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The Pomeranchuk Singularity in a Class of Reggeon Field Theories Suggested by Direct Channel Unitarity

Apr, 1974
23 pages
Published in:
  • Phys.Rev.D 10 (1974) 6, 1939
  • Published: Sep 15, 1974
DOI:
Report number:
  • NAL-PUB-74-036-THY,
  • NAL-PUB-74-36-THY,
  • FERMILAB-PUB-74-036-T
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197319741975023
Abstract:
ithin the context of a generalized Reggeon calculus we study the infrared J→1,t→0 limit of a class of models whose "bare" structure arises from elastic amplitudes of the form A(s,t)=s(lns)νJν(a−t−−√lns). Such amplitudes are suggested by the implementation of s-channel unitarity via eikonalization of a "Born term," via absorption models, and via the multiperipheral bootstrap. We employ the renormalization group to study the renormalized Pomeranchuk singularity when the interaction involves a triple coupling. Our major result is that for ν=0 these theories are infrared-free. The total cross section behaves as σT(s)∼γ1−γ2[(lns)(lnlns)12], where γ1 factorizes. Scaling laws for the Reggeon proper vertex functions are given.