Convergent polynomial expansion and scaling in inelastic charge-exchange scattering processes

Journal Article · Thu May 01 04:00:00 EDT 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.21.2548· OSTI ID:5361629

Parida, M K; Giri, N

A method of approach developed in a previous paper for elastic diffraction scattering process at high energies using Mandelstam analyticity and convergent polynomial expansion (CPE) is applied in this paper for several inelastic charge-exchange processes. A conformal mapping Z of the unsymmetrically cut costheta plane, which does not develop any spurious cut in the mapped plane or require any knowledge of zeros, is combined with that of the s plane to construct a variable chi(s,t) which has the potentialities to reproduce some known scaling variables and Regge behavior and to provide information on the asymptotic behavior of the slope parameter of the type (lns)/sup m/, with m=0, 1, 2, ... . At high energies and away from the peak region the variable becomes approx. b(s)(lnt)/sup 2/. Because of the absence of any spurious cut in the mapped plane, it is possible to obtain information on the existence of entire function for the differential-cross-section ratio f(s,t) at asymptotic energies. However, at finite energies, neither the rate of convergence nor the nature of the polynomials in the CPE in Z or chi is uniquely fixed. At asymptotic energies the polynomials are uniquely the Laguerre polynomials and the CPE goes over to the optimized polynomial expansion (OPE). The approach from the CPE to the OPE is faster in the chi plane for physical values of s if m>0. The possible existence of the scaling function at asymptotic energies as a series in Laguerre polynomials in chi is pointed out. The first term in the CPE gives a good fit to the high-energy data on the slope parameter for each of the six processes ..pi../sup -/p ..-->.. ..pi../sup 0/n, ..pi../sup -/p ..-->.. etan, K/sup -/p ..-->.. K-bar/sup 0/n, K/sup +/n ..-->.. K/sup 0/p, K/sup +/p ..-->.. K/sup 0/..delta../sup + +/, and K/sup -/n ..-->.. K-bar/sup 0/..delta../sup -/. The asymptotic behavior of the slope parameter for every process is approx. lns.

• Research Organization: P.G. Department of Physics, Sambalpur University, Jyoti Vihar, Burla 768017, Orissa, India
• OSTI ID: 5361629
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 21:9; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

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)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYON-BARYON INTERACTIONS
BASIC INTERACTIONS
CHARGE-EXCHANGE INTERACTIONS
CONFORMAL MAPPING
CROSS SECTIONS
DIFFERENTIAL CROSS SECTIONS
FUNCTIONS
HADRON-HADRON INTERACTIONS
INELASTIC SCATTERING
INTERACTIONS
KAON-NUCLEON INTERACTIONS
KAON-PROTON INTERACTIONS
LAGUERRE POLYNOMIALS
MESON-BARYON INTERACTIONS
MESON-NUCLEON INTERACTIONS
NUCLEON-NUCLEON INTERACTIONS
PARTICLE INTERACTIONS
PION-NUCLEON INTERACTIONS
PION-PROTON INTERACTIONS
POLYNOMIALS
PROTON-NUCLEON INTERACTIONS
PROTON-PROTON INTERACTIONS
SCALING LAWS
SCATTERING
STRONG INTERACTIONS
TOPOLOGICAL MAPPING
TRANSFORMATIONS