New dispersion relations and their application to partial-wave amplitudes
After reviewing the commonly used dispersion relations, a systematic investigation of more generalized dispersion relations on parametrized curves in the Mandelstam plane fors-u crossing-symmetric amplitudes is made with the aim of obtaining dispersion relations which receive contributions from all three channels, however, in such a way that knowledge of the absorptive parts is only required in regions well inside the various Lehmann ellipses. In addition we require that the dispersion relations receive no contributions from kinematic singularities arising from the parametrization and that they allow partial-wave projections to be made in a relatively simple manner. It is found that dispersion relations on hyperbolic curves in the Mandelstam plane are a natural solution of the problem. The dispersion relations are written in a remarkably simple form similar to the usual fixed-t dispersion relation but with an additionalt-channel contribution. As an interesting application, we derive generalized partial-wave dispersion relations for elastic pion-nucleon scattering, where the left-hand cut contribution is explicitly given by convergent partial-wave series in the crossed channels
- Research Organization:
- Universtaet Trier-Kaiserlautern, Ger.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-29-013995
- OSTI ID:
- 4356863
- Journal Information:
- Nuovo Cimento, A, Journal Name: Nuovo Cimento, A Journal Issue: 2 Vol. 18; ISSN 0369-3546
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
Similar Records
ANALYTICAL PROPERTIES OF THE AMPLITUDE FOR THE SCATTERING OF $pi$ MESONS BY K MESONS
A MANDELSTAM REPRESENTATION IN POTENTIAL SCATTERING
PARTIAL-WAVE DISPERSION RELATIONS FOR THE PROCESS $pi$ + $pi$ $Yields$ N + / anti N/
Thesis/Dissertation
·
Sun Dec 31 23:00:00 EST 1961
·
OSTI ID:4081723
A MANDELSTAM REPRESENTATION IN POTENTIAL SCATTERING
Journal Article
·
Sat Oct 31 23:00:00 EST 1959
· Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B
·
OSTI ID:4179430
PARTIAL-WAVE DISPERSION RELATIONS FOR THE PROCESS $pi$ + $pi$ $Yields$ N + / anti N/
Journal Article
·
Mon Mar 14 23:00:00 EST 1960
· Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys.Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D
·
OSTI ID:4188805