# Structure functions at small $x$ from worldlines: Unpolarized distributions

## Abstract

The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann functional integrals, to compute spinor and color traces in these amplitudes. Further, semi-classical approximations to quantum mechanical world- line trajectories provide useful intuition in a wide range of dynamical problems. We develop here the world-line approach to compute deeply inelastic structure functions in the small $x$ Regge limit of QCD. In a shockwave approximation valid in this limit, we show how one recovers the well-known dipole model for unpolarized structure functions. In a follow-up work, we will discuss the world-line computation of polarized structure functions at small $x$.

- Authors:

- Publication Date:

- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1560902

- Alternate Identifier(s):
- OSTI ID: 1570678

- Report Number(s):
- BNL-212178-2019-JAAM

Journal ID: ISSN 2470-0010; PRVDAQ; 054007

- Grant/Contract Number:
- SC0012704

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 5; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Tarasov, Andrey, and Venugopalan, Raju.
```*Structure functions at small x from worldlines: Unpolarized distributions*. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.054007.

```
Tarasov, Andrey, & Venugopalan, Raju.
```*Structure functions at small x from worldlines: Unpolarized distributions*. United States. doi:10.1103/PhysRevD.100.054007.

```
Tarasov, Andrey, and Venugopalan, Raju. Tue .
"Structure functions at small x from worldlines: Unpolarized distributions". United States. doi:10.1103/PhysRevD.100.054007.
```

```
@article{osti_1560902,
```

title = {Structure functions at small x from worldlines: Unpolarized distributions},

author = {Tarasov, Andrey and Venugopalan, Raju},

abstractNote = {The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann functional integrals, to compute spinor and color traces in these amplitudes. Further, semi-classical approximations to quantum mechanical world- line trajectories provide useful intuition in a wide range of dynamical problems. We develop here the world-line approach to compute deeply inelastic structure functions in the small x Regge limit of QCD. In a shockwave approximation valid in this limit, we show how one recovers the well-known dipole model for unpolarized structure functions. In a follow-up work, we will discuss the world-line computation of polarized structure functions at small x.},

doi = {10.1103/PhysRevD.100.054007},

journal = {Physical Review D},

issn = {2470-0010},

number = 5,

volume = 100,

place = {United States},

year = {2019},

month = {9}

}

#### Figures / Tables:

^{−}shrinks to a point.

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*