1. José Antonio Oller Universidad de Murcia. Spain. In collaboration with L. Roca (Murcia), C. Schat (Murcia; CONICET and U.Buenos Aires, Argentina) TexPoint fonts used in EMF: A AA A AA A A A AA A AA A AA A AA 1.Scalar radius of the pion. Introduction. 2.Dispersion relation. Omnès representation. Watson’s final state theorem. 3.Ynduráin’s approach. 4.Extended method. 5.Results. Conclusions I. 6.. Introduction. 7.Dispersive Approach. 8.. 9.Conclusions II.

2. 1. Introducion The non-strange I=0 pion scalar form factor:

4. Consequences in the scattering lengths of CGL Yall :75 ± 0:07fm 2 \robust"lowerbound: h r 2 i ¼ s =0:70 ± 0:06fm 2

6. 2. Disperson Relations The pion non-strange scalar form factor

7. For the scalar form factor F(z) vanishes as 1/z because of QCD. (Brodsky-Farrar counting rules). Hard gluon 1/t t π π

8. One must first remove the zeroes (also the poles for the general case, not in the present one) of F(t) and consider the function

10. Corolary:

11. 3. Ynduráin’s method Weak point of the argument Not always compatible

13. From F.J.Ynduráin, PLB578,99(2004)

14. This approach was critized by Ananthanarayan, Caprini, Leutwyler, IJMP A21,954 (2006) (ACGL).

15. 4. Extended Y’s method L. Roca and J.A.O. Phys. Lett. B651,139(2007) arXiv:0704.0039 [hep-ph]

17. degrees 180 360

20. 5. Numerical Analysis

29. Explodes at around 1 GeV

42. No axial vector exchanges

48. 6. Multipion states Extremely small

57. One has then two channels diagonalized that are elastic

59. two loops