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Title: Convergent polynomial expansion, lines of zeros, and slopes of diffraction scattering

Abstract

Using Mandelstam analyticity and conformal mapping new variables are constructed so as to extend the domain of applicability of the convergent polynomial expansion (CPE) to all energies. It is found that the CPE exists for all energies if the scattering amplitude possesses at least one zero in the physical region. The CPE goes over to the optimized polynomial expansion (OPE) for higher energies. The approach from CPE to OPE is faster the higher the energy is, the farther the left-hand cut is than the right-hand cut, and the closer the position of zero is to the backward direction. The variables are found to be potentially useful in describing diffraction scattering at forward angles at all energies. A universal formula has been developed that relates slope parameters to equations of boundaries of spectral functions and lines of zeros. The formula gives a good account of the world data on shrinkage, antishrinkage, and shrinkage-antishrinkage of forward peaks at all energies. Good fits to the data on shrinkage for pp and K/sup +/p scattering, and antishrinkage in pp scattering have been obtained with known theoretical boundaries and suitable lines of zeros. Reasonably good fits to the data for K/sup -/p and ..pi../sup +more » -/scattering with oscillations at lower energies have been obtained with effective shapes of spectral functions and suitable lines of zeros. In some cases our lines of zero found from this analysis appear to be different from those of Odorico. From the present approach to the scattering problem we observe that the imaginary part of the amplitude that yields b(s) ..-->.. infinity for some values of s must vanish at one point at least in the backward hemisphere.« less

Authors:
Publication Date:
Research Org.:
Physics Department, Sambalpur University, Jyoti Vihar, Burla 768017, Sambalpur, Orissa, India
OSTI Identifier:
7075086
Resource Type:
Journal Article
Journal Name:
Phys. Rev., D; (United States)
Additional Journal Information:
Journal Volume: 17:3
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; KAON PLUS-PROTON INTERACTIONS; SCATTERING AMPLITUDES; PION-PROTON INTERACTIONS; PROTON-PROTON INTERACTIONS; CONFORMAL MAPPING; DIFFRACTION MODELS; MANDELSTAM REPRESENTATION; PARTIAL WAVES; SPECTRAL FUNCTIONS; AMPLITUDES; BARYON-BARYON INTERACTIONS; FUNCTIONS; HADRON-HADRON INTERACTIONS; INTERACTIONS; KAON-NUCLEON INTERACTIONS; KAON-PROTON INTERACTIONS; MATHEMATICAL MODELS; MESON-BARYON INTERACTIONS; MESON-NUCLEON INTERACTIONS; NUCLEON-NUCLEON INTERACTIONS; PARTICLE INTERACTIONS; PARTICLE MODELS; PION-NUCLEON INTERACTIONS; PROTON-NUCLEON INTERACTIONS; TOPOLOGICAL MAPPING; TRANSFORMATIONS; 645206* - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions, Baryon No. = 1- (-1987); 645207 - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions, Baryon No. Greater than 1- (-1987)

Citation Formats

Parida, M K. Convergent polynomial expansion, lines of zeros, and slopes of diffraction scattering. United States: N. p., 1978. Web. doi:10.1103/PhysRevD.17.785.
Parida, M K. Convergent polynomial expansion, lines of zeros, and slopes of diffraction scattering. United States. doi:10.1103/PhysRevD.17.785.
Parida, M K. Wed . "Convergent polynomial expansion, lines of zeros, and slopes of diffraction scattering". United States. doi:10.1103/PhysRevD.17.785.
@article{osti_7075086,
title = {Convergent polynomial expansion, lines of zeros, and slopes of diffraction scattering},
author = {Parida, M K},
abstractNote = {Using Mandelstam analyticity and conformal mapping new variables are constructed so as to extend the domain of applicability of the convergent polynomial expansion (CPE) to all energies. It is found that the CPE exists for all energies if the scattering amplitude possesses at least one zero in the physical region. The CPE goes over to the optimized polynomial expansion (OPE) for higher energies. The approach from CPE to OPE is faster the higher the energy is, the farther the left-hand cut is than the right-hand cut, and the closer the position of zero is to the backward direction. The variables are found to be potentially useful in describing diffraction scattering at forward angles at all energies. A universal formula has been developed that relates slope parameters to equations of boundaries of spectral functions and lines of zeros. The formula gives a good account of the world data on shrinkage, antishrinkage, and shrinkage-antishrinkage of forward peaks at all energies. Good fits to the data on shrinkage for pp and K/sup +/p scattering, and antishrinkage in pp scattering have been obtained with known theoretical boundaries and suitable lines of zeros. Reasonably good fits to the data for K/sup -/p and ..pi../sup + -/scattering with oscillations at lower energies have been obtained with effective shapes of spectral functions and suitable lines of zeros. In some cases our lines of zero found from this analysis appear to be different from those of Odorico. From the present approach to the scattering problem we observe that the imaginary part of the amplitude that yields b(s) ..-->.. infinity for some values of s must vanish at one point at least in the backward hemisphere.},
doi = {10.1103/PhysRevD.17.785},
journal = {Phys. Rev., D; (United States)},
number = ,
volume = 17:3,
place = {United States},
year = {1978},
month = {2}
}