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Invariant color calculus and generalized Balitsky-Kovchegov hierarchy

Invariant color calculus and generalized Balitsky-Kovchegov hierarchy We derive generalization of the Balitsky-Kovchegov (BK) equation for a dipole, which consists of a parton and an antiparton of arbitrary charge. At first, we develop one method of indexless transformation of color expressions. The method is based on an evaluation of the Casimir operator on a tensor product. From the Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner equation, we derive the evolution equation for a single parton and prove gluon Reggeization in an arbitrary color channel. We show that there is a color duplication of such Regge poles. Higher t -channel color exchange has its own Regge pole, which residue is proportional to the quadratic Casimir. Taking a fundamental representation, we derive the usual BK equation and shed new light on the meaning of linear and nonlinear terms. Finally, we discuss a linearized version of the generalized BK equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Invariant color calculus and generalized Balitsky-Kovchegov hierarchy

Popov, Alexey V
Physical Review D , Volume 79 (1) – Jan 1, 2009
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Publisher
American Physical Society (APS)
Copyright
Copyright © 2009 The American Physical Society
ISSN
1550-2368
DOI
10.1103/PhysRevD.79.014020
Publisher site
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Abstract

We derive generalization of the Balitsky-Kovchegov (BK) equation for a dipole, which consists of a parton and an antiparton of arbitrary charge. At first, we develop one method of indexless transformation of color expressions. The method is based on an evaluation of the Casimir operator on a tensor product. From the Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner equation, we derive the evolution equation for a single parton and prove gluon Reggeization in an arbitrary color channel. We show that there is a color duplication of such Regge poles. Higher t -channel color exchange has its own Regge pole, which residue is proportional to the quadratic Casimir. Taking a fundamental representation, we derive the usual BK equation and shed new light on the meaning of linear and nonlinear terms. Finally, we discuss a linearized version of the generalized BK equation.

Journal

Physical Review D – American Physical Society (APS)

Published: Jan 1, 2009

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