E01-004:  The Charged Pion Form Factor - II


The $\pi^+$ electric form factor, $F_{\pi}$, is a topic of fundamental importance to our understanding of hadronic structure.  The success of QCD sum rule calculations, constituent quark models, and Bethe-Salpeter equation approaches can all be tested in the difficult and poorly understood gap between the ``soft'' and ``hard'' regions at intermediate $Q^2$.  The pion holds a unique place in this regard, because its $q\bar{q}$ valence structure is 
relatively simple, and the asymptotic normalization of the wave function is known from $\pi\rightarrow\mu\nu$ decay.  

Our earlier E93-021 result extends the region of high quality $F_{\pi}$ data to 1.6 $(GeV/c)^2$.  $d\sigma_L/dt$ data were obtained in the kinematical region where the $t$-pole process is dominant.  Values for $F_{\pi}$ were extracted from the longitudinal cross section using a recently developed Regge model, and the data globally follow a monopole form obeying the pion charge radius.  No other precise data exist above $Q^2$=0.7 $(GeV/c)^2$.  Even at $Q^2=1.6$ $(GeV/c)^2$, the old Cornell $F_{\pi}$ values are widely scattered, and are not based on a true L/T separation.  The higher energy beam that is now available will allow us to perform high quality $F_{\pi}$ measurements with the existing Hall C instrumentation up to $Q^2=2.5$ $(GeV/c)^2$.  This is the region where the theoretical calculations for $F_{\pi}$ begin to diverge, and the data are used as input to several of the QCD-related models of $F_{\pi}$ to constrain the treatment of the soft contributions.

The higher-energy beam also allows us to perform high quality measurements at higher $W$ than in $93-021.  As the extraction of $F_{\pi}$ from the data inherently depend upon a model of the $p(e,e'\pi^+)n$ reaction, the higher $W$ is advantageous because it allows measurements to be taken closer to the $\pi^+$ pole than otherwise, where $t$-channel contributions dominate.  This higher $W$ will also allow the Regge model used in the extraction of the form factor from the $d\sigma_L/dt$ data to be applied with greater authority, resulting in a smaller anticipated model dependence to the obtained result.

Extending the range of reliable experimental data to higher $Q^2$ is clearly needed to delineate the role of hard versus soft contributions at intermediate $Q^2$, and so aid the further development and tests of the QCD-based models currently under development.  Our anticipated data up to $Q^2=2.5$ $(GeV/c)^2$ will be of sufficient quality to distinguish between at least a number of these models, and so will contribute effectively to our knowledge of hadronic structure.


Garth Huber
Department of Physics
University of Regina
Regina, SK S4S-0A2   CANADA
http://www.phys.uregina.ca/sparro/huber/
TEL: (306)585-4240
FAX: (306)585-5659