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Title: Convergent polynomial expansion and scaling in diffraction scattering. I. pp scattering

Abstract

Using Mandelstam analyticity of the s and costheta planes and conformal mapping, a variable chi is constructed which has the potentialities of reproducing Regge behavior and/or some known scaling variables. The role of the physical region in the mapped plane for the optimized polynomial expansion (OPE) is emphasized. Ambiguities in using the OPE in terms of Laguerre polynomials at finite energies are pointed out. However, at finite energies there exists a convergent polynomial expansion (CPE) for which the nature of polynomials and the rate of convergence vary with energy. The first term in the expansion gives a good fit to the world data on forward slopes for pp scattering for all energies with effective shapes of spectral function, but yields a good fit to the high-energy data for s > 35 GeV/sup 2/ with the theoretical boundaries. The possible existence of a scaling function at asymptotic energies as a series in Laguerre polynomials in the new variable chi is pointed out. Available high-energy data on the pp cross-section ratio for p/sub lab/ > or = 50 GeV/c and all angles exhibit scaling in this variable. It is found that at high energies scaling occurs even for larger-vertical-bart vertical-bar data lyingmore » well outside the diffraction peak. The implication of this type of scaling in the data analysis at high energies using OPE is pointed out. The energy dependence of dip position at high energies is predicted to be vertical-bart/sub d/(s) vertical-bar = 4m/sup 2//sub ..pi../ )sinh(4.35 +- 0.05)/4m/sub ..pi..//sup 2/b (s))/sup 1/2/)/sup 2/, which is in very good agreement with the existing data.« less

Authors:
Publication Date:
Research Org.:
Institute of Physics, A/105, Saheed Nagar, Bhubaneswar-751 007, Orissa, India
OSTI Identifier:
6444340
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; PROTON-PROTON INTERACTIONS; ELASTIC SCATTERING; SCALE INVARIANCE; SCATTERING AMPLITUDES; ANALYTIC FUNCTIONS; ASYMPTOTIC SOLUTIONS; DIFFRACTION MODELS; GEV RANGE 10-100; GEV RANGE 100-1000; ISOLATED VALUES; MANDELSTAM REPRESENTATION; S MATRIX; TEV RANGE; THEORETICAL DATA; AMPLITUDES; BARYON-BARYON INTERACTIONS; DATA; DATA FORMS; ENERGY RANGE; FUNCTIONS; GEV RANGE; HADRON-HADRON INTERACTIONS; INFORMATION; INTERACTIONS; INVARIANCE PRINCIPLES; MATHEMATICAL MODELS; MATRICES; NUCLEON-NUCLEON INTERACTIONS; NUMERICAL DATA; PARTICLE INTERACTIONS; PARTICLE MODELS; PROTON-NUCLEON INTERACTIONS; SCATTERING; 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. I. pp scattering. United States: N. p., 1979. Web. doi:10.1103/PhysRevD.19.150.
Parida, M K. Convergent polynomial expansion and scaling in diffraction scattering. I. pp scattering. United States. doi:10.1103/PhysRevD.19.150.
Parida, M K. Mon . "Convergent polynomial expansion and scaling in diffraction scattering. I. pp scattering". United States. doi:10.1103/PhysRevD.19.150.
@article{osti_6444340,
title = {Convergent polynomial expansion and scaling in diffraction scattering. I. pp scattering},
author = {Parida, M K},
abstractNote = {Using Mandelstam analyticity of the s and costheta planes and conformal mapping, a variable chi is constructed which has the potentialities of reproducing Regge behavior and/or some known scaling variables. The role of the physical region in the mapped plane for the optimized polynomial expansion (OPE) is emphasized. Ambiguities in using the OPE in terms of Laguerre polynomials at finite energies are pointed out. However, at finite energies there exists a convergent polynomial expansion (CPE) for which the nature of polynomials and the rate of convergence vary with energy. The first term in the expansion gives a good fit to the world data on forward slopes for pp scattering for all energies with effective shapes of spectral function, but yields a good fit to the high-energy data for s > 35 GeV/sup 2/ with the theoretical boundaries. The possible existence of a scaling function at asymptotic energies as a series in Laguerre polynomials in the new variable chi is pointed out. Available high-energy data on the pp cross-section ratio for p/sub lab/ > or = 50 GeV/c and all angles exhibit scaling in this variable. It is found that at high energies scaling occurs even for larger-vertical-bart vertical-bar data lying well outside the diffraction peak. The implication of this type of scaling in the data analysis at high energies using OPE is pointed out. The energy dependence of dip position at high energies is predicted to be vertical-bart/sub d/(s) vertical-bar = 4m/sup 2//sub ..pi../ )sinh(4.35 +- 0.05)/4m/sub ..pi..//sup 2/b (s))/sup 1/2/)/sup 2/, which is in very good agreement with the existing data.},
doi = {10.1103/PhysRevD.19.150},
journal = {Phys. Rev., D; (United States)},
number = ,
volume = 19:1,
place = {United States},
year = {1979},
month = {1}
}