Zeros of the multiparticle generating function in hadronic scattering models
Feynman and Wilson have proposed an analogy between the physics of multiparticle production and the description of a gas of molecules in statistical mechanics. The zeros of the grand partition function are known to play an essential role in the thermodynamic description of a gas. Motivated by the Feynman-Wilson gas analogy, Khuri has recently shown that the zeros of the multiparticle generating function play an equally important role in hadronic scattering. In particular, Khuri has shown that hadronic theories satisfying unitarity and the Froissart bound and having a nonshrinking nearest zero of the multiparticle generating function will have an improved Froissart bound on the total hadronic cross section. The improvement of the bound resulting from a nonshrinking nearest zero is essentially from ln(s/s$sub 0$$)$$sup 2$ to ln(s/s$sub 0$). This work applies a number of mathematical techniques of statistical mechanics to study the behavior of the nearest zero of the multiparticle generating function in a general class of hadronic production models. Sufficient conditions are found which control the shrinkage of the nearest zero in production models with general, multibody interactions. The reduction of the conditions to the simpler case of two-body interactions and the physical interpretation of the sufficient conditions are discussed. Multiperipheral models are shown to be a small subclass of the two-body interaction models. (AIP)
- Research Organization:
- The Rockefeller University, New York, New York 10021
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-33-031359
- OSTI ID:
- 4018219
- Journal Information:
- Phys. Rev., D, v. 13, no. 2, pp. 315-328, Journal Name: Phys. Rev., D, v. 13, no. 2, pp. 315-328; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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