1. The Fubini-Furlan-Rossetti sum rule

8. LET

9. Pion Photoproduction    (k) i 4 Lorentz invariant functions of = (s-u)/4M N and t  + N !  + N Lorentz invariance, and P, C and T symmetries:

10. PCAC hypothesis current algebra Pion Low Energy Theorems soft pion limit LET for pion photoproduction Born with pseudovector coupling the contribution from is zero

11. Dispersion Relations at fixed t LET soft pion limit ( = 0, t =0 )

12. POLE BORN-PV obtained from tree-level Feynman diagrams:

13. FFR Sum Rule Fubini, Furlan, Rossetti, Nuovo Cimento 43 (1966) 161 Dispersion Relation with Im A 1 from MAID2003 HBChPT Corrections from physical pion mass as function of at fixed FFR discrepancy Heavy Baryon Chiral Perturbation Theory

16. pion threshold soft pion point physical region of pion photoproduction

17. extrapolation to the unphysical region

18. FFR Discrepancy  from HBChPT (heavy baryon chiral perturbation theory ) Dispersion integral at fixed t=t thr with Im A 1 from MAID03

19. EXP t =0) (t=t thr ) MAID03 ( t =0) (t=t thr ) HBChPT MAID03 Proton 1.793 1.792 1.662.29/2.33/2.37 2.24 Neutron 1.913 1.986 1.822.52/2.56/2.79 2.44 HBChPT: Bernard, Kaiser, Meissner, Z. Phys. C70 (1996) Bernard, Kaiser, Meissner, Phys. Lett. B378 (1996) Bernard, Kaiser, Meissner, Eur. Phys. J. A11 (2001) S wave at O (p 4 ) P waves at O(p 3 ) S and P waves at O (p 4 ) FFR +  ( thr, t thr ) FFR ( = 0,t=0 )  p, -n-n  (0, t thr )

20. neutron proton FFR discrepancy  from MAID03 Pasquini, Drechsel, Tiator, Eur. Phys. J A23 (2005) t = t thr

21. Integrands from MAID03 third resonance region D 13 (1520)  1232)  loops t = t thr  S +  S   S +  S =   V +  V =   V +  V = 

22. PROTON Bernard, et al., PLB378 (1996) HBChPT at O(p 3 ) Bernard, et al., ZPC70 (1996) HBChPT at O(p 3 ) DR-MAID Bernard, et al. EPJ A11 (2001) HBChPT at O(p 4 ) Mainz experiment, Schmidt, et al., PRL 87 (2001) t = t thr

23. NEUTRON Bernard, et al., ZPC70 (1996) HBChPT at O(p 3 ) DR-MAID Bernard, et al. EPJ A11 (2001) HBChPT at O(p 4 ) Bernard, et al., PLB378 (1996) HBChPT at O(p 3 ) t = t thr

24. Summary  FFR sum rule: relation between the anomalous magnetic moment and single pion-photoproduction on the nucleon in the soft pion limit (m  2 =0, =t=0)  Predictions at =, t=0 : extrapolation of MAID amplitudes in the unphysical region give very good results  p = 1.792 (exp: 1.793)  n = - 1.986 (exp: -1.913)  Corrections to the sum rule from the physical pion mass:  (, t thr ) good agreement between MAID and HBChPT in the threshold region ( = thr ) problems at low  thr because of the non-relativistic approximation of HBChPT