# Fermionic Glauber operators and quark reggeization

## Abstract

We derive, in the framework of soft-collinear effective field theory (SCET), a Lagrangian describing the t-channel exchange of Glauber quarks in the Regge limit. The Glauber quarks are not dynamical, but are incorporated through non-local fermionic potential operators. These operators are power suppressed in |t|/s relative to those describing Glauber gluon exchange, but give the first non-vanishing contributions in the Regge limit to processes such as $$q\overline{q}$$→ $gg$ and $$q\overline{q}$$→$γγ$. They therefore represent an interesting subset of power corrections to study. The structure of the operators, which describe certain soft and collinear emissions to all orders through Wilson lines, is derived from the symmetries of the effective theory combined with constraints from power and mass dimension counting, as well as through explicit matching calculations. Lightcone singularities in the fermionic potentials are regulated using a rapidity regulator, whose corresponding renormalization group evolution gives rise to the Reggeization of the quark at the amplitude level and the BFKL equation at the cross section level. We verify this at one-loop, deriving the Regge trajectory of the quark in the 3 color channel, as well as the leading logarithmic BFKL equation. Results in the $$\overline{6}$$ and 15 color channels are obtained by the simultaneous exchange of a Glauber quark and a Glauber gluon. SCET with quark and gluon Glauber operators therefore provides a framework to systematically study the structure of QCD amplitudes in the Regge limit, and derive constraints on higher order amplitudes.

- Authors:

- Univ. of California, Berkeley, CA (United States). Berkeley Center for Theoretical Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group
- California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Institute for Theoretical Physics
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1485078

- Grant/Contract Number:
- AC02-05CH11231; SCD011090; SC0011632

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 2; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Perturbative QCD; Resummation

### Citation Formats

```
Moult, Ian, Solon, Mikhail P., Stewart, Iain W., and Vita, Gherardo.
```*Fermionic Glauber operators and quark reggeization*. United States: N. p., 2018.
Web. doi:10.1007/jhep02(2018)134.

```
Moult, Ian, Solon, Mikhail P., Stewart, Iain W., & Vita, Gherardo.
```*Fermionic Glauber operators and quark reggeization*. United States. doi:10.1007/jhep02(2018)134.

```
Moult, Ian, Solon, Mikhail P., Stewart, Iain W., and Vita, Gherardo. Wed .
"Fermionic Glauber operators and quark reggeization". United States. doi:10.1007/jhep02(2018)134. https://www.osti.gov/servlets/purl/1485078.
```

```
@article{osti_1485078,
```

title = {Fermionic Glauber operators and quark reggeization},

author = {Moult, Ian and Solon, Mikhail P. and Stewart, Iain W. and Vita, Gherardo},

abstractNote = {We derive, in the framework of soft-collinear effective field theory (SCET), a Lagrangian describing the t-channel exchange of Glauber quarks in the Regge limit. The Glauber quarks are not dynamical, but are incorporated through non-local fermionic potential operators. These operators are power suppressed in |t|/s relative to those describing Glauber gluon exchange, but give the first non-vanishing contributions in the Regge limit to processes such as $q\overline{q}$→ $gg$ and $q\overline{q}$→$γγ$. They therefore represent an interesting subset of power corrections to study. The structure of the operators, which describe certain soft and collinear emissions to all orders through Wilson lines, is derived from the symmetries of the effective theory combined with constraints from power and mass dimension counting, as well as through explicit matching calculations. Lightcone singularities in the fermionic potentials are regulated using a rapidity regulator, whose corresponding renormalization group evolution gives rise to the Reggeization of the quark at the amplitude level and the BFKL equation at the cross section level. We verify this at one-loop, deriving the Regge trajectory of the quark in the 3 color channel, as well as the leading logarithmic BFKL equation. Results in the $\overline{6}$ and 15 color channels are obtained by the simultaneous exchange of a Glauber quark and a Glauber gluon. SCET with quark and gluon Glauber operators therefore provides a framework to systematically study the structure of QCD amplitudes in the Regge limit, and derive constraints on higher order amplitudes.},

doi = {10.1007/jhep02(2018)134},

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

issn = {1029-8479},

number = 2,

volume = 2018,

place = {United States},

year = {2018},

month = {2}

}