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\begin{document}

\title{
Precision Measurements of the Electromagnetic Properties of
Light Pseudoscalar Mesons at JLAB via the Primakoff Effect}

\author{A. Gasparian}

\address{
Department of Physics, Hampton University, Hampton, VA 23668, USA.}
\maketitle

The appearance of chiral anomaly and the prediction of the Goldstone
bosons 
due to spontaneous breaking of chiral symmetry are two basic
characteristics
of QCD at low energies. Understanding the properties of pseudoscalar
mesons, 
which involve both Goldstone bosons and the chiral anomaly, are
fundamentally 
important in confinement scale QCD. The three neutral pseudoscalar mesons
$\pi^0$, 
$\eta$ and $\eta'$, with the first two being Goldstone bosons, represent
one of 
the most interesting systems in low energy QCD.
This system contains fundamental information about the effects of SU(3)
and isospin 
breaking by the $u$, $d$, and $s$ quark masses, leading to important
mixing effects 
among the mesons, as well as two types of chiral anomalies. Therefore, 
a study of the two-photon decays of the $\pi^0$, $\eta$ and $\eta'$ and
their transition
form factors at very small $Q^2$ will allow  one to determine the $\eta$,
$\eta'$
mixing angle and one constant ${\cal O}(p^6)$ in the chiral Lagrangian,
providing
a test of the low energy limit of QCD in a relatively clean setting.

Because of the small mass of $\pi^0$ meson, the prediction of the chiral
anomaly for 
the $\pi^0 \rightarrow \gamma \gamma$ decay width is more accurate and
exact in the 
limit when the $u$- and $d$-quark masses vanish. In this limit the
predicted
decay width depends only on the number of color in QCD ($N_{c}$) and the
pion
decay constant ($F_{\pi}$)~\cite{Do92}:

\vspace{-0.45cm}
\begin{eqnarray}
\Gamma(\pi^0 \to \gamma\gamma) = (\alpha_{\rm em}^2 N_c^2 M_\pi^3) / 
 (576 \pi^3 F_\pi^2) 
%\nonumber
\end{eqnarray}

\vspace{-0.15cm}
However, the real world current-quark  masses are of the order of 5-7 MeV.
The total estimated value of corrections due to this explicit breaking of
chiral 
symmetry is at the level of $\sim$2\%~\cite{Do92}. Given the definite
precision of
the theoretical
prediction, it should be experimentally tested to a level of accuracy
which is 
consistent with theoretical uncertainties.

The PrimEx collaboration at Jefferson Lab is planning to perform a
precision measurement 
of the neutral pion lifetime using the small angle coherent
photoproduction of 
$\pi^0$'s in the Coulomb field of a nucleus, {\em i.e.}, the Primakoff
effect~\cite{E99-014}. 
This measurement will be a state-of-the-art experimental determination of
the 
lifetime with a precision of less than 1.5\%.

In the past, three general experimental techniques have been used to
access the neutral 
pion decay width: direct measurement of the lifetime, 
$\gamma \gamma$ collisions, and the Primakoff effect. 
The result from the most recent lifetime measurement~\cite{At85}
has the smallest quoted error ($\pm3.5\%$) and lies nearly two sigma 
below the value predicted from ChPT. 
It is interesting to note that the loop corrections ($\sim2\%$) tend 
to increase the predicted width. All Primakoff type of experiments so far
have been 
performed with bremsstrahlung beams and have a typical error about
$\sim10\%$~\cite{Br74}.
The present experimental knowledge of the $\pi^0$ lifetime is at the
$\sim7\%$ 
level. Therefore, the proposed measurement at the percent level will fill 
this important gap between theory and experiment.

The PrimEx experiment will use the Jefferson Lab Hall~B high intensity and
high 
energy CW tagged photon facility which will provide two distinct
advantages over 
previous experiments involving bremsstrahlung beams. First, the
quasi-monochromatic 
nature of the tagged beam will enable a clean kinematical separation of
the 
Primakoff mechanism from various background  processes, and secondly, the
tagging 
technique will enable significantly better control of systematic errors
associated 
with the photon flux normalization.
%
The primary experimental equipment
includes:~the Hall~B photon tagger, three 5\% r.l. solid $\pi^0$
production targets, 
a pair production luminosity monitor, and
an electromagnetic hybrid calorimeter (HYCAL) for the $\pi^0$ decay
photons, with
Pb-glass modules and a central insertion of high resolution PbWO$_4$
crystals.

We will take data with sufficient angular resolution to check the 
shape of the Primakoff peak. Three spin zero targets will be studied
($^{12}$C, $ ^{116}$Sn, and $^{208}$Pb). These nuclei have form 
factors which are well known and will
be used to test the $Z^{2}$ dependence of the cross section. 
The strong energy dependence of the cross section on $E_\gamma$ will be
measured 
in the range from 4.6 to 5.7 GeV. The study of the Primakoff peak
as a function of these three variables will be used to empirically
determine the systematic errors.

Currently, we are in the stage of preparation of the experimental setup.
We plan to have all detectors ready for the beam tests by the end of 
year 2001. We expect to have the first experimental data for the pion
lifetime 
in 2002.

With the 12 GeV CEBAF energy upgrade we will be able to perform the second 
part of this experimental program: radiative width and electromagnetic 
transition form factor measurements for the more massive $\eta$ and
$\eta'$
mesons~\cite{12gevprop}. This comprehensive program will provide
fundamental tests 
of both QCD and QCD inspired models.

\vspace{0.20cm}
\noindent
(This project is supported under NSF grant PHY-0079840.)

\vspace{-0.15cm}
\section*{References}

\vspace{-0.15cm}
\begin{thebibliography}{99}

\bibitem{Do92} J.F. Donoghue, {\it et al.}, {\it Dynamics of the Standard
Model}, (1992).

\bibitem{E99-014} Jefferson Lab proposal E99014
(url:~www.jlab.org/primex).

\bibitem{At85} H.W. Atherton {\it et al.}, \Journal{\PLB}{158}{81}{1985}.

\bibitem{Br74} A. Browman {\it et al.}, \Journal{\PRL}{33}{1400}{1974}.

\bibitem{12gevprop} See
url:~www.jlab.org/div\_dept/physics\_division/GeV.html.

\end{thebibliography}

\end{document}

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