Next-to-leading order Balitsky-Kovchegov equation beyond large $N_{\mathrm{c}}$

Abstract

We calculate finite-$N_{\mathrm{c}}$ corrections to the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation. We find analytical expressions for the necessary correlators of six Wilson lines in terms of the two-point function using the Gaussian approximation. In a suitable basis, the problem reduces from the diagonalization of a six-by-six matrix to the diagonalization of a three-by-three matrix, which can easily be done analytically. We study numerically the effects of these finite-$N_{\mathrm{c}}$ corrections on the NLO BK equation. In general, we find that the finite-$N_{\mathrm{c}}$ corrections are smaller than the expected $1/N_{\mathrm{c}}^2\sim 10\%$. The corrections may be large for individual correlators, but have less of an influence on the shape of the amplitude as a function of the dipole size. They have an even smaller effect on the evolution speed as a function of rapidity.

arXiv comment17 pages, 9 figures

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