next up previous
Next: References Up: 7 Models for form Previous: 7.1 VMD for near

7.2 Models for F.F. near and charge radii

Far from resonance peaks, the role played by V-mesons can be reproduced by other dynamical mechanisms. This is the case for charge radii and their related slope parameters, both defined around . In VMD, the previously discussed expressions for lead to simple formulae and reasonable values for the pseudoscalar charge radii

These values satisfy the VMD-relation but are only in rough agreement with data (eqs.(14) and (15)). The situation can easily be improved, as discussed in ref. [15], and extended to the transition F.F. and their slope parameters (b and ). In all these cases (the case is somehow exceptional, as we already discussed), the V-meson mass fixes correctly the scale with near .

But constituent-quark model ideas can also be useful in this field. A simple quark-loop gives finite predictions for charge radii, which are quite close to those from VMD provided the quark mass is fixed to , near the constituent quark-mass value (see, ref. [16] for details and related work). SU(3)-breaking can similarly be introduced through the mass difference. Further reasonable predictions are also known for the slope parameters [16] thus supporting the general idea of - or QCD-duality, i.e., that VMD (or mesonic) contributions and (fermionic) quark-loop effects are somehow dual or equivalent and, in particular, cannot be added [18].

ChPT is, however, the more valid and QCD inspired approach to account for the pseudoscalar charge radii. The charge radius is unambiguously predicted to be near experiment. For charged pions and kaons one obtains reasonable values and the VMD-like relation . Improvements and further details can be found in ref. [15] in these proceedings.



Carlos E.Piedrafita