Corrections to Linear Trajectories from Dual Loop Amplitudes
Obvious non-unitarity of dual-resonant amplitudes is the reason for going to higher — order (loop) corrections with appropriate square-root threshold singularities. This accounts for unitarity in a perturbative way  which means that upon writing the connected part iR of the S-matrix as a sum over all these loop amplitudes the unitarity relation  is seen to split up into a perturbative series of relations where internal lines represent δ+(q2−m n 2 )≡θ(qo)δ(q2−m n 2 ), mn being the masses of the intermediate resonances.
KeywordsInternal Line Perturbative Series Intermediate Resonance Abelian Integral Trajectory Correction
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