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% Some useful journal names
\def\NCA{\em Nuovo Cimento}
\def\NIM{\em Nucl. Instr. Meth.}
\def\IJMPA{{\em Int. Jour. Mod. Phys.} A}
\def\NIMA{{\em Nucl. Instr. Meth.} A}
\def\NPA{{\em Nucl. Phys.} A}
\def\NPB{{\em Nucl. Phys.} B}
\def\NPP{\em Nucl. Part. Phys.}
\def\PLB{{\em Phys. Lett.} B}
\def\SJPN{\em Sov. Jour. Part. Nucl.}
\def\SJNP{\em Sov. Jour. Nucl. Phys.}
\def\PRL{\em Phys. Rev. Lett.}
\def\PR {\em Phys. Rev.} 
\def\PRC{{\em Phys. Rev.} C}
\def\PRD{{\em Phys. Rev.} D}
\def\ZPC{{\em Z. Phys.} C}

\begin{center} 
{Contribution to International Workshop \cite {trieste} on Hadron Structure
and Hadron
Spectroscopy,\\ Trieste, Italy, Feb. 2002}\\
\vspace{0.1cm} 
{\Large\bf Pion Polarizabilities at CERN COMPASS\\}
\vspace{0.1cm} 
\textsc{\large Murray Moinester
\footnote{ together with: F. Balestra, R. Bertini, M.P.
Bussa, M. Colantoni, O. Denisov, A. Dolgopolov, M. Faessler, A. Ferrero,
L. Ferrero, J. Friedrich, V. Frolov, R. Garfagnini, N.
Grasso, V. Kolossov, R. Kuhn, A. Maggiora, M. Maggiora, A.
Manara, Y. Mikhailov, V. Obraztsov, A.
Olchevski, D. Panzieri, S. Paul, G, Piragino, J.
Pochodzalla, V. Poliakov, A. Sadovski, M. Sans, L.
Schmitt, H. Siebert, A. Skachkova, T. Walcher, A.
Zvyagin} 
\\ for the COMPASS collaboration}\\
\textit{R. and B. Sackler Faculty of Exact Sciences,\\ 
School of Physics and Astronomy, Tel
Aviv University,\\ 69978 Tel Aviv, Israel\\ 
murraym@tauphy.tau.ac.il\\}
\end{center}
%\vspace{0.5cm}                                                

\begin{center}
Abstract: 
\end{center}

%\vspace{0.1cm}

{\bf Objective:}
  
The electric $(\bar{\alpha})$ and magnetic $(\bar{\beta})$ pion
Compton polarizabilities characterize the pion's deformation in the
electromagnetic field of the $\gamma$ during $\gamma\pi$
Compton scattering.  They depend on the rigidity of the pion's
internal structure as a composite particle. The 
polarizabilities deduced by Antipov et al. in their
low statistics Primakoff experiment ($\sim$ 7000 events) were
$\bar{\alpha}_{\pi} = -\bar{\beta}_{\pi} = 6.8 \pm 1.4 \pm 1.2$,
in units of $10^{-43}$ cm$^3$.  
This value, ignoring the large error bars, is about three times
larger than the chiral perturbation
theory ($\chi$PT) prediction.  Taking into account the very
high beam intensity, fast data acquisition, high acceptance and
good resolution of the CERN COMPASS experiment, one
can expect from
COMPASS statistics a factor 6000 higher, a data sample that
includes many tests to control systematic errors, and a 
significantly reduced total measurement 
uncertainty for $\bar{\alpha}_{\pi}$, 
of order 0.4. 

{\bf Methodology:} 

CERN COMPASS 
studies pion-photon interactions to achieve a unique
Primakoff physics program centered on pion polarizability
studies. We will use a 190 GeV pion beam and a
virtual
photon target, and magnetic spectrometers and calorimeters to
measure the complete kinematics of pion-photon reactions.  COMPASS
was set up during 2000/01, including a successful Primakoff test
run, and then began data taking with a muon beam for the 
proton spin physics component of its program. COMPASS will next
run
its spin physics program and Primakoff program preparations,
followed by its pion beam physics program, including 
pion
polarizability.  For pion polarizability,
$\gamma\pi$ scattering will be measured via radiative pion
scattering (pion Bremsstrahlung) in the nuclear Coulomb field:  
$\pi + Z \rightarrow \pi' + \gamma + Z.$ A virtual photon from the
Coulomb field of the target nucleus is scattered from the pion and
emerges as a real photon accompanying the pion at small forward
angles in the laboratory frame, while the target nucleus (in the
ground state)  recoils with a small transverse momentum kick p$_t$.  
The radiative pion scattering reaction is equivalent to $\gamma$ +
$\pi$ $\rightarrow$ $\gamma$ + $\pi$ scattering for
laboratory $\gamma$'s of order 1 GeV incident on a target $\pi$
at rest.  The pion polarizabilities are determined by their effect
on the shape of the measured $\gamma \pi$ Compton scattering
angular distribution.

{\bf Significance:}  

The pion polarizabilities are key observables, and provide
stringent tests of our understanding of chiral symmetry, its
spontaneous breakdown, the role of explicit symmetry breaking in
QCD, and consequently the very foundations of nuclear physics.  
The $\chi$PT effective Lagrangian, using data from
radiative pion beta decay, predicts the pion electric and magnetic
polarizabilities $\bar{\alpha}_{\pi}$ = -$\bar{\beta}_{\pi}$ = 2.7
$\pm$ 0.4.
New high
precision pion polarizability measurements via radiative pion
scattering data from COMPASS will provide important new
tests of this QCD chiral dynamics prediction.

%\end{abstract}

\pagenumbering{arabic}
\newpage
\section{Scientific Background:} 

Pion polarizabilities will be measured at the CERN COMPASS experiment
\cite{trieste,paul,cd,bormio,tm,of}, a new high priority approved
spectrometer facility
at
CERN that uses muon and pion beams for studies of hadron structure and
spectroscopy.  The polarizabilities are obtained from measurements of the $\gamma
\pi \rightarrow \gamma \pi$ gamma-pion Compton scattering. For the pion, chiral
perturbation theory ($\chi$PT) leads to precision predictions for the
polarizabilities \cite{hols1,buergi,babu2}. Precision measurements of
polarizabilities
therefore subject the $\chi$PT techniques of QCD to new and serious tests.

%\newpage
\subsection{Pion Polarizabilities via Primakoff Scattering}


\indent

For the pion polarizability, $\gamma\pi$ scattering was measured (with large
uncertainties)  with 40 GeV pions \cite{anti1} via radiative pion scattering
(pion Bremsstrahlung) in the nuclear Coulomb field:
\begin{equation}
\label{eq:polariz}
\pi + Z \rightarrow \pi' + \gamma + Z'.
\end{equation}

In this measurement, the incident pion Compton scatters from a virtual photon in
the Coulomb field of a nucleus of atomic number Z; and the final state $\gamma$
and pion are detected in coincidence.  The radiative pion scattering reaction is
equivalent to  $\gamma$ + $\pi^{-}$ $\rightarrow$  $\gamma$ + $\pi^{-}$
scattering for laboratory $\gamma$'s of order 1 GeV incident on a target
$\pi^{-}$ at rest. It is an example of the well tested Primakoff formalism
\cite{jens,ziel} that relates processes involving real photon interactions to
production cross sections involving the exchange of virtual photons.

In the 40 GeV radiative pion scattering experiments, it was shown experimentally
\cite{anti1} and theoretically \cite{galp} that the Coulomb amplitude clearly
dominates, and yields sharp peaks in t-distributions at very small squared four
momentum transfers (t) to the target nucleus t $\leq 6 \times 10^{-4}$
(GeV/c)$^{2}$. Backgrounds from strong  processes were low, and are expected 
to be even lower at the higher energy ($\sim$ 190 GeV) planned for the
CERN COMPASS
experiment.

{\bf All polarizabilities in this paper are expressed in units of
$10^{-43}$ cm$^3$}. The $\chi$PT 1-loop prediction \cite {hols1,buergi}
for
the pion polarizability is $\bar{\alpha}_{\pi}=~-\bar{\beta}_{\pi} =
2.7 \pm ~0.4$; with values $\bar{\alpha}_{\pi}= 2.4 \pm
~0.5;~\bar{\beta}_{\pi} = -2.1 \pm ~0.5$, at two-loop \cite {buergi}.  
Holstein \cite {hols1} showed that meson exchange via a pole diagram
involving the a$_1$(1260) resonance provides the main contribution
($\bar{\alpha}_{\pi}$ = 2.6) to the polarizability.  Xiong, Shuryak, Brown
(XSB)  \cite{xsb} assuming a$_1$ dominance find $\bar{\alpha}_{\pi}$ =
1.8.

In fact, the a$_1(1260)$ width and the pion polarizability are related to
an interesting question, which is whether or not one can expect gamma ray
rates from the quark gluon plasma to be higher than from the hot hadronic
gas phase in relativistic heavy ion collisions. XSB calculate photon
production from a hot hadronic gas via the reaction $\pi^- + \rho^0
\rightarrow \pi^- + \gamma$. They assume that this reaction proceeds
through the a$_1$(1260). For a$_1$(1260) $\rightarrow \pi \gamma$, the
experimental width \cite {ziel} is $\Gamma = 0.64 \pm 0.25$ MeV. 
XSB \cite {xsb} used an estimated radiative width 
$\Gamma$ = 1.4 MeV, higher than the experimental value
\cite {ziel}, as determined in the Primakoff reaction 
$\pi Z \rightarrow a_1 Z$, followed by $a_1^- \rightarrow \pi^- \rho$. 
It is with this
estimated width that they calculate the pion
polarizability to be $\bar{\alpha}_{\pi}$ = 1.8. COMPASS can
experimentally check the a$_1$ dominance assumption of XSB
via the inverse detailed balance Primakoff reaction $\pi Z \rightarrow a_1
Z$, 
and the
consistency of the expected relationship of this radiative width and the
pion polarizability \cite {qgp}.
 
For the kaon, $\chi$PT predicts \cite {cd,hols1,pol} $\bar{\alpha}_{K^-}$
= 0.5 . The kaon polarizability measurements at COMPASS should complement
those for pion polarizabilities for chiral symmetry tests away from the
chiral limit. A more extensive study of kaon polarizabilities was given
by Ebert and Volkov \cite {ev}. Until now, only an upper limit
\cite {gb} at 90\% confidence was measured (via energy shifts in heavy Z
kaonic atoms) for the $K^-$, with $\bar{\alpha}_{K} \leq 200.$


\subsection{Pion Polarizabilities}

For the $\gamma\pi$ interaction at low energy, 
chiral perturbation theory ($\chi$PT) provides a rigorous way to
make predictions via a Chiral Lagrangian having only 
renormalized coupling
constants L$^r_i$ \cite{gass1} as empirical parameters. With a perturbative
expansion of the effective
Lagrangian, the method establishes relationships between different processes in terms
of the L$^r_i$. For example, the radiative pion beta decay and electric pion
polarizability are expressed as \cite{hols1}:

\begin{equation}
F_A/F_V = 32\pi^2(L^r_9+L^r_{10});~ \bar{\alpha}_{\pi} = 
\frac{4\alpha_f}{m_{\pi}F^{2}_{\pi}}(L^r_9+L^r_{10});
\label{eq:fafv}
\end{equation}

%\nextpage
where F$_\pi$ is the pion decay constant, F$_A$ and F$_V$  are the axial vector and
vector coupling constants in the decay, and $\alpha_f$ is the fine structure
constant. The experimental ratio F$_A$/F$_V$  = 0.45 $\pm$ 0.06, leads to
$\bar{\alpha}_{\pi}$ = -$\bar{\beta}_{\pi}$ = 2.7 $\pm$ 0.4, where the error shown is
due to the uncertainty in the F$_A$/F$_V$ measurement \cite{hols1,babu2}.

The pion polarizabilities deduced by Antipov et al. \cite{anti1} in their
low statistics
experiment ($\sim$ 7000 events) were $\bar{\alpha}_{\pi} = -\bar{\beta}_{\pi} =
6.8 \pm 1.4 \pm 1.2$, with the analysis constraint that
$\bar{\alpha}_{\pi} +
\bar{\beta}_{\pi} = 0$, as expected theoretically \cite {hols1}.  The deduced
polarizability value, not counting the large error bars, is some three times
larger than the $\chi$PT prediction. {\bf The available polarizability results
have large uncertainties. There is a clear need for new and improved radiative
pion scattering data.}


\section{Research Goals and Expected Significance:}

We studied the statistics attainable and uncertainties achievable for the
pion polarizabilities in the COMPASS experiment, based on Monte Carlo
simulations. We begin with an estimated $\sigma(Pb)=0.5 mb$ Compton
scattering cross
section per Pb nucleus and a total inelastic cross section per Pb nucleus
of 0.8 barn.  High statistics will allow systematic studies, with fits
carried out for different regions of photon energy $\omega$, Z$^2$, etc.; 
and polarizability determinations with statistical uncertainties lower
than 
0.1. 

The expected pion beam flux is $2 \times 10^{7}$ pions/sec, while the spill
structure provides a 5 second beam every 16 seconds.  For pion polarizability, in
2 months of running at 100\% efficiency, we obtain 3.2$\times$ 10$^{13}$
beam
pions. We use a 0.8~\%
interaction length target, 3 mm Lead plate with target density 
$N_t=10^{22} cm^{-2}$. The Primakoff interaction rate is then 
$R = \sigma(Pb) \cdot N_t= 5. \times$ 10$^{-6}$. Therefore, in a 2 month
run, one obtains
1.6 $\times$
10$^{8}$ Primakoff polarizability events at 100\% efficiency.  Considering
efficiencies for tracking (92\%), $\gamma$ detection (58\%), accelerator and
COMPASS operation (60\%), analysis cuts to reduce backgrounds (75\%), we estimate
a global efficiency of
$\epsilon$(total)=24\%, or 4.$\times$ 10$^7$ useful 
pion polarizability events per 2 month run.
Prior to the data production run,   
time is also needed to calibrate ECAL2, to make the tracking detectors
operational, to bring the DAQ to a stable mode, and for other contingencies.
The above
expected statistics in a two month data production run is 
a factor 6000 higher than the
7000 events of the previous pion polarizability Primakoff experiment.

We can also access kaon polarizabilities considering the approximately 1\%
kaon component of the beam One requires the CERN CEDAR Cerenkov beam
detector for the kaon particle identification. Statistics of order
$4. \times 10^5$ events would allow a first time determination of the 
kaon polarizability. 

COMPASS provides a unique opportunity to investigate pion polarizabilities. 
Taking into account the very high beam intensity,
fast data acquisition, high acceptance and good resolution of the COMPASS
setup, one can expect from COMPASS the highest statistics and a
`systematics-free' data sample that includes many tests to control
possible systematic errors. 

\section{Detailed description of Research Program:}

COMPASS is a fixed target experiment which will run primarily with a 160 GeV
polarized muon beam and a 190 GeV pion beam.
In order to achieve a good energy resolution within a wide energy range,
COMPASS is designed as a two stage spectrometer with 1.0 Tm and 5.2 Tm
conventional magnets. The tracking stations are composed of different
detector
types to cover a large area while achieving a good spatial resolution in the
vicinity of the beam. Most of the tracking detectors operate on the principle
of gas amplification, while some are silicon strip detectors. At the end of each
stage, an electromagnetic and a
hadronic calorimeter detects the energies of the gammas, electrons
and hadrons.  The calorimeters of the first stage and the EM calorimeter of
the second stage have holes through which the beam passes. 

We considered elsewhere in detail the beam, detector, and trigger
requirements for
polarizability studies in the CERN COMPASS experiment \cite {cd,bormio,tm}.
We describe here the pion polarizability
measurements via the
reaction $\pi^{-}$ + Z $\rightarrow$ $\pi^{-'}$ + $\gamma$ + Z$'$.

\begin{figure}[tbc]
\centerline{\epsfig{file=diagram.eps,width=7cm,
height=5cm}}
\caption{The Primakoff $\gamma$-hadron Compton process and kinematic variables
(4-momenta): p1, p1$^\prime$ = for initial/final hadron, p2, p2$^\prime$ = for 
initial/final target, k, k$^\prime$ = for initial/final gamma, and $\theta$ 
the scattering angle of the $\gamma$ in the alab frame.}
\label{fig:diagram}
\end{figure}

\subsection{Monte Carlo Simulations}

The setup we used for the Monte Carlo simulations was the official setup for the
year 2001 run with the addition of three GEM stations and six silicon stations
as projected for the year 2002 run. The additional detectors allow 
more precise tracking. We carried out the polarizability simulations using (1)
the POLARIS event generator with (2) the CERN COMPASS GEANT (COMGEANT) package
\cite {va},
whose output is a ZEBRA file with the information on the traces left by
particles in detectors, (3) the \coral\ \compass\ reconstruction and
analysis
library, structured as a set of modules:  an input package is used to read the
ZEBRA files produced by \comgeant, \traffic (TRAck Finding and FItting in
Compass), calorimeter and RICH packages, a ROOT
output package, the detector data decoding package, etc., and (4) the new CERN
histograming and display and fit program ROOT.  We use the terms
\emph{generated} and \emph{reconstructed}, the first denoting the input physics
events to \comgeant\ from POLARIS and the latter the output of \coral\ which
contains the reconstruction of these events in the the COMPASS spectometer.



POLARIS produces events of the type Eq.~\ref{eq:polariz}, based on the
theoretical Primakoff $\gamma\pi$ Compton scattering cross section. The
four-momentum of each particle is p1, p2, p1$^\prime$, p2$^\prime$, k,
k$^\prime$, respectively, as shown in Fig.~\ref{fig:diagram}. In the
one-photon exchange domain, this reaction is equivalent to $\gamma + \pi
\rightarrow \gamma^\prime + \pi^\prime$, and the four-momentum of the
incident virtual photon is k = q = p2$-$p2$^\prime$. We have therefore t=k$^2$
with t the square of the four-momentum transfer to the nucleus, F(t) the
nuclear form factor (essentially unity at small t, $\sqrt{\rm{s}}$ the mass
of the $\gamma\pi$ final state, and t$_0$ the minimum value of t to produce a
mass $\sqrt{\rm{s}}$. The momentum modulus $|\vec{k}|$ (essentially equal to
p$_T$) of the virtual photon is in the transverse direction, and is equal and
opposite to the momentum p$_T$ transferred to the target nucleus.  The pion
polarizability is extracted via a fit of the theoretical cross section to the
scattered $\gamma$ angular distribution in the projectile (alab) rest frame.
The total Primakoff cross section is computed by integrating numerically the
differential cross section $\sigma(s,t,\theta)$ of Eq.~\ref{eq:Primakoff_1}
below for the Primakoff Compton process.

\subsection{Primakoff $\gamma\pi$ Compton Event Generator}

We describe the event generator for the radiative scattering of the pion in
the Coulomb field of a nucleus \cite{pol}. In the pion alab frame, the
nuclear Coulomb field of target M$_Z$ effectively provides a virtual photon beam
incident on a
pion target at rest. We have for the variable t=k$^2 =q^2 \equiv$ M$^2$,
where t
is
the 4-momentum transferred to the nucleus, and M is the virtual photon mass.
Since t=2M$_Z$[M$_Z$-E(Z',lab)]$<$0, the virtual photon mass is imaginary. To
approximate real pion Compton scattering, the virtual photon should be taken
to be almost real. For small t, the electromagnetic contribution to the
scattering amplitude is large compared to meson and Pomeron
(diffractive) exchange
contributions.
Radiative corrections for Primakoff scattering have been calculated to be 
very small \cite {ak}. 


The Primakoff differential cross section of the process of Eq.~\ref{eq:polariz} in
the alab frame may be expressed as \cite{starkov}:
\begin{equation}
\label{eq:Primakoff_1}
\frac
{{d}^3{\sigma}}
{{dt}{d}{\omega}{d\cos{\theta}}}
=
\frac
{\alpha_{f}{Z}^2}
{\pi\omega}
\cdot
\frac
{t-t_{0
}}
{t^2}
\cdot
\frac
{{d}\sigma_{\gamma\pi}{(}\omega,\theta{)}}
{{d}{\cos}{\theta}}\cdot F^2(t),
\end{equation}
where the $\gamma\pi$ cross section is given by:
\begin{equation}
\label{eq:Primakoff_2}
\frac
{{d}\sigma_{\gamma\pi}{(}\omega,\theta{)}}
{{d}{\cos}{\theta}}
=
\frac
{{2}{\pi}{\alpha_{f}}^2}
{{m}_{\pi}^2}
\cdot
\{
{F}_{\gamma\pi}^{pt}{(}{\theta}{)}
+
\frac
{{m_{\pi}}{\omega}^2}
{\alpha_{f}}
\cdot
\frac
{\bar{\alpha}_{\pi}{(}1+{\cos}^{2}{\theta}{)}+2\bar{\beta}_{\pi}{\cos\theta}}
{{(}{1+\frac{\omega}{m_{\pi}}{(1-\cos{\theta})}}{)}^3}
\}.
\end{equation}
Here, t$_0$=$(m_{\pi}\omega/p_{b})^2$, with $p_{b}$ the incident pion beam
momentum in the laboratory, $\theta$ the scattering angle of the real photon
relative to the incident virtual photon direction in the alab frame, $\omega$ the
energy of the virtual photon in the alab frame, $Z$ the nuclear charge, $m_\pi$
the pion mass, $\alpha_{f}$ the fine structure constant, 
F(t) is the nuclear electromagnetic form factor (approximately unity in the
range $t < 2.5 \times 10^{-4} GeV^2$), 
and $\bar{\alpha_\pi}$,
$\bar{\beta_\pi}$ the pion electric and magnetic polarizabilities. The energy of
the incident virtual photon in the alab (pion rest) frame is:
\begin{equation}
\omega \sim  (s - {m_{\pi}}^2)/2m_{\pi}.
\label{eq:omega}
\end{equation}
For COMPASS, this radiative pion scattering reaction is then equivalent to
$\gamma$ +
$\pi$ $\rightarrow$ $\gamma$ + $\pi$ scattering for
laboratory $\gamma$'s with energy of order $\omega =1 GeV$ incident on a
target $\pi$
at rest.  
The function ${F}_{\gamma\pi}^{pt}{(}{\theta}{)}$ describing the Thomson cross
section for $\gamma$ scattering from a point pion is given by:
\begin{equation}
\label{eq:Primakoff_3}
{F}_{\gamma\pi}^{pt}{(}{\theta}{)}=
\frac{1}{2}\cdot
\frac
{1+{\cos}^{2}{\theta}}
{{(}{1+\frac{\omega}{m_{\pi}}{(1-\cos{\theta})}}{)}^2}
{.}
\end{equation}

From Eq.~\ref{eq:Primakoff_2}, the cross section depends on
$(\bar{\alpha}_{\pi}+\bar{\beta}_{\pi})$ at small $\theta$, and on
$(\bar{\alpha}_{\pi}-\bar{\beta}_{\pi})$ at large $\theta$. A precise fit of the
theoretical cross section (Eq.~\ref{eq:Primakoff_1}-\ref{eq:Primakoff_3}) to the
measured angular distribution of scattered $\gamma$'s, allows one to extract the
pion electric and magnetic polarizabilities. Fits will be done for different
regions of $\omega$ for better understanding of the systematic uncertainties. We
will carry out analyses with and without the dispersion sum rule constraint
\cite {hols1} that $\bar{\alpha}_{\pi}+\bar{\beta}_{\pi}\approx0.4$. We can
achieve a significantly smaller uncertainty for the polarizability by including
this constraint in the fits.

The event generator produces events in the alab frame, characterized by the
kinematical variables t, $\omega$ and $\cos\theta$, and distributed with the 
probability of the theoretical Compton Primakoff cross section
(Eq.~\ref{eq:Primakoff_1}-\ref{eq:Primakoff_3}). Then, the $\gamma\pi$ scattering
kinematics are calculated. The virtual photon incident along the recoil direction
$\vec{k}/|\vec{k}|$, is scattered on the pion "target", and emerges as a real photon
with energy/momentum $\omega^{\prime}$/$|\vec{k}^{\prime}|$ at an angle $\theta$:
\begin{equation}
\label{eq:Compton}
{\large
\omega^{\prime}=\frac
{\omega{(}{1}+\frac
{\omega^2{-}{|\vec{k}|}^2}{{2}{m}_{\pi}{\omega}}
{)}}
{
{1}{+}
\frac{\omega}{{m}_{\pi}}
{(}{1-}
\frac{|\vec{k}|}{\omega}
\cos\theta
{)}
}
}
\end{equation}

The photon azimuthal angle around the recoil direction is randomly generated
using a uniform distribution. The four-vector components of all reaction
participants (pion, photon and recoil nucleus) are then calculated in the alab
frame. The azimuthal angle of the recoil nucleus is also randomly generated by a
uniform distribution. Finally, the reaction kinematics are transformed to the lab
frame by a Lorentz boost.

For the measurement of the pion polarizabilities, one must fit the theoretical cross
section (\ref{eq:Primakoff_1}-\ref{eq:Primakoff_3}) to measured distributions, after
correcting for acceptances. The sensitivity to the polarizability increases with
increasing $\omega$ energy and at back angles. A convenient method is to use the
$\cos\theta$ distribution integrated over t and 
for different ranges of $\omega$, since this shows clearly
the sensitivity to the polarizability. 

\subsection{Design of the Primakoff Trigger\label{sec:how}}

The small Primakoff cross section and the high statistics required for extracting
polarizabilities require a data run at high beam intensities and with good
acceptance. This sets the main requirements for the trigger system: (1) to act as a
"beam killer" by accepting only Primakoff scattered pions, and suppressing the
high rate background associated with non-interacting
beam pions, (2) to avoid cutting the   acceptance at the important $\gamma$ back
angles in the alab frame, where the hadron polarizability measurement is most
sensitive, (3) to cope with background in the $\gamma$ calorimeter from low energy
$\gamma$'s or delta electrons.

We achieve these objectives via a COMPASS Primakoff trigger that makes use of a
beam veto, a target recoil detector, the calorimeters and various hodoscopes.  
A coincidence is required of the scattered pion with a $\gamma$ measured in the
ECAL2 calorimeter.  We demonstrated the feasibility and field operation of such
a trigger, via Monte Carlo simulations \cite {cd,bormio,tm,sans,kuhn,mlc} and via
beam tests
with the COMPASS spectrometer \cite{pvcs}.

For the reaction given in Eq. ~\ref{eq:polariz}, for illustration at 300 GeV pion
beam energy,
the laboratory outgoing $\gamma$'s are emitted within an angular cone of within
5 mrad, and the corresponding outgoing $\pi$'s are emitted within 2 mrad. Most
events have $\gamma$ energies between $0-280$ GeV, and $\pi$ energies between
$20-300$ GeV.

Our MC shows that we lose very little polarizability information by applying an
"energy cut" trigger condition that rejects events with the outgoing pion energy
having more than 240 GeV. Correspondingly, the final state $\gamma$ has less
than 60 GeV. The 240 GeV cut acts as a beam killer.  The 60 GeV cut will also be
very effective in reducing the $\gamma$ detector (ECAL2) trigger rate, since a
large part of the background $\gamma$ rate is below 60 GeV. 

\begin{figure}[tbc]
\centerline{\epsfig{file=acceptance.eps,width=12cm,
height=7cm}}
\caption{MC simulation showing the acceptance of the
$\gamma\pi\rightarrow\gamma\pi$ reaction in terms of the invariant four
momentum transfer t to the target,the squared invariant energy s of the final
state $\gamma\pi$, the angular distribution versus $\cos(\theta)$ with
$\theta$ the $\gamma$ scattering angle in the alab frame, and the virtual photon
energy $\omega$ 
in the alab frame. The overlayed spectra correspond to different cuts
on the final state $\pi$ momentum.}
\label{fig:acceptance}
\end{figure}

The polarizability insensitivity to these cuts results from the fact that the
most forward (in alab frame) Compton scattering angles have the lowest
laboratory $\gamma$ energies and largest laboratory angles. In addition, the
cross section in this forward alab angle range is much less sensitive to the
polarizabilities. This is seen from Eq. \ref{eq:Primakoff_2}, since with
$\bar{\alpha}_{\pi}+\bar{\beta}_{\pi}\approx 1$ used in our MC, the
polarizability component is small at forward compared to back angles. The
acceptance is reduced by the energy cut for the forward alab angles (shown in
Fig.~\ref{fig:acceptance}), but is unaffected at the important alab back angles.
Summarizing, the pion and $\gamma$ energy constraints at the trigger level
fulfill the "beam killer" requirement and at the same time remove backgrounds
coming from low energy $\gamma$'s, delta electrons, and e$^+$e$^-$ pairs
incident on ECAL2, etc. Similar results are obtained for the effectiveness of an
energy loss trigger for simulations carried out at 190 GeV pion beam energy.


%\subsection{Trigger}
%\protect\label{trigmeas}

Test beam studies for the trigger were performed in Sept. 2000~ \cite{pvcs}. 
The setup for the test beam was the following (see figure~\ref{trigsetup}): 
a beam counter upstream of the 
target (S); a beam veto counter (beam killer) in front of ECAL2, covering the 
hole for the deflected primary beam (B); a hodoscope 80\cm\ $\times$ 96\cm , 
situated in front of ECAL2 (H), displaced horizontally by 20\cm\ from the 
position of the deflected beam; a veto system around the target and the 
electromagnetic calorimeter (ECAL2). 


\begin{figure}[h]
        \centerline{\includegraphics[scale=0.8]{trigsetup.eps}}
        \sl\caption{\small Trigger setup for the Primakoff measurement in 
COMPASS. 
	It consits of 
	a beam counter (S), beam veto counter (B), a hodoscope (H), a veto system around
	the target and the electromagnetic calorimeter (ECAL2).}
    \protect\label{trigsetup}
\end{figure}

 According to the signature of the 
reaction, a beam particle is expected in S. 
Particles scattered by the target, should give a signal in H. 
No signal should be registered in the beam killer B, but a highly energetic
photon 
should be detected in ECAL2. 
The test beam demonstrated that an acceptable rate for the trigger can be achieved. 
The requirements to achieve this rate are the following: the coincidence between the 
energy deposition in the ECAL2 above a threshold of 
0.2 to 0.3$\times E_{beam}$ and the 
existence of a charged particle in the corresponding acceptance of H. 
The use of the beam killer B and of the veto counter does not improve much the rate 
reduction. The target veto could be used offline 
to reject background reactions with large momentum transfer to the target. 

Some interesting numbers that are quoted include the following:
from a beam intensity of $6\cdot 10^{6}$/spill with a 3\mm\ lead target, 
the trigger rate was found to be 2.5 $\times 10^5$/spill. The trigger
gives a reduction factor of 
24. The idea of the trigger is not to reduce too strongly the number of events 
since this will be done offline when analysing the events.
The size of the hodoscope needed to cover the acceptance of the simulated 
scattered pions was calculated by plotting the simulated hit distribution of the 
scattered pions at the position where the hodoscope will be situated. 
Figure~\ref{trighod} shows that the size needed for the hodoscope is 1
meter 
in horizontal direction and 40 cm. in vertical direction. 

\begin{figure}[h]
%        \centerline{\includegraphics[scale=1]{trighod.eps}}
\centerline{\epsfig{file=trighod.eps,width=7cm,height=5cm}}
        \sl\caption{\small Simulated hit distribution 
of the scattered pion at 30 meters 
			from the target. The lines indicate the possible size of
			the trigger hodoscope.}
    \protect\label{trighod}
\end{figure}

\subsection{Beam Requirements}

In COMPASS, two beam Cherenkov detectors (CEDARS) far upstream of the target
provide $\pi/K/p$ particle identification (PID). The incoming hadron momentum
is measured in the beam spectrometer. Before and after the target, charged
particles are tracked by high resolution silicon tracking detectors. The
measurement of both initial and final state momenta provides constraints to
identify the reaction. The final state pion and $\gamma$ momenta are
measured downstream in the magnetic spectrometer and in the $\gamma$
calorimeter, respectively.  These measurements allow a precise determination
of the small p$_T$ kick to the target nucleus, the main signature of the
Primakoff process, and the means to separate Primakoff from
meson  exchange
scattering events.

We can get quality statistics for the pion study with high beam intensities at
the CERN SPS.  We will take data with different beam energies and
targets, with
both positive and negative beams, as part of efforts to control systematic
errors. We can take data with the muon beam also for muon Primakoff
Compton
scattering, to test our methodologies, and to provide a comparison later of 
pion Primakoff Compton scattering (depending on pion polarizability) with
respect to muon
Primakoff Compton scattering (with zero muon polarizability).

\subsection{Target and Target Detectors\label{sec:target}}

The target platform is moveable and allows easy insertion of a normal solid
state target, e.\,g.\ a cylindric lead plate 40\mm\ in diameter and 3\mm\ in
width. We also plan Primakoff scattering on nuclei with Z$<82$ to check the
expected Z$^2$ cross section dependence. We use silicontracking detectors
before and immediately after the targets.  These are essential for Primakoff
reactions as the scattering angle has to be measured with a precision
of order 100 $\mu$rad, because it contains much of the
information.  We veto target
break-up events by a target veto recoil detector, and by selecting low-t
events in the off-line analysis. The recoil detector is currently developed
and tested. A particle momentum of about 100\mev\ should be sufficient to
trigger a veto coincidence in its scintillator and Lead glass layers. This
veto will limit the angular acceptance to about 100\mrad\ to reject events
where fragments of the nucleus or particles produced in diffractive processes
leave the target with bigger angles to the beam axis.

\subsection{The Magnetic Spectrometer and the t-Resolution}

We achieve good momentum resolution for the incident and final state pions and
$\gamma$'s, and therefore good four momentum t-resolution.  The relative
momentum resolution for \Ppim\ with all interactions accounted for is 1\% for
energies above 35\gev\ and up to 2.5\% below this mark. The angular resolution
in a single coordinate for a pion of momentum p is 7.9 mrad-Gev/p. All
generated pions with energy greater than 2\gev\ were in the acceptance of the
spectrometer, the reconstruction efficiency with interactions enabled is 92\%.

The angular resolution for the final state $\pi$ is controlled by minimizing the
multiple scattering in the targets and detectors. With a lead target of 1\%
interaction length (2 g/cm$^2$,~30\% radiation length), multiple Coulomb
scattering (MCS) of the beam and outgoing pion in the target gives an rms
angular resolution of order 40 $\mu$rad, small compared to the intrinsic
tracking detector angular resolution. The target contributes to the resolution
of the transverse momentum p$_T$ via the p$_T$ generated through MCS.  
Considering $t~=~p_T^2$, including all other effects \cite{cd,bormio,tm}, we
aim for a p$_T$ resolution less than 15 MeV, corresponding to $\Delta t$ better
than $\approx$ 2.5 $\times 10^{-4}$ GeV$^2$.

This resolution will allow an effective t-cut to minimize contributions to the
data from diffractive processes. The goal is achievable, based on the t
distributions measured at a 200 GeV low statistics, high resolution experiment
for $\pi^- Z \rightarrow \pi^- \pi^0 Z$ \cite{jens} and $\pi^- Z \rightarrow
\pi^-
\gamma Z$ \cite{ziel} Primakoff scattering at 200 GeV at FNAL. The t
distribution of the $\pi^- \rightarrow \pi^- \gamma$ data agrees well with the
Primakoff formalism out to t~=~$10^{-3}$ GeV$^2$, which indicates that the
data are indeed dominated by Coulomb production. Minimum material (radiation
and interaction lengths) in COMPASS will also give a higher acceptance, since
that allows $\gamma$'s to arrive at ECAL2 with minimum interaction losses, and
minimum $e^+e^-$ backgrounds.

\subsection{The $\gamma$ Calorimeter ECAL2}

The position resolution in the second $\gamma$ calorimeter ECAL2 for the photon
is 1.0\mm\ corresponding to an angular resolution of 30\murad. In the
interesting energy range the energy resolution is better than 1\% after taking
into account the leakage into the hadron calorimeter HCAL. The photon acceptance
is 98\% due to the beam hole of ECAL2 while the reconstruction efficiency is
58\% as a result of pair production within the spectrometer.

This $\gamma$ detector is equipped with 3.8 by 3.8 cm$^2$ GAMS lead glass blocks
to make a total active area of order 1.5 m diameter.  The central area needed
for the polarizability measurement is only 30$\times$30 cm$^2$, and is already
completely instrumented with modern ADC readouts.

The p$_T$ kicks of the COMPASS magnets are 0.45 GeV/c for SM1 (4 meters from
target) and 1.2 GeV/c for SM2 (16 meters from target).  The fields of both
magnets are set $\it{additive}$ for maximum deflection of the beam from the zero
degree (neutral ray) line.  We thereby attain at least 10 cm for the distance
between the zero degree line and the hole edge. This is important since the
Primakoff $\gamma$'s are concentrated around the zero degree line and a good
$\gamma$ measurement requires clean signals from 9 blocks, centered on the hit
block.  From MC simulations, the number of Primakoff scattered pions below 40
GeV is less than 0.3\%, so that 40 GeV pions are about the lowest energy of
interest.

\section {Simulation Results for 190  GeV Pion Beam}

 The most recent COMPASS Primakoff polarizability simulation results 
\cite {sans,kuhn,mlc}
are given now.
We evaluated the single particle detection properties of
the \compass\
spectrometer. The key results are
a momentum resolution for pions of 1\% above 35\gev\ and up to 2.5\%
below 35\gev\ accompanied by an angular resolution of $7.9\mrad\gev/p$
and an energy resolution for photons of 1.5\% above 90\gev\ 
accompanied by an angular resolution of 30\murad. 
The photon
reconstruction inefficiency is given by the conversion probability
before leaving the second spectrometer magnet; the corresponding
efficiency is 58\%. The single pion reconstruction efficiency is about
92\%.

We describe the results of the simulation of Primakoff Compton scattering and of
hadronic backgrounds. We study the influence of the COMPASS detector resolutions
and reconstruction algorithms on the extraction of the polarizabilities.  We
achieve this via a simulation of Primakoff Compton scattering of \Ppim\ on Lead
at a beam energy of 190\gev\ at five different pairs of
$\bar\alpha$ and
$\bar\beta$ 
polarizability parameters with a total statistics of five times 620,000
events, each
sample corresponding to the analyzed events from roughly a day of \compass\ data
taking.

The following cuts are used to recognize Primakoff events: there has
to be a photon hit in the ECAL2 above a certain energy and a negative
charged track which carries the complementary energy. The cut on the
photon energy has to be well above the energy deposition of hadrons in
the electromagnetic calorimeter that is of the order of some\gev. In
order to select the so-called ``hard events'' with most information on
the pion polarizabilities, this cut is raised to 30--50\% of the beam
energy.  In this simulation a cut on the photon energy at 90\gev\ was
implemented in the generator, so it was natural to use 80\gev\ in the
reconstruction. The energy window for the sum of pion and photon was
set to 180--196\gev\ to allow for the longitudinal energy leakage of
ECAL2. The figures 5-8 were all produced only with the events that were
left after applying these two cuts. 


The reconstructed count rates have to be corrected for the inefficiency of the
detector before fitting the cross section.  The data of all five samples are
merged to calculate the dependence of the reconstruction efficiency on the
photon energy in the laboratory frame. \Figref{sim:rec:photon} shows the
generated and---with the cuts applied---the reconstructed photon energy in the
laboratory frame, \figref{sim:rec:eff} shows the corresponding efficiency with
fit parameters. As expected from our studies of single photon and pion
efficiencies, the overall efficiency is between 50-55\%. Fig. 7 shows the
beam energy distribution used in the simulation. 


Compared to the generated $t=\lvec q^2$ distribution,
the reconstructed $\lvec q^2$ is smeared out 
due to the transverse momentum transfer error induced
by angle reconstruction errors of the final state.  For example, quadratically
adding the errors for 110\gev\ photon energy and 80\gev\ pion momentum yields an
error of 15\mev. 
Nevertheless the rise is steep enough to permit a cut at
$-\lvec q^2<1000\mev^2$, as seen in Fig. 8. Such a cut only reduces the
efficiency by 6\%.

 We studied the efficiency for the selected events with small $t$ and where the
sum of the energy of the $\pi^-$ and the $\gamma$ is, within some resolution,
equal to the energy of the beam.  We found that this efficiency was independent
of $t$, with no bias by the acceptance of the detector. Regardless of the cut in
$t$, the important shape of the $\gamma \pi$ angular distribution is not
affected.

\twoplots{egamma.eps}{Photon energy in the laboratory
  frame}{generated (white) and re\-con\-struc\-ted (shaded) photon
  energy in the laboratory frame. The data of all five samples is
  merged ($2.9\cdot10^6$ events)}{sim:rec:photon}
{efficiency.eps}{Reconstruction efficiency for
  Primakoff}{reconstruction efficiency vs. photon energy in the
  laboratory frame. The error bars are the binomial errors
  corresponding to the generated statistics shown in the left hand
  plot}{sim:rec:eff}

\twoplots{beam.eps}{Reconstructed beam
  energy}{reconstructed beam energy}
{sim:rec:beam}{tRC.eps}{Four-momentum transfer: $\lvec
  q^2$}{generated (white) and re\-con\-struc\-ted (shaded) $\lvec
  q^2$}{sim:rec:q2}



%-----------------------------------------------------------------
\subsection{Retrieving the polarizabilities}
%-----------------------------------------------------------------

The generated and reconstructed
four-momenta are transformed to the projectile (alab) frame. 
The fit is performed using the \ROOT\ interface to the MINUIT
package. 
To get the reconstructed differential cross section the event rates
had to be corrected for the inefficiency of the detector.
We observe that $\oalpha$ and $\obeta$ are anti-correlated, with the consequence
that  
$\oalpha+\obeta$ is determined with a much smaller error than
$\oalpha-\obeta$. The polarizability
effect is proportional to $\oalpha+\obeta$ for $\cos\theta=1$ and
$\oalpha-\obeta$ for $\cos\theta=-1$, increasing with the photon
energy like $\omega^2$. So $\oalpha-\obeta$ is mostly determined in
the region with least events while $\oalpha+\obeta$ is better known
because the cross section has a steep rise towards positive
$\cos\theta$.

  We carried out fits to determine the polarizabilities for each sample of
620,000 simulated events, each sample corresponding to different 
($\oalpha$,$\obeta$) pairs. Reducing the statistical errors by 8, scaling to
the
assumed  
4. $\times 10^{7}$ events, we estimate 
the statistical uncertainties for the two month COMPASS run to be about 0.05
for $\oalpha$ and $\obeta$, 0.01 for
$\oalpha+\obeta$ and 0.1 for $\oalpha-\obeta$. Including systematic
uncertainties, we aim to achieve better than 0.4 uncertainties in
$\oalpha$ and $\obeta$.

%-----------------------------------------------------------------
\subsection{The hadronic background}
%-----------------------------------------------------------------

To investigate the corruption of the measured Primakoff cross section
by hadronic background events, a large sample of minimum bias events
was produced with the Fritiof pion-Nucleus event generator. 
The analysis of $4.5 \times 10^6$  events by the exact
process described above accepts only 34 events, 27 of them were in the
fit range for the polarizabilities \cite{kuhn}.

As Fritiof only simulates hadronic interaction the mechanism for accepting
some of the events is the production of \Ppiz\ or \Peta. Because of the cut
on the total energy sum of the pion and the photon, most of this background is
rejected, as the remaining particles also receive their part of the energy.
One may tighten this cut because the background would be much more affected
than the real events.

The generated final state in all 34 cases contains a nucleon. This suggests
that the nucleus was disintegrated in the reaction. The fragments are tracked
by \comgeant, but there is no single particle ID to label them. Thus, they
unfortunately are not part of the list of particles emerging from the primary
vertex. Every event contains particles with polar angles bigger than
20\degree\, and a target recoil would see some of those events not stopped
inside the target.

The overall signal to noise ratio for hadronic background can be estimated from
the ratio of the cross sections and the background suppression. The hadronic
interaction length of Lead of $194\g\cm^{-2}$ corresponds to a cross section of
1.77\b, the suppression factor of 26/4500000 reduces this to 10\mub. This has to
be compared to the cross section of Primakoff Compton scattering---with a
produced photon energy of at least 90\gev---of about 500\mub. The ratio of 50:1
will be further improved by the inclusion of the target recoil veto and by a more
sophisticated kinematics reconstruction.

\section{Conclusions}

COMPASS
is on track to measure the $\gamma\pi$ Compton 
scattering cross sections, as a central part of its Primakoff
physics program, thereby enabling determinations of the pion 
polarizabilities. The experiment will allow serious tests of $\chi$PT;
and of different available polarizability calculations in
QCD. 


\section {Acknowledgments} 
 
This research was supported in part by the Israel Science Foundation founded by
the Israel
Academy of Sciences and Humanities.  



%\newpage
\begin{thebibliography}{99}



\bibitem {trieste} International Workshop on Hadron Structure and Hadron
Spectroscopy, Trieste, Italy, Feb. 2002, 
http://www.ts.infn.it/conferences/iwts2002/

\bibitem{paul}
F. Bradamante, S. Paul et al., CERN Proposal COMPASS,\\
http://wwwcompass.cern.ch/, CERN/SPSLC 96-14, SPSC/P297; CERN/SPSLC 96-30,\\
SPSC/P297, Addendum 1;  
http://www-nuclear.tau.ac.il/$\sim$murraym/primaphysreps.html

\bibitem{cd}
M. A. Moinester, V. Steiner, Pion and Kaon Polarizabilities and
Radiative Transitions,\\ Proc. `Chiral Dynamics Workshop' 
U. Mainz, Sept. 1997, hep-ex/9801008. 

\bibitem{bormio}
M. A. Moinester, V. Steiner, S. Prakhov, Hadron-Photon
Interactions in COMPASS,\\ 
Proc. XXXVII Meeting on Nuclear Physics, Bormio,
Italy, Jan. 1999, hep-ph/9910039

\bibitem{tm}
M. A. Moinester, Pion Polarizabilities and Hybrid Meson
Structure at COMPASS,\\ Contribution to the APS DNP Town Meeting on
Electromagnetic \& Hadronic Physics, \\Dec. 2000, Newport News, Va.,
hep-ex/0012063

\bibitem {of} A. Olchevski, M. Faessler, M. A. Moinester, Experimental
Requirements for COMPASS
Initial\\
Primakoff Physics Program, COMPASS Collaboration Meeting presentations, 
1999-2002.

\bibitem{hols1}
B. R. Holstein, {\em Comments} \Journal{\NPP}{19}{239}{1990}.

\bibitem{buergi} U. Burgi, Nucl. Phys. B479 (1996) 392; Phys. Lett. B377
(1996) 147.

\bibitem{babu2}
D. Babusci, S. Bellucci, G. Giordano, G. Matone,
A. M. Sandorfi, M. A. Moinester,\\ \Journal{\PLB}{277}{158}{1992}.

\bibitem{anti1}
Yu. M. Antipov et al., \Journal{\PLB}{121}{445}{1983},
\Journal{\ZPC}{26}{495}{1985}.

\bibitem{jens} 
T. Jensen et al., \Journal{\PRD}{27}{26}{1983}.

\bibitem{ziel}
M. Zielinski et al., \Journal{\PRL}{52}{1195}{1984}.

\bibitem{galp}
A. S. Galperin et al., \Journal{\SJNP}{32}{545}{1980}.

\bibitem{xsb} 
L. Xiong, E. Shuryak, G. Brown, \Journal{\PRD}{46}{3798}{1992}.

\bibitem {qgp} M. A. Moinester, Pion Polarizability, Radiative
Transitions, and Quark Gluon Plasma Signatures,
Chiral Dynamics Workshop, M.I.T., July 1994, hep-ph/9410215. 

\bibitem {ev} D. Ebert, M. K. Volkov, Phy. Atom. Nucl. 60 , 796 (1997). 

\bibitem {gb} G. Backenstoss et al., \Journal{\PLB}{43}{431}{1973}.  

\bibitem{gass1}
J. Gasser and H. Leutwyler, \Journal{\NPB}{250}{465}{1985}. 

\bibitem{va}
V. Alexakhine et al., COMPASS GEANT (COMGEANT),\\
http://valexakh.home.cern.ch/valexakh/wwwcomg/index.html 

 
\bibitem{pol}
M. Buenerd, Nucl. Instr.  Meth. A136
(1995) 128; V. Steiner, M. A. Moinester, M. Buenerd,\\ POLARIS, A Monte Carlo
event generator for polarizability experiments, 1995, unpublished.
 
\bibitem {ak} A. Akhundov, S. Gerzon, S. Kananov, M.A. Moinester,
Z. Phys. 66C (1995)279.                                             

\bibitem{starkov}
N. I. Starkov et al. \Journal{\SJNP}{36}{1212}{1982}.

\bibitem{pvcs} A Sadovski et al., Test beam studies for a trigger for a Primakoff
measurement,\\ COMPASS collaboration meeting, Oct. 2000, Dubna, Russia.  
  
\bibitem{sans} M. Sans Merce, Ph.D. thesis, Ludwig Maximilians University,
Munich, 2001.

\bibitem{kuhn} R. Kuhn, Diploma thesis, Technical University, Munich, 2001.

\bibitem{mlc} M. Colantoni et al., Proc. XL Meeting on Nuclear Physics, Bormio,
Italy, Jan. 2002.




%
\end{thebibliography}

\end{document}


 


    

hep-ex0206038.extracted_bib
\begin{thebibliography}{99}



\bibitem {trieste} International Workshop on Hadron Structure and Hadron
Spectroscopy, Trieste, Italy, Feb. 2002, 
http://www.ts.infn.it/conferences/iwts2002/

\bibitem{paul}
F. Bradamante, S. Paul et al., CERN Proposal COMPASS,\\
http://wwwcompass.cern.ch/, CERN/SPSLC 96-14, SPSC/P297; CERN/SPSLC 96-30,\\
SPSC/P297, Addendum 1;  
http://www-nuclear.tau.ac.il/$\sim$murraym/primaphysreps.html

\bibitem{cd}
M. A. Moinester, V. Steiner, Pion and Kaon Polarizabilities and
Radiative Transitions,\\ Proc. `Chiral Dynamics Workshop' 
U. Mainz, Sept. 1997, hep-ex/9801008. 

\bibitem{bormio}
M. A. Moinester, V. Steiner, S. Prakhov, Hadron-Photon
Interactions in COMPASS,\\ 
Proc. XXXVII Meeting on Nuclear Physics, Bormio,
Italy, Jan. 1999, hep-ph/9910039

\bibitem{tm}
M. A. Moinester, Pion Polarizabilities and Hybrid Meson
Structure at COMPASS,\\ Contribution to the APS DNP Town Meeting on
Electromagnetic \& Hadronic Physics, \\Dec. 2000, Newport News, Va.,
hep-ex/0012063

\bibitem {of} A. Olchevski, M. Faessler, M. A. Moinester, Experimental
Requirements for COMPASS
Initial\\
Primakoff Physics Program, COMPASS Collaboration Meeting presentations, 
1999-2002.

\bibitem{hols1}
B. R. Holstein, {\em Comments} \Journal{\NPP}{19}{239}{1990}.

\bibitem{buergi} U. Burgi, Nucl. Phys. B479 (1996) 392; Phys. Lett. B377
(1996) 147.

\bibitem{babu2}
D. Babusci, S. Bellucci, G. Giordano, G. Matone,
A. M. Sandorfi, M. A. Moinester,\\ \Journal{\PLB}{277}{158}{1992}.

\bibitem{anti1}
Yu. M. Antipov et al., \Journal{\PLB}{121}{445}{1983},
\Journal{\ZPC}{26}{495}{1985}.

\bibitem{jens} 
T. Jensen et al., \Journal{\PRD}{27}{26}{1983}.

\bibitem{ziel}
M. Zielinski et al., \Journal{\PRL}{52}{1195}{1984}.

\bibitem{galp}
A. S. Galperin et al., \Journal{\SJNP}{32}{545}{1980}.

\bibitem{xsb} 
L. Xiong, E. Shuryak, G. Brown, \Journal{\PRD}{46}{3798}{1992}.

\bibitem {qgp} M. A. Moinester, Pion Polarizability, Radiative
Transitions, and Quark Gluon Plasma Signatures,
Chiral Dynamics Workshop, M.I.T., July 1994, hep-ph/9410215. 

\bibitem {ev} D. Ebert, M. K. Volkov, Phy. Atom. Nucl. 60 , 796 (1997). 

\bibitem {gb} G. Backenstoss et al., \Journal{\PLB}{43}{431}{1973}.  

\bibitem{gass1}
J. Gasser and H. Leutwyler, \Journal{\NPB}{250}{465}{1985}. 

\bibitem{va}
V. Alexakhine et al., COMPASS GEANT (COMGEANT),\\
http://valexakh.home.cern.ch/valexakh/wwwcomg/index.html 

 
\bibitem{pol}
M. Buenerd, Nucl. Instr.  Meth. A136
(1995) 128; V. Steiner, M. A. Moinester, M. Buenerd,\\ POLARIS, A Monte Carlo
event generator for polarizability experiments, 1995, unpublished.
 
\bibitem {ak} A. Akhundov, S. Gerzon, S. Kananov, M.A. Moinester,
Z. Phys. 66C (1995)279.                                             

\bibitem{starkov}
N. I. Starkov et al. \Journal{\SJNP}{36}{1212}{1982}.

\bibitem{pvcs} A Sadovski et al., Test beam studies for a trigger for a Primakoff
measurement,\\ COMPASS collaboration meeting, Oct. 2000, Dubna, Russia.  
  
\bibitem{sans} M. Sans Merce, Ph.D. thesis, Ludwig Maximilians University,
Munich, 2001.

\bibitem{kuhn} R. Kuhn, Diploma thesis, Technical University, Munich, 2001.

\bibitem{mlc} M. Colantoni et al., Proc. XL Meeting on Nuclear Physics, Bormio,
Italy, Jan. 2002.




%
\end{thebibliography}