Abstract
In this paper we derive the high energy evolution equation in the Gribov-Zwanziger approach for the confinement of quarks and gluons. We demonstrate that the new equation generates an exponential decrease of the scattering amplitude at large impact parameter and resolves the main difficulties of color glass condensate high energy effective theory. Such behavior occurs if the gluon propagator in Gribov-Zwanziger approach does not vanish at small momenta. Solving the nonlinear equation for deep inelastic scattering, we show that the suggested equation leads to a Froissart disc with radius (${R}_{F}$), which increases as ${R}_{F}\ensuremath{\propto}Y=\mathrm{ln}(1/x)$, and with a finite width for the distribution over $|b\ensuremath{-}{R}_{F}|$.
Highlights
INTRODUCTIONN ð1Þ generates a scattering amplitude which decreases as a power of b at large impact parameter (see Ref. [2] for review)
It is well known that the Balitsky-Kovchegov (BK) equation [1]∂∂Y1⁄4NαðSrZ; b;d2Y2πÞr0 Kðr0; r − r0; rÞ N b1 2 ðr r0Þ; Y þN r0 ; − Nðr;b;YÞ −NN ð1Þ generates a scattering amplitude which decreases as a power of b at large impact parameter
We demonstrate that the new equation generates an exponential decrease of the scattering amplitude at large impact parameter and resolves the main difficulties of color glass condensate high energy effective theory
Summary
N ð1Þ generates a scattering amplitude which decreases as a power of b at large impact parameter (see Ref. [2] for review). Using two ingredients: the observation from Sec. II that the large impact parameter behavior stems from the gluon reggeization in the momentum representation and the general expression for the gluon reggeization through the gluon propagators [3,4,5], we find the behavior of the kernel for the BFKL evolution in the case of GribovZwanziger confinement. II that the large impact parameter behavior stems from the gluon reggeization in the momentum representation and the general expression for the gluon reggeization through the gluon propagators [3,4,5], we find the behavior of the kernel for the BFKL evolution in the case of GribovZwanziger confinement We show that this mechanism of confinement introduces a new dimensional parameter, and it leads to the exponential decrease of the scattering amplitude at large b, but only if the gluon propagator does not vanish at zero momentum.
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