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4.1 Pion form factor

The pion form factor has been measured in a rather wide range of -values as shown in Fig.(2). The time-like region, , has been accurately explored by various -machines not only in the interesting region around the resonances, where and are large, but also at much higher -values. Experimental details and references can be seen in the reviews by Bauer et al [1] and Dolinsky et al [2]. The reaction (inverse electroproduction), on the other hand, allows to cover the lower -region just above .

For -values in the space-like region, good data are also available (most of them from elastic scattering, but also from the (-electroproduction) reaction ; see ref. [3], for details). Some of them are also shown in Fig.(2).

 
Figure 2: A plot of the pion form factor versus energy as determined from colliding beams, inverse electroproduction and electroproduction measurements. Details and fits can be found in ref.[1]  

All the gross features of these data are approximately explained by a simple -meson Breit-Wigner dominating this pion form factor. This reasonable simple-pole description clearly suggests and illustrates the success of naive vector-meson dominance models (VMD). Interesting modifications to this simple one-pole behaviour have been detected around the and peaks, showing again the relevance of vector-mesons even in isospin violating channels. Other structures seem to be present at higher energies as discussed in ref. [4]. At asymptotic energies, the Brodsky-Farrar quark counting rules, derived from QCD, predict the simple pole dependence [5].

From the well measured behaviour around , the pion charge radius can be defined. We quote the value

 

coming essentially from ref.[6] but coinciding with several independent measurements and their global mean value [7] with one exception: that coming from old data [8] on and leading to .

As far as Daphne is concerned, a high precision measurement of the pion form factor near the threshold, as well as in the region around the -meson, is crucial for reducing the theoretical error in the hadronic contribution to the muon anomalous magnetic moment (see Franzini's contribution to this chapter). Similarly, Daphne offers exceptional opportunities to improve the measurements of around the -peak. This is essential to understand the contaminations in the mainly -meson wave function.



next up previous
Next: 4.2 Kaon F.F. Up: 4 Pseudoscalar form factors Previous: 4 Pseudoscalar form factors



Carlos E.Piedrafita