Accession Number : AD0634706

Title :   HIGH ENERGY BEHAVIOUR OF SCATTERING AMPLITUDES AND CROSS SECTIONS USING CROSSING SYMMETRY AND HOLOMORPHY IN TWO VARIABLES.

Descriptive Note : Technical rept.,

Corporate Author : MARYLAND UNIV COLLEGE PARK DEPT OF PHYSICS AND ASTRONOMY

Personal Author(s) : Eden, R. J.

Report Date : DEC 1965

Pagination or Media Count : 8

Abstract : For a symmetric amplitude F+(Z,t) (for example the sum of positive pion-proton and negative pion-proton scattering amplitudes), where Z =E + t/4m and E is the centre of mass energy; crossing symmetry and hermitean analyticity lead to the relation, for Z real, F+(-Z +i0,t) = F+*(Z+i0,t). This is an exact relation and can be used to determine not only the phase of the leading term for large Z, but also of other terms except for ambiquities in sign, which are resolved by other conditions. In this paper smooth functions are used that involve powers of E or of log E for which one can easily show that if Imf+(E) = E exp. alpha, then f+(E) = +(-iE) exp. alpha C; IF Imf+(E) = (log E) exp beta, then f+(E) =+(log E -i(pi)/2) exp beta, scattering by Meiman. It is ma main purpose here to show how these results from crossing and analyticity in E can be combined with holomorphy in the variable t and temperedness in E within the domain of holomorphy. The method is a general one but its effect is most spectacular in the neighbourhood of the Greenberg-Low bound (Author)

Descriptors :   (*NUCLEAR SCATTERING, MATHEMATICAL ANALYSIS), (*NUCLEAR CROSS SECTIONS, MATHEMATICAL ANALYSIS), FIELD THEORY, GROUPS(MATHEMATICS), SPECIAL FUNCTIONS(MATHEMATICAL)

Subject Categories : Nuclear Physics & Elementary Particle Physics
      Quantum Theory and Relativity

Distribution Statement : APPROVED FOR PUBLIC RELEASE