Weakly model dependent pion form factor with physically interpretable parameters

Conclusion

We have constructed the pion form factor model satisfying fundamental principles, providing some freedom for the asymptotic behaviour and depending only on the adjustable parameters with a definite physical interpretation. The explicit incorporation of the pion form factor left-hand cut from the second Riemann sheet into a model was carried out for the first time. As a result we have described (contrary to the previous attempts [18, 19]) the pion form factor data from the range of momenta −9·770 GeV² ≦t ≦ 9·579 GeV² and data on theP-wave isovectorππ phase shift in the elastic region simultaneously with the adjustable parameters acquiring very reasonable values. The asymptotic behaviour was enforced by the data to be consistent with the naive quark model prediction. The calculated values of the pion charge radius as well as theP-wave isovectorππ scattering length coincide with the world averaged values. With regard to these positive features of our pion form factor model it can be employed for the reliable calculation (via unitarity) of theP-wave isovectorππ scattering partial amplitude outside the physical region, which could be useful in a saturation of various sum rules inππ scattering physics.