# The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

## Abstract

Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. Furthermore, this equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We also compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. By enabling the asymptotic expansion we find that the perturbative seed is correct; we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-discmore »

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1360709

- Report Number(s):
- LA-UR-16-27653

Journal ID: ISSN 1029-8479; TRN: US1702168

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; Perturbative QCD; Resummation

### Citation Formats

```
Neill, Duff.
```*The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts*. United States: N. p., 2017.
Web. doi:10.1007/JHEP01(2017)109.

```
Neill, Duff.
```*The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts*. United States. doi:10.1007/JHEP01(2017)109.

```
Neill, Duff. Wed .
"The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts". United States.
doi:10.1007/JHEP01(2017)109. https://www.osti.gov/servlets/purl/1360709.
```

```
@article{osti_1360709,
```

title = {The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts},

author = {Neill, Duff},

abstractNote = {Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. Furthermore, this equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We also compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. By enabling the asymptotic expansion we find that the perturbative seed is correct; we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.},

doi = {10.1007/JHEP01(2017)109},

journal = {Journal of High Energy Physics (Online)},

number = 1,

volume = 2017,

place = {United States},

year = {Wed Jan 25 00:00:00 EST 2017},

month = {Wed Jan 25 00:00:00 EST 2017}

}

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