skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Convergent polynomial expansion and scaling in diffraction scattering. II. Convergent polynomial expansion for all energies, slope parameters, and scaling in pp, p-barp, K/sup + -/p, and. pi. /sup + -/p scattering

Abstract

Using simple considerations of Mandelstam analyticity of the s plane along with that of the costheta plane by conformal mapping and the convergent polynomial expansion (CPE), a variable chi (s,t) is constructed which has the potentialities of reproducing some known scaling variables, Regge behavior, and providing information about asymptotic behavior of slope parameters in diffraction scattering of the type- (lns)/sup p/, where p = 0, 1,2. CPE in terms of Laguerre polynomials in the proposed variable is possible for all energies, but maximum convergence of the series is possible only at asymptotic energies. Use of the first one or two terms in the CPE in chi provides improved fits to the forward slope data at all energies and reasonably good fits to the high-energy slope parameter data at vertical-bartvertical-bar = 0.2 GeV/sup 2/, for pp, p-barp, K/sup + -/p and ..pi../sup + -/p shipped scattering. Information on the asymptotic behavior of slope parameters for these processes is obtained. Data analysis reveals that the strong behaviors in the amplitudes for all these processes cannot be present inside the corresponding figures of converegence in the mapped planes for all energies except near the threshold. A fit to the slope-parameter data for anymore » process determines unknown parameters in the corresponding chi. When the cross-section-ratio data for different processes are plotted against the corresponding chi's all the data for every process starting from p/sub lab/ = 3 GeV/c up to the highest available energy and within the range vertical-bartvertical-bar < or = vertical-bartvertical-bar/sub max/: where vertical-bartvertical-bar/sub max/ = 1.25, 0.5, 2.0, 1.0, and 1.25 GeV/sup 2/ for pp, p-barp, K/sup +/p, K/sup -/p, and ..pi../sup + -/p scattering, respectively, lie on a scaling curve.« less

Authors:
Publication Date:
Research Org.:
Physics Department Sambalpur University, Jyoti Vihar-768 017, Orissa, India
OSTI Identifier:
6465637
Resource Type:
Journal Article
Journal Name:
Phys. Rev., D; (United States)
Additional Journal Information:
Journal Volume: 19:1
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; KAON MINUS-PROTON INTERACTIONS; DIFFERENTIAL CROSS SECTIONS; SCATTERING AMPLITUDES; KAON PLUS-PROTON INTERACTIONS; PION-PROTON INTERACTIONS; PROTON-ANTIPROTON INTERACTIONS; PROTON-PROTON INTERACTIONS; DIFFRACTION MODELS; GEV RANGE 01-10; ISOLATED VALUES; LAGUERRE POLYNOMIALS; SCALING LAWS; THEORETICAL DATA; AMPLITUDES; BARYON-BARYON INTERACTIONS; CROSS SECTIONS; DATA; DATA FORMS; ENERGY RANGE; FUNCTIONS; GEV RANGE; HADRON-HADRON INTERACTIONS; INFORMATION; INTERACTIONS; KAON-NUCLEON INTERACTIONS; KAON-PROTON INTERACTIONS; MATHEMATICAL MODELS; MESON-BARYON INTERACTIONS; MESON-NUCLEON INTERACTIONS; NUCLEON-ANTINUCLEON INTERACTIONS; NUCLEON-NUCLEON INTERACTIONS; NUMERICAL DATA; PARTICLE INTERACTIONS; PARTICLE MODELS; PION-NUCLEON INTERACTIONS; POLYNOMIALS; PROTON-NUCLEON INTERACTIONS; 645205* - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions, Baryon No. = 0- (-1987); 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 and scaling in diffraction scattering. II. Convergent polynomial expansion for all energies, slope parameters, and scaling in pp, p-barp, K/sup + -/p, and. pi. /sup + -/p scattering. United States: N. p., 1979. Web. doi:10.1103/PhysRevD.19.164.
Parida, M K. Convergent polynomial expansion and scaling in diffraction scattering. II. Convergent polynomial expansion for all energies, slope parameters, and scaling in pp, p-barp, K/sup + -/p, and. pi. /sup + -/p scattering. United States. doi:10.1103/PhysRevD.19.164.
Parida, M K. Mon . "Convergent polynomial expansion and scaling in diffraction scattering. II. Convergent polynomial expansion for all energies, slope parameters, and scaling in pp, p-barp, K/sup + -/p, and. pi. /sup + -/p scattering". United States. doi:10.1103/PhysRevD.19.164.
@article{osti_6465637,
title = {Convergent polynomial expansion and scaling in diffraction scattering. II. Convergent polynomial expansion for all energies, slope parameters, and scaling in pp, p-barp, K/sup + -/p, and. pi. /sup + -/p scattering},
author = {Parida, M K},
abstractNote = {Using simple considerations of Mandelstam analyticity of the s plane along with that of the costheta plane by conformal mapping and the convergent polynomial expansion (CPE), a variable chi (s,t) is constructed which has the potentialities of reproducing some known scaling variables, Regge behavior, and providing information about asymptotic behavior of slope parameters in diffraction scattering of the type- (lns)/sup p/, where p = 0, 1,2. CPE in terms of Laguerre polynomials in the proposed variable is possible for all energies, but maximum convergence of the series is possible only at asymptotic energies. Use of the first one or two terms in the CPE in chi provides improved fits to the forward slope data at all energies and reasonably good fits to the high-energy slope parameter data at vertical-bartvertical-bar = 0.2 GeV/sup 2/, for pp, p-barp, K/sup + -/p and ..pi../sup + -/p shipped scattering. Information on the asymptotic behavior of slope parameters for these processes is obtained. Data analysis reveals that the strong behaviors in the amplitudes for all these processes cannot be present inside the corresponding figures of converegence in the mapped planes for all energies except near the threshold. A fit to the slope-parameter data for any process determines unknown parameters in the corresponding chi. When the cross-section-ratio data for different processes are plotted against the corresponding chi's all the data for every process starting from p/sub lab/ = 3 GeV/c up to the highest available energy and within the range vertical-bartvertical-bar < or = vertical-bartvertical-bar/sub max/: where vertical-bartvertical-bar/sub max/ = 1.25, 0.5, 2.0, 1.0, and 1.25 GeV/sup 2/ for pp, p-barp, K/sup +/p, K/sup -/p, and ..pi../sup + -/p scattering, respectively, lie on a scaling curve.},
doi = {10.1103/PhysRevD.19.164},
journal = {Phys. Rev., D; (United States)},
number = ,
volume = 19:1,
place = {United States},
year = {1979},
month = {1}
}