# Fluctuations of the gluon distribution from the small- $x$ effective action

## Abstract

The computation of observables in high-energy QCD involves an average over stochastic semiclassical small-x gluon fields. The weight of various configurations is determined by the effective action. We introduce a method to study fluctuations of observables, functionals of the small-x fields, which does not explicitly involve dipoles. We integrate out those fluctuations of the semiclassical gluon field under which a given observable is invariant. Thereby we obtain the effective potential for that observable describing its fluctuations about the average. Here, we determine explicitly the effective potential for the covariant gauge gluon distribution both for the McLerran-Venugopalan (MV) model and for a (nonlocal) Gaussian approximation for the small-x effective action. This provides insight into the correlation of fluctuations of the number of hard gluons versus their typical transverse momentum. We find that the spectral shape of the fluctuations of the gluon distribution is fundamentally different in the MV model, where there is a pileup of gluons near the saturation scale, versus the solution of the small-x JIMWLK renormalization group, which generates essentially scale-invariant fluctuations above the absorptive boundary set by the saturation scale.

- Authors:

- City Univ. (CUNY), NY (United States). Baruch College. Dept. of Natural Science, and The Graduate School and Univ. Center
- Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center

- Publication Date:

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

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

- OSTI Identifier:
- 1425493

- Alternate Identifier(s):
- OSTI ID: 1395593

- Report Number(s):
- RBRC-1238; BNL-203300-2018-JAAM; RBRC-1233; BNL-200010-2018-JAAM

Journal ID: ISSN 2470-0010; PRVDAQ; TRN: US1802120

- Grant/Contract Number:
- SC0012704; FG02-09ER41620; SC0002307

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Dumitru, Adrian, and Skokov, Vladimir. Fluctuations of the gluon distribution from the small- x effective action. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.056029.
```

```
Dumitru, Adrian, & Skokov, Vladimir. Fluctuations of the gluon distribution from the small- x effective action. United States. doi:10.1103/PhysRevD.96.056029.
```

```
Dumitru, Adrian, and Skokov, Vladimir. Fri .
"Fluctuations of the gluon distribution from the small- x effective action". United States. doi:10.1103/PhysRevD.96.056029. https://www.osti.gov/servlets/purl/1425493.
```

```
@article{osti_1425493,
```

title = {Fluctuations of the gluon distribution from the small- x effective action},

author = {Dumitru, Adrian and Skokov, Vladimir},

abstractNote = {The computation of observables in high-energy QCD involves an average over stochastic semiclassical small-x gluon fields. The weight of various configurations is determined by the effective action. We introduce a method to study fluctuations of observables, functionals of the small-x fields, which does not explicitly involve dipoles. We integrate out those fluctuations of the semiclassical gluon field under which a given observable is invariant. Thereby we obtain the effective potential for that observable describing its fluctuations about the average. Here, we determine explicitly the effective potential for the covariant gauge gluon distribution both for the McLerran-Venugopalan (MV) model and for a (nonlocal) Gaussian approximation for the small-x effective action. This provides insight into the correlation of fluctuations of the number of hard gluons versus their typical transverse momentum. We find that the spectral shape of the fluctuations of the gluon distribution is fundamentally different in the MV model, where there is a pileup of gluons near the saturation scale, versus the solution of the small-x JIMWLK renormalization group, which generates essentially scale-invariant fluctuations above the absorptive boundary set by the saturation scale.},

doi = {10.1103/PhysRevD.96.056029},

journal = {Physical Review D},

number = 5,

volume = 96,

place = {United States},

year = {2017},

month = {9}

}

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