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

Journal Article · Mon Jan 01 04:00:00 EST 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.19.164· OSTI ID:6465637

Parida, M K

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.

• Research Organization: Physics Department Sambalpur University, Jyoti Vihar-768 017, Orissa, India
• OSTI ID: 6465637
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 19:1; ISSN PRVDA
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
BARYON-BARYON INTERACTIONS
CROSS SECTIONS
DATA
DATA FORMS
DIFFERENTIAL CROSS SECTIONS
DIFFRACTION MODELS
ENERGY RANGE
FUNCTIONS
GEV RANGE
GEV RANGE 01-10
HADRON-HADRON INTERACTIONS
INFORMATION
INTERACTIONS
ISOLATED VALUES
KAON MINUS-PROTON INTERACTIONS
KAON PLUS-PROTON INTERACTIONS
KAON-NUCLEON INTERACTIONS
KAON-PROTON INTERACTIONS
LAGUERRE POLYNOMIALS
MATHEMATICAL MODELS
MESON-BARYON INTERACTIONS
MESON-NUCLEON INTERACTIONS
NUCLEON-ANTINUCLEON INTERACTIONS
NUCLEON-NUCLEON INTERACTIONS
NUMERICAL DATA
PARTICLE INTERACTIONS
PARTICLE MODELS
PION-NUCLEON INTERACTIONS
PION-PROTON INTERACTIONS
POLYNOMIALS
PROTON-ANTIPROTON INTERACTIONS
PROTON-NUCLEON INTERACTIONS
PROTON-PROTON INTERACTIONS
SCALING LAWS
SCATTERING AMPLITUDES
THEORETICAL DATA