$ radiative decays into tauonic pairs:
\[ \NS \to \gamma A_1(\to \tau^+\tau^-)\ ;\ \ \ n=1,2,3. \]

\begin{figure}[!htb]
\begin{center}
\includegraphics[width=15pc,angle=270]{Spectroscopy/plot_BLEP.eps}
\caption{\label{fig:ups_gamma_a_univers}
Plot of $X_d=\cos{\theta_A}$ $\tan{\beta}$ (blue points)
and $A_1$ mass in GeV (red crosses) versus $\tan{\beta}$.
All points were generated using the NMHDECAY code \cite{Ellwanger:2005dv}
satisfying both LEP and$B$ physics constraints
using a particular set of NMSSM parameters \cite{SanchisLozano:2008}.}
\end{center}
\end{figure}

As this light Higgs acquires its couplings to Standard Model fermions via mixing
with the Standard Model Higgs, it therefore couples to mass, and will decay to the
heaviest available Standard Model fermion.  In the region $M_{A_1} > 2 M_\tau$, there
are
two measurements which have sensitivity: lepton universality of $\Upsilon$
decays, and searches for a monochromatic photon peak in tauonic $\Upsilon$
decays. \\

{\bf{The measurement of lepton universality}}
 compares the branching ratios of $\Upsilon$ to $e^+e^-$,
$\mu^+\mu^-$ and $\tau^+\tau^-$
\cite{SanchisLozano:2003ha,SanchisLozano:2006gx},
which should all be identical up to kinematic
factors in the Standard Model, due to the gauge symmetry.
It is relevant especially when the $A_1$ mass is
within about 500 MeV of an $\Upsilon$ mass, so that the monochromatic photon
signal is buried under backgrounds.  It is also the best measurement
when $M_{A_1} > M_\Upsilon$, which causes there to be a photon spectrum,
rather than monochromatic line.

Using the NMHDECAY code \cite{Ellwanger:2005dv}, we have
randomly generated masses and couplings for the $A_1$ Higgs
below the $B\bar{B}$ threshold, under the condition of passing
all current LEP and $B$ physics bounds built into the
NMHDECAY \cite{Domingo:2007dx}.
We actually chose a physically-motivated
set of NMSSM parameters favoring the existence of a scenario
with of a light $A_1$ \cite{SanchisLozano:2007wv,SanchisLozano:2008}.

In Fig.~\ref{fig:ups_gamma_a_univers} we plot the resulting points
of our scan
for the $A_1$ mass and $X_d$ values as a function of $\tan{\beta}$.
Let us stress that, in view of the available large $X_d$ values,
such a light \CP-odd Higgs could provide a signal in
$\Upsilon$ leptonic decays, whose first hint
would be an apparent breaking of lepton universality, {\it e.g.}
at the few percent level. Indeed, the tauonic mode would be (slightly)
enhanced by the New Physics channel with respect
to the electronic and muonic modes, because of the large leptonic
mass difference
\cite{SanchisLozano:2003ha,SanchisLozano:2006gx, Fullana:2007uq}.
The degree of enhancement of the tauonic channel (\ie, of the
New Physics contribution) obviously depends on the
assumed set of the NMSSM parameters (notably $\tan{\beta}$) but seems
sizeable for reasonable values of them, as can be seen from
Fig.~\ref{fig:ups_gamma_a_univers}.

Moreover, the observation (non-observation) of a monochromatic photon
from the radiative process
would become the smoking gun pointing out (excluding)
the existence of such a light
non-standard Higgs boson.

\begin{figure}[!htb]
\begin{center}
\includegraphics[width=16pc]{Spectroscopy/xlimit.eps}
\caption{\label{fig:ups_gamma_a_mono}
Plot of the $5 \sigma$ discover potential of \superb\
with $\Upsilon(3S)$ data, in the mode $\Upsilon(3S) \to \pi^+ \pi^-
\Upsilon(1S) \to \pi^+ \pi^- \tau^+ \tau^- \gamma$ (solid black) and
$\Upsilon(3S) \to \tau^+ \tau^- \gamma$ (dashed red). An integrated
luminosity of 1 ab$^{-1}$ was assumed.}
\end{center}
\end{figure}

{\bf{In the search for monochromatic photons} }
the first relevant decay mode is $\ThreeS \to \OneS \pi^+
\pi^-$
first, followed by $\OneS \to \gamma \tau^+ \tau^-$, which has only a
4.5\%
branching fraction, but has low background.
The second decay mode is $\ThreeS \to \gamma
\tau^+ \tau^-$, which suffers from much worse backgrounds
from $e^+ e^- \to \tau^+\tau^- \gamma$ events, but also has a rate that is
more than a factor of ten higher.
The corresponding exclusion plots are in Fig.~\ref{fig:ups_gamma_a_mono}.


\subsection*{Invisible decays and light dark matter}

Finally, if Dark Matter is lighter than 5 GeV, it will require a Super $B$
Factory to determine its properties.  Generally, in this mass region one
needs
two particles, the dark matter particle $\chi$, and a boson that couples
it to
the Standard Model $U$.  The most promising searches are in
invisible and radiative decays of the $\Upsilon$, which can be measured in
the mode $\ThreeS \to \pi^+ \pi^- \OneS \to \pi^+ \pi^- +
invisible$, which is sensitive to a vector $U$.  However, to substantially
improve on existing measurements from Belle and CLEO, far-forward tagging
must
be incorporated into the design of the detector.  This is needed to veto
events
in which the $\OneS$ decays to a two-body state, with decay
products that disappear down the beampipe~\cite{McElrath:2005bp}.

The second most promising signature is radiative decays $\Upsilon \to
\gamma + invisible$.  This is probably the most
favored mode theoretically,
and is
sensitive to a scalar or pseudoscalar $U$.  The  mediator
coupling the Standard Model particles to final-state $\chi$'s
can be a pseudoscalar Higgs, $U=A_1$, which can be naturally
light, and would appear in this mode~\cite{Gunion:2005rw}.
In such models the Dark Matter can be naturally be a bino-like neutralino.

\section{Summary}

\superb\ will open a unique window on this physics because it
allows a high statistics study of the current hints of new aggregations
of quarks and gluons. Besides the physics one can study in running at the
$\FourS$ resonance, the following alternative energies are of interest:
$\ThreeS$ (at least 0.3 ab$^{-1}$) and a high luminosity scan between 4-5
GeV (5 MeV steps of 0.2 fb$^{-1}$ each would require a total of
40 fb$^{-1}$)~\cite{footnote2}.
While this is not huge statistics, this scan is only feasible with
\superb. The only possible competitor, BES-III, is not planning to scan
above 4 GeV, since their data sample would, in any case, be lower than that
 of the $B$ Factories alone.

Finally, the search for exotic particles among the decay products of the
bottomonia can probe regions of the parameters space of non-minimal
supersymmetric models that cannot be otherwise explored directly, for
instance at LHC. These studies are particularly efficient when producing
$\NS$ mesons with $n<4$.

The superiority of \superb\  with respect to the planned upgrade of Belle
lies both in the ten times higher statistics, which broadens the range of
cross sections the experiment is sensitive to, but also in the flexibility
to change center of mass energy.

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Belle, X.~L. Wang {\em et~al.}, %``Observation of Two Resonant Structures
%in  e+e- to pi+ pi- psi(2S) via Initial State Radiation at Belle'',\newblock
 arXiv:0707.3699 [hep-ex].
%%CITATION = ARXIV:0707.3699;%%


\bibitem{Aubert:2007pa}
\babar\ Collaboration, B.~Aubert, %``Study of the Exclusive Initial-State-Radiation
%Production  of the DDbar System'', \newblock
arXiv:0710.1371 [hep-ex].
%%CITATION = ARXIV:0710.1371;%%

%\bibitem{Abe:2007jn}
%Belle, K.~Abe {\em et~al.}, %``Observation of a charmoniumlike state
%produced in  association with a J/psi in e+ e- annihilation at s**1/2 approx.
%10.6-GeV'',\newblock
% Phys. Rev. Lett. {\bf 98}, 082001 (2007).
%%CITATION = PRLTA,98,082001;%%

%\bibitem{Abe:2004zs}
%Belle, K.~Abe {\em et~al.}, %``Observation of a near-threshold omega
%J/psi
%mass  enhancement in exclusive B --> K omega J/psi decays'', \newblock
%Phys. Rev. Lett. {\bf 94}, 182002 (2005), [hep-ex/0408126].
%%CITATION = HEP-EX/0408126;%%

%\bibitem{Uehara:2005qd}
%Belle, S.~Uehara {\em et~al.},% ``Observation of a chi'/c2 candidate in
%gamma  gamma --> D anti-D production at Belle'',\newblock
% Phys. Rev. Lett. {\bf 96}, 082003 (2006), [hep-ex/0512035].
%%CITATION = HEP-EX/0512035;%%

%\bibitem{Aubert:2007vj}
%Babar, T.~B. collaboration and B.~Aubert, %``Observation of $Y(3940) \to
%J/\psi  \omega$ in $B \to J/\psi \omega K$ at BABAR'', \newblock
%arXiv:0711.2047 [hep-ex].
%%CITATION = ARXIV:0711.2047;%%

\bibitem{belle:2007wg}
Belle, K.~Abe {\em et~al.}, %``Observation of a resonance-like structure
%in the $\pi^\pm \psi\prime$ mass distribution in exclusive $B\to K \pi^\pm
%  psi\prime$ decays'',\newblock
arXiv:0708.1790.

\bibitem{Maiani:2007vr}
  L.~Maiani, A.~D.~Polosa and V.~Riquer,
  %``Indications of a Four-Quark Structure for the X(3872) and X(3876) Particles
  %from Recent Belle and \babar\  Data,''
  Phys.\ Rev.\ Lett.\  {\bf 99}, 182003 (2007)
  [arXiv:0707.3354 [hep-ph]].
  %%CITATION = PRLTA,99,182003;%%

%\cite{Abe:2007tk}
\bibitem{Abe:2007tk}
  K.~F.~Chen {\it et al.}  [Belle Collaboration],
  %``Observation of e+e- -> Upsilon(1S)pi+pi- and Upsilon(2S)pi+pi- at
  %sqrt{s}~10.87 GeV,''
  arXiv:0710.2577 [hep-ex].
  %%CITATION = ARXIV:0710.2577;%%

\bibitem{Schael:2006cr}
  S.~Schael {\it et al.}  [ALEPH Collaboration],
  %``Search for neutral MSSM Higgs bosons at LEP,''
  Eur.\ Phys.\ J.\  C {\bf 47} (2006) 547.

\bibitem{Dermisek:2005gg}
  R.~Dermisek and J.~F.~Gunion,
  %``Consistency of LEP event excesses with an h --> a a decay scenario
and
  %low-fine-tuning NMSSM models,''
  Phys.\ Rev.\ D \textbf{73} (2006) 111701.



\bibitem{Dermisek:2006py}
  R.~Dermisek, J.~F.~Gunion and B.~McElrath,
  %``Probing NMSSM scenarios with minimal fine-tuning by searching for decays of
  %the Upsilon to a light CP-odd Higgs boson,''de
  Phys.\ Rev.\  D {\bf 76} (2007) 051105
  [arXiv:hep-ph/0612031].




\bibitem{SanchisLozano:2007wv}
  M.~A.~Sanchis-Lozano,
  %``A light non-standard Higgs boson: to be or not to be at a (Super) B
  %factory?,''
  arXiv:0709.3647 [hep-ph].



%\cite{Fayet:2007ua}
\bibitem{Fayet:2007ua}
  P.~Fayet,
  %``U-boson production in e+ e- annihilations, psi and Upsilon decays,
and
  %light Dark Matter,''
  Phys.\ Rev.\  D {\bf 75}, 115017 (2007)
  [arXiv:hep-ph/0702176];
  %%CITATION = PHRVA,D75,115017;%%
%\cite{Fayet:2006sp}
%\bibitem{Fayet:2006sp}
  P.~Fayet,
  %``Constraints on light Dark Matter and U bosons, from psi, Upsilon, K+,
pi0,
  %eta and eta' decays,''
  Phys.\ Rev.\  D {\bf 74}, 054034 (2006)
  [arXiv:hep-ph/0607318].
  %%CITATION = PHRVA,D74,054034;%%

%\cite{Bird:2006jd}
\bibitem{Bird:2006jd}
  C.~Bird, R.~Kowalewski and M.~Pospelov,
  %``Dark Matter pair-production in b --> s transitions,''
  Mod.\ Phys.\ Lett.\  A {\bf 21}, 457 (2006)
  [arXiv:hep-ph/0601090].
  %%CITATION = MPLAE,A21,457;%%



\bibitem{McElrath:2005bp}
  B.~McElrath,
  %``Invisible quarkonium decays as a sensitive probe of dark matter,''
  Phys.\ Rev.\ D {\bf 72}, 103508 (2005).


%\cite{Gunion:2005rw}
\bibitem{Gunion:2005rw}
    J.~F.~Gunion, D.~Hooper and B.~McElrath,
    %``Light neutralino Dark Matter in the NMSSM,''
    Phys.\ Rev.\  D {\bf 73}, 015011 (2006)
    [arXiv:hep-ph/0509024].
    %%CITATION = PHRVA,D73,015011;%%


%\cite{Wilczek:1977zn}
\bibitem{Wilczek:1977zn}
  F.~Wilczek,
  %``Decays Of Heavy Vector Mesons Into Higgs Particles,''
  Phys.\ Rev.\ Lett.\  {\bf 39}, 1304 (1977).
  %%CITATION = PRLTA,39,1304;%%


\bibitem{Fullana:2007uq}
  E.~Fullana and M.~A.~Sanchis-Lozano,
  %``Hunting a light CP-odd non-standard Higgs boson through its tauonic
decay
  %at a (Super) B factory,''
  Phys.\ Lett.\  B {\bf 653} (2007) 67
  [arXiv:hep-ph/0702190].


%\cite{Domingo:2007dx}
\bibitem{Domingo:2007dx}
  F.~Domingo and U.~Ellwanger,
  %``Updated Constraints from B Physics on the MSSM and the NMSSM,''
  JHEP {\bf 0712} (2007) 090
  [arXiv:0710.3714 [hep-ph]].


\bibitem{SanchisLozano:2003ha}
  M.~A.~Sanchis-Lozano,
  %``Leptonic universality breaking in Upsilon decays as a probe of new
  %physics,''
  Int.\ J.\ Mod.\ Phys.\  A {\bf 19} (2004) 2183
  [arXiv:hep-ph/0307313]..


%\cite{SanchisLozano:2006gx}
\bibitem{SanchisLozano:2006gx}
  M.~A.~Sanchis-Lozano,
  %``Proposal for testing lepton universality in Upsilon decays at a
B-factory
  %running on the Upsilon(3S),''
  J.\ Phys.\ Soc.\ Jap.\  {\bf 76} (2007) 044101
  [arXiv:hep-ph/0610046].

\bibitem{Ellwanger:2005dv}
  U.~Ellwanger and C.~Hugonie,
  %``NMHDECAY 2.0: An updated program for sparticle masses, Higgs masses,
  %couplings and decay widths in the NMSSM,''
  Comput.\ Phys.\ Commun.\  {\bf 175} (2006) 290
  [arXiv:hep-ph/0508022].



\bibitem{SanchisLozano:2008} M.~A.~Sanchis-Lozano, in preparation.

\bibitem{footnote2}
  We assumed $\sigma(e^+e^-\to Y)*\BR~50{\rm pb}$ as measured for the
  $Y(4320)$ in Ref.~\cite{Aubert:2006ge} and require at least ten thousand
  events per resonance.




%\cite{Mangano:2007gi}
%\bibitem{Mangano:2007gi}
%  M.~L.~Mangano and P.~Nason,
%  %``Radiative quarkonium decays and the NMSSM Higgs interpretation of
%the
  %hyperCP Sigma+ --> p mu+ mu- events,''
%  Mod.\ Phys.\ Lett.\  A {\bf 22}, 1373 (2007)
%  [arXiv:0704.1719 [hep-ph]].
  %%CITATION = MPLAE,A22,1373;%%



\end{thebibliography}

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