# Accession Number:

## AD0621334

# Title:

## REAL PART OF THE SCATTERING AMPLITUDE AND THE BEHAVIOR OF THE TOTAL CROSS SECTION AT HIGH ENERGIES,

# Descriptive Note:

# Corporate Author:

## FLOYD NEWMAN LAB OF NUCLEAR STUDIES CORNELL UNIV ITHACA N Y

# Personal Author(s):

# Report Date:

## 1964-09-21

# Pagination or Media Count:

## 10.0

# Abstract:

Certain theorems first pointed out by Meiman are used to include the information contained in analyticity in energy and crossing symmetry in the derivation of upper bounds for the forward scattering amplitude. Theorems are obtained relating the asymptotic behavior of the ratio of the real part to the imaginary part of the forward amplitude on the one hand, to that of the total cross section on the other. Except for the special case where RefImfpilnE as the incident laboratory energy E approaches infinity, it is found that the Froissart bound can be improved. It is found that the GreenbergLow bound which follows from axiomatic field theory can always be improved by a fractional power of E under the physical assumption that the amplitude does not become purely real as E approaches infinity. It is found that the asymptotic behavior RefcE is not allowed. This sheds light on the question of the elementary nature of vector mesons. An inequality is given which, in principle, could lead to an experimental check of analyticity and crossing with data obtained only from a finite range of energy. Author