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Register a new userGribov-Zwanziger confinement, high energy evolution and large impact parameter behaviour of the scattering amplitude
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E. Gotsman
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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 CGC (Colour Glass Condensate) high energy effective theory. Such behaviour occurs if the gluon propagator in Gribov-Zwanziger approach, does not vanish at small momenta. Solving the non-linear 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 ,propto Y = ln (1/x)$, and with a finite width for the distribution over $| b - R_F|$.
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In this paper we solved the new evolution equation for high energy scattering amplitudethat stems from the Gribov-Zwanziger approach to the confinement of quarks and gluons. We found that (1) the energy dependence of the scattering amplitude turns out to be the same as for QCD BFKL evolution; (2) the spectrum of the new equation does not depend on the details of the Gribov-Zwanzinger approach and (3) all eigenfunctions coincide with the eigenfunctions of the QCD BFKL equation at large transverse momenta $kappa,geq,1$. The numerical calculations show that there exist no new eigenvalues with the eigenfunctions which decrease faster than solutions of the QCD BFKL equation at large transverse momenta. The structure of the gluon propagator in Gribov-Zwanziger approach, that stems from the lattice QCD and from the theoretical evaluation, results in the exponential suppression of the eigenfunctions at long distances and in the resolution of the difficulties, which the Colour Glass Condensate (CGC) and some other approaches, based on perturbative QCD, face at large impact parameters. We can conclude that the confinement of quark and gluons, at least in the form of Gribov-Zwanziger approach, does not influence on the scattering amplitude except solving the long standing theoretical problem of its behaviour at large impact parameters.
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