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The Reggeon Calculus for α\alpha > 1

Sep, 1973
31 pages
Report number:
  • NAL-PUB-73-69-THY,
  • FERMILAB-PUB-73-069-T
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19731974197501
Abstract:
We study the Reggeon calculus when Reggeons have α\alpha(0) > 1 and vacuum quantum numbers . We sum all the Regge cuts in the weak coupling regime where the p Reggeon couplings rpr_p are small. The resulting amplitude saturates the Froissart bound provided the triple Regge coupling r3r_3 is dominant. In impact parameter space the amplitude is a uniform absorbing disk whose radius expands like ℓ\ellns . The leading asymptotic term factorizes even when there are arbitrary couplings of the external particles to many Reggeons. In the angular momentum plane the Pomeron is a pair of cuts on the trajectories αp(t)=1±2[α′(α−1)t]12\alpha_p (t) = 1 \pm 2 [ \alpha^{\prime} (\alpha - 1) t ] ^{\frac{1}{2}}