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The Fubini-Furlan-Rossetti sum rule

The Fubini-Furlan-Rossetti sum rule. LET.   (k). i. Pion Photoproduction.  + N !  + N. Lorentz invariance, and P , C and T symmetries:. 4 Lorentz invariant functions of  = (s-u)/4M N and t. soft pion limit. the contribution from is zero.

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The Fubini-Furlan-Rossetti sum rule

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  1. The Fubini-Furlan-Rossettisum rule

  2. LET

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

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

  5. Dispersion Relations at fixedt soft pion limit ( = 0, t =0 ) LET

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

  7. Corrections from physical pion mass as function of  at fixed FFR Sum Rule Fubini, Furlan, Rossetti, Nuovo Cimento 43 (1966) 161 FFR discrepancy Heavy Baryon Chiral Perturbation Theory HBChPT Dispersion Relation with Im A1 from MAID2003

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

  9. extrapolation to the unphysical region

  10. FFR Discrepancy  from HBChPT(heavy baryon chiral perturbation theory ) Dispersion integral at fixed t=tthr with Im A1 from MAID03

  11. p, -n 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 (p4) P waves at O(p3) S and P waves at O (p4)

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

  13. S + S = -0.16 S + S = -0.20 V + V = 3.48 V + V = 4.68 Integrands from MAID03 t = tthr third resonance region D13(1520) loops  (1232) loops third resonance region

  14. PROTON Bernard, et al., ZPC70 (1996) HBChPT at O(p3) t = tthr Bernard, et al., PLB378 (1996) HBChPT at O(p3) Bernard, et al. EPJ A11 (2001) HBChPT at O(p4) DR-MAID Mainz experiment,Schmidt, et al., PRL 87 (2001)

  15. NEUTRON t = tthr Bernard, et al., ZPC70 (1996) HBChPT at O(p3) Bernard, et al., PLB378 (1996) HBChPT at O(p3) Bernard, et al. EPJ A11 (2001) HBChPT at O(p4) DR-MAID

  16. 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:(, tthr) • good agreement between MAID and HBChPT in the threshold region ( = thr) • problems at low  < thrbecause of the non-relativistic approximation of HBChPT

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