Holomorphy domains and asymptotic forms of scattering amplitudes and partial wave amplitudes

Journal Article · Fri Mar 01 04:00:00 EST 1963 · Il Nuovo Cimento

DOI:https://doi.org/10.1007/BF02813087· OSTI ID:4728894

Challifour, J. L.; Eden, R. J.

The use and limitations of the integral transforms that relate scattering amplitudes A(s,z) (z = cos θ ) to partial wave amplitudes a(l,s) are studied. From a modification of the Regge representation, the holomorphy domains of A(s,z) in the z plane when a(l,s) is assumed to be holomorphic and of exponential type in a wedge in the l plane are studied. The inverse relation giving a(l,s) in terms of A(s,z) is also studied under certain assumed analyticity properties of A(s,z) in the variable z, with particular reference to the holomorphy and asymptotic form in l of a(l,s). We also study the analytic continuation in s of a(l,s) using its integral representation in terms of A(s,z), which is necessary in a relativistic theory. It is found that there is a phase difference between the partial wave amplitude defined for s> 4M² and continued to s < 4M², and the amplitude defined for s < 4M². This difference is related to the kinematic branch cut off a(l,s) along s < 4M² when l is complex.

• Research Organization: Cambridge Univ., Eng.
• Sponsoring Organization: USDOE
• NSA Number: NSA-17-020877
• OSTI ID: 4728894
• Journal Information: Il Nuovo Cimento, Journal Name: Il Nuovo Cimento Journal Issue: 5 Vol. 27; ISSN 1827-6121
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
CROSS SECTIONS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
FIELD THEORY
MATHEMATICS
PARTIAL WAVES
QUANTUM MECHANICS
SCATTERING