## Gauge-Invariant Scaling Model of Current Interactions with Regge Behavior and Finite Fixed-Pole Sum Rules

## Abstract

A general nonperturbative model for the entire Compton amplitude which incorporates Bjorken scaling, gauge invariance, and Regge behavior is presented. We show that a covariantly regularized model based on the infinite-momentum-frame techniques of Drell, Levy, and Yan is equivalent to the manifestly covariant nonperturbative parton model of Landshoff, Polkinghorne, and Short. We also demonstrate that a general consequence of composite theories of hadrons with field-theoretic constituents which incorporates the above properties is the existence of a constant energy-independent and q ^{2}-independent term in T _{1}(ν, q ^{2}) (a "Kronecker delta" δ _{J0} term) and a J = 0 fixed pole in T _{2}(ν, q ^{2}). Sum rules for general Compton amplitudes are derived and a discussion of mass renormalization for electromagnetic self-energy corrections of hadrons is presented. We demonstrate that such sum rules are always finite, even in the presence of Regge behavior, when subtraction terms in the underlying parton-proton u-channel dispersion relation are taken into account. Here, analytic continuation in α is thus justified.

- Authors:

- Stanford Univ., Stanford, CA (United States)
- Stanford Univ., Stanford, CA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Stanford Univ., Stanford, CA (United States); Daresbury Nuclear Physics Lab. (England)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1442850

- Report Number(s):
- SLAC-PUB-1243

Journal ID: ISSN 0556-2821; PRVDAQ; TRN: US1900936

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review. D, Particles Fields

- Additional Journal Information:
- Journal Volume: 8; Journal Issue: 10; Journal ID: ISSN 0556-2821

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Brodsky, Stanley J., Close, Francis E., and Gunion, J. F. Gauge-Invariant Scaling Model of Current Interactions with Regge Behavior and Finite Fixed-Pole Sum Rules. United States: N. p., 1973.
Web. doi:10.1103/PhysRevD.8.3678.
```

```
Brodsky, Stanley J., Close, Francis E., & Gunion, J. F. Gauge-Invariant Scaling Model of Current Interactions with Regge Behavior and Finite Fixed-Pole Sum Rules. United States. doi:10.1103/PhysRevD.8.3678.
```

```
Brodsky, Stanley J., Close, Francis E., and Gunion, J. F. Thu .
"Gauge-Invariant Scaling Model of Current Interactions with Regge Behavior and Finite Fixed-Pole Sum Rules". United States. doi:10.1103/PhysRevD.8.3678. https://www.osti.gov/servlets/purl/1442850.
```

```
@article{osti_1442850,
```

title = {Gauge-Invariant Scaling Model of Current Interactions with Regge Behavior and Finite Fixed-Pole Sum Rules},

author = {Brodsky, Stanley J. and Close, Francis E. and Gunion, J. F.},

abstractNote = {A general nonperturbative model for the entire Compton amplitude which incorporates Bjorken scaling, gauge invariance, and Regge behavior is presented. We show that a covariantly regularized model based on the infinite-momentum-frame techniques of Drell, Levy, and Yan is equivalent to the manifestly covariant nonperturbative parton model of Landshoff, Polkinghorne, and Short. We also demonstrate that a general consequence of composite theories of hadrons with field-theoretic constituents which incorporates the above properties is the existence of a constant energy-independent and q2-independent term in T1(ν, q2) (a "Kronecker delta" δJ0 term) and a J = 0 fixed pole in T2(ν, q2). Sum rules for general Compton amplitudes are derived and a discussion of mass renormalization for electromagnetic self-energy corrections of hadrons is presented. We demonstrate that such sum rules are always finite, even in the presence of Regge behavior, when subtraction terms in the underlying parton-proton u-channel dispersion relation are taken into account. Here, analytic continuation in α is thus justified.},

doi = {10.1103/PhysRevD.8.3678},

journal = {Physical Review. D, Particles Fields},

number = 10,

volume = 8,

place = {United States},

year = {1973},

month = {11}

}