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Title: General bounds on form factors and propagators from analyticity and unitarity: Application to the nucleon renormalization constant. [Upper bound, strong-coupling constant]

Abstract

The following extremal problem is solved: Let O be an operator whose lowest-mass coupling is to the two particles A and B and is given by a form factor F which is analytic in a complex plane cut along a section L of the real line. Given values of F, at points not on L, and the partial-wave amplitudes for AB scattering in the channels with the same quantum numbers as O, over some portion of L, what is the optimal lower bound for a given positively weighted integral over L of the spectral function of O, consistent with the elastic and inelastic unitarity relations on L The solution involves a system of two inhomogeneous singular integral equations of the Muskhelishvili type, which can be reduced to a singular integral equation of the Fredholm type. The results are applied to establish an upper bound of 0.25 for the nucleon renormalization constant, using the strong-coupling constant and ..pi..N scattering data in the P/sub 11/ and S/sub 11/ channels up to a c.m. energy of 1.7 GeV. The bound indicates that the nucleon is at least 75% composite. (AIP)

Authors:
;
Publication Date:
Research Org.:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
OSTI Identifier:
7335813
Resource Type:
Journal Article
Journal Name:
Phys. Rev., D; (United States)
Additional Journal Information:
Journal Volume: 15:1
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FORM FACTORS; UNITARITY; NUCLEONS; RENORMALIZATION; BOUNDARY CONDITIONS; CHIRALITY; DISPERSION RELATIONS; LIMITING VALUES; PARTIAL WAVES; PROPAGATOR; SYMMETRY BREAKING; BARYONS; ELEMENTARY PARTICLES; FERMIONS; HADRONS; PARTICLE PROPERTIES; 645206* - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions, Baryon No. = 1- (-1987)

Citation Formats

Baluni, V, and Broadhurst, D J. General bounds on form factors and propagators from analyticity and unitarity: Application to the nucleon renormalization constant. [Upper bound, strong-coupling constant]. United States: N. p., 1977. Web. doi:10.1103/PhysRevD.15.230.
Baluni, V, & Broadhurst, D J. General bounds on form factors and propagators from analyticity and unitarity: Application to the nucleon renormalization constant. [Upper bound, strong-coupling constant]. United States. https://doi.org/10.1103/PhysRevD.15.230
Baluni, V, and Broadhurst, D J. Sat . "General bounds on form factors and propagators from analyticity and unitarity: Application to the nucleon renormalization constant. [Upper bound, strong-coupling constant]". United States. https://doi.org/10.1103/PhysRevD.15.230.
@article{osti_7335813,
title = {General bounds on form factors and propagators from analyticity and unitarity: Application to the nucleon renormalization constant. [Upper bound, strong-coupling constant]},
author = {Baluni, V and Broadhurst, D J},
abstractNote = {The following extremal problem is solved: Let O be an operator whose lowest-mass coupling is to the two particles A and B and is given by a form factor F which is analytic in a complex plane cut along a section L of the real line. Given values of F, at points not on L, and the partial-wave amplitudes for AB scattering in the channels with the same quantum numbers as O, over some portion of L, what is the optimal lower bound for a given positively weighted integral over L of the spectral function of O, consistent with the elastic and inelastic unitarity relations on L The solution involves a system of two inhomogeneous singular integral equations of the Muskhelishvili type, which can be reduced to a singular integral equation of the Fredholm type. The results are applied to establish an upper bound of 0.25 for the nucleon renormalization constant, using the strong-coupling constant and ..pi..N scattering data in the P/sub 11/ and S/sub 11/ channels up to a c.m. energy of 1.7 GeV. The bound indicates that the nucleon is at least 75% composite. (AIP)},
doi = {10.1103/PhysRevD.15.230},
url = {https://www.osti.gov/biblio/7335813}, journal = {Phys. Rev., D; (United States)},
number = ,
volume = 15:1,
place = {United States},
year = {1977},
month = {1}
}