Abstract
It is well known that high-energy scattering of a meson from some hadronic target can be described by the interaction of that target with a color dipole formed by two Wilson lines corresponding to fast quark-antiquark pair. Moreover, the energy dependence of the scattering amplitude is governed by the evolution equation of this color dipole with respect to rapidity. Similarly, the energy dependence of scattering of a baryon can be described in terms of evolution of a three-Wilson-lines operator with respect to the rapidity of the Wilson lines. We calculate the evolution of the 3-quark Wilson loop operator in the next-to-leading order (NLO) and present a quasi-conformal evolution equation for a composite 3-Wilson-lines operator. We also obtain the linearized version of that evolution equation describing the amplitude of the odderon exchange at high energies.
Highlights
Over longitudinal momentum (≡ rapidity) into two parts: the coefficient functions with Y > η and the matrix elements of the Wilson-line operators with Y < η
It is well known that the high-energy scattering of a meson from some hadronic target can be described by the interaction of that target with a color dipole formed by two Wilson lines corresponding to the fast quark-antiquark pair
We calculated the evolution of the 3-quark Wilson loop operator in the Next-to-Leading Order (NLO), and we presented a quasi-conformal evolution equation for a composite 3-Wilson-line operator
Summary
Let us consider the proton scattering off a hadron target like another proton or a nucleus. The result of the integration over the rapidities Y > η gives the proton impact factor proportional to the product of two proton wavefunctions integrated over the longitudinal momenta. This impact factor is multiplied by a “color tripole” — 3QWL operator made of three (light-like) Wilson lines with rapidities up to η: Bmnl ≡ εi j h εijhUmi i Unjj Ulhh ≡ Um · Un · Ul,. At the second step the integrals over the gluons with the rapidity Y < η give the matrix element of the triple Wilson-line operator B123 between the target states. In the leading order the rapidity evolution of this operator was calculated in ref. [25, 26] while in this paper we present the result for the NLO evolution
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