# Solving effective field theory of interacting QCD pomerons in the semiclassical approximation

## Abstract

Effective field theory of Balitsky, Fadin, Kuraev, and Lipatov (BFKL) pomerons interacting by QCD triple pomeron vertices is investigated. Classical equations of motion for the effective pomeron fields are presented being a minimal extension of the Balitsky-Kovchegov equation that incorporates both merging and splitting of the pomerons and that is self-dual. The equations are solved for symmetric boundary conditions. The solutions provide the dominant contribution to the scattering amplitudes in the semiclassical approximation. We find that for rapidities of the scattering larger than a critical value Y{sub c} at least two classical solutions exist. Curiously, for each of the two classical solutions with the lowest action the symmetry between the projectile and the target is found to be spontaneously broken, being however preserved for the complete set of classical solutions. The solving configurations at rapidities Y>Y{sub c} consist of a Gribov field being strongly suppressed even at very large gluon momenta and the complementary Gribov field that converges at high Y to a solution of the Balitsky-Kovchegov equation. Interpretation of the results is given and possible consequences are shortly discussed.

- Authors:

- II Institute for Theoretical Physics, University of Hamburg (Germany)
- DESY Theory Group, Hamburg (Germany)
- (Poland)

- Publication Date:

- OSTI Identifier:
- 20929554

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevD.75.114015; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUNDARY CONDITIONS; EQUATIONS OF MOTION; GLUONS; MATHEMATICAL SOLUTIONS; PARTICLE RAPIDITY; POMERANCHUK PARTICLES; QUANTUM CHROMODYNAMICS; SCATTERING; SCATTERING AMPLITUDES; SEMICLASSICAL APPROXIMATION; SYMMETRY

### Citation Formats

```
Bondarenko, S., Motyka, L., and Institute of Physics, Jagellonian University, Cracow.
```*Solving effective field theory of interacting QCD pomerons in the semiclassical approximation*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.114015.

```
Bondarenko, S., Motyka, L., & Institute of Physics, Jagellonian University, Cracow.
```*Solving effective field theory of interacting QCD pomerons in the semiclassical approximation*. United States. doi:10.1103/PHYSREVD.75.114015.

```
Bondarenko, S., Motyka, L., and Institute of Physics, Jagellonian University, Cracow. Fri .
"Solving effective field theory of interacting QCD pomerons in the semiclassical approximation". United States.
doi:10.1103/PHYSREVD.75.114015.
```

```
@article{osti_20929554,
```

title = {Solving effective field theory of interacting QCD pomerons in the semiclassical approximation},

author = {Bondarenko, S. and Motyka, L. and Institute of Physics, Jagellonian University, Cracow},

abstractNote = {Effective field theory of Balitsky, Fadin, Kuraev, and Lipatov (BFKL) pomerons interacting by QCD triple pomeron vertices is investigated. Classical equations of motion for the effective pomeron fields are presented being a minimal extension of the Balitsky-Kovchegov equation that incorporates both merging and splitting of the pomerons and that is self-dual. The equations are solved for symmetric boundary conditions. The solutions provide the dominant contribution to the scattering amplitudes in the semiclassical approximation. We find that for rapidities of the scattering larger than a critical value Y{sub c} at least two classical solutions exist. Curiously, for each of the two classical solutions with the lowest action the symmetry between the projectile and the target is found to be spontaneously broken, being however preserved for the complete set of classical solutions. The solving configurations at rapidities Y>Y{sub c} consist of a Gribov field being strongly suppressed even at very large gluon momenta and the complementary Gribov field that converges at high Y to a solution of the Balitsky-Kovchegov equation. Interpretation of the results is given and possible consequences are shortly discussed.},

doi = {10.1103/PHYSREVD.75.114015},

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

number = 11,

volume = 75,

place = {United States},

year = {Fri Jun 01 00:00:00 EDT 2007},

month = {Fri Jun 01 00:00:00 EDT 2007}

}