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

## Abstract

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 themore »

- Authors:

- Publication Date:

- Research Org.:
- P.G. Department of Physics, Sambalpur University, Jyoti Vihar, Burla 768017, Orissa, India

- OSTI Identifier:
- 5361629

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev., D; (United States)

- Additional Journal Information:
- Journal Volume: 21:9

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; KAON-PROTON INTERACTIONS; CHARGE-EXCHANGE INTERACTIONS; PION-PROTON INTERACTIONS; PROTON-PROTON INTERACTIONS; CONFORMAL MAPPING; DIFFERENTIAL CROSS SECTIONS; INELASTIC SCATTERING; LAGUERRE POLYNOMIALS; SCALING LAWS; BARYON-BARYON INTERACTIONS; BASIC INTERACTIONS; CROSS SECTIONS; FUNCTIONS; HADRON-HADRON INTERACTIONS; INTERACTIONS; KAON-NUCLEON INTERACTIONS; MESON-BARYON INTERACTIONS; MESON-NUCLEON INTERACTIONS; NUCLEON-NUCLEON INTERACTIONS; PARTICLE INTERACTIONS; PION-NUCLEON INTERACTIONS; POLYNOMIALS; PROTON-NUCLEON INTERACTIONS; SCATTERING; STRONG 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, and Giri, N.
```*Convergent polynomial expansion and scaling in inelastic charge-exchange scattering processes*. United States: N. p., 1980.
Web. doi:10.1103/PhysRevD.21.2548.

```
Parida, M K, & Giri, N.
```*Convergent polynomial expansion and scaling in inelastic charge-exchange scattering processes*. United States. doi:10.1103/PhysRevD.21.2548.

```
Parida, M K, and Giri, N. Thu .
"Convergent polynomial expansion and scaling in inelastic charge-exchange scattering processes". United States. doi:10.1103/PhysRevD.21.2548.
```

```
@article{osti_5361629,
```

title = {Convergent polynomial expansion and scaling in inelastic charge-exchange scattering processes},

author = {Parida, M K and Giri, N},

abstractNote = {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.},

doi = {10.1103/PhysRevD.21.2548},

journal = {Phys. Rev., D; (United States)},

number = ,

volume = 21:9,

place = {United States},

year = {1980},

month = {5}

}