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A construction of functions that satisfy crossing symmetry and unitarity

Research paper by J. Kupsch

Indexed on: 21 Jan '16Published on: 21 Jan '16Published in: Il Nuovo Cimento A (1971-1996)



Abstract

We construct π0π0 amplitudes with arbitrary polynomial increase in the double spectral region that satisfy crossing symmetry and the inelastic-unitarity bounds Imfl(s)−|fl(s)|2⩾0,l=0, 1, 2, ..., for alls>4. Exact elastic unitarity is then obtained by an iteration procedure which was proposed by Mandelstam and discussed in detail by Atkinson. The resulting amplitude which fulfils crossing symmetry, elastic unitarity and the unitarity bounds in the inelastic region is the sum of Regge terms with bounded trajectories and a once-subtracted Mandelstam representation which guarantees the unitarity of the whole amplitude.