# 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}

}