Gundzik, M. G. ; Sudarshan, E. C. G. (1972) Some consequences of a piecewiseanalytic scattering amplitude Physical Review D  Particles, Fields, Gravitation and Cosmology, 6 (3). pp. 798806. ISSN 15507998

PDF
 Publisher Version
1MB 
Official URL: http://prd.aps.org/abstract/PRD/v6/i3/p798_1
Related URL: http://dx.doi.org/10.1103/PhysRevD.6.798
Abstract
In the indefinitemetric quantum field theory formulated by one of the authors and in related work the scattering amplitude does not satisfy the usual Mandelstam analyticity. It becomes piecewise analytic at the threshold for the production of at least one of the negativemetric particles of the theory, i.e., the amplitude above the threshold is not the analytic continuation of the amplitude. Some consequences of such a piecewiseanalytic scattering amplitude are investigated. The physical twobody scattering amplitude G(s, t) is taken to be of the form G(s, t)=F(s, t)+h_{1}(s, t)θ(ss_{0})+h_{2} (s, t)θ(tt_{0})+h_{3}(s, t)θ(uu_{0}), where F(s, t) and the h_{i}(s, t) are analytic functions of s and t with the negativemetric thresholds occurring at s=s_{0}, t=t_{0}, and u=u_{0} in the s, t, and u channels, respectively. The modified forms of the Pomeranchuk theorem, dispersion relations, and finiteenergy sum rules due to this general form of piecewise analyticity are derived and the interpretation of experimental results in terms of them are discussed. In particular, the modified forward dispersion relations for π^{+}p and π^{−}p scattering differ from the normal forms by a function ξ(ν) which depends on the piecewiseanalytic contributions h_{i}(s, t) above, where ν is the laboratory momentum of the pion. The forward dispersion relations for the symmetric and antisymmetric combinations of the real part of the π^{+}p and π^{−}p scattering amplitudes D^{+}(ν) and D^{−}(ν), respectively, are tested. The best fits to the latest total crosssection data for π^{±}p scattering from 8 to 65 GeV/c which do not satisfy the Pomeranchuk theorem are used. No test for D^{−}(ν) which must be twice subtracted is possible since it depends strongly on the πN coupling constant f^{2} which is itself determined by dispersion relations. The result for D^{+}(ν) allows for a violation, but the evidence is not compelling.
Item Type:  Article 

Source:  Copyright of this article belongs to The American Physical Society. 
ID Code:  51055 
Deposited On:  27 Jul 2011 12:42 
Last Modified:  18 May 2016 05:08 
Repository Staff Only: item control page