Abstract
We discuss the high energy scattering of hadrons with the multi-Regge kinematics. The effective 2D model for the interaction between the produced hard gluons appears as a result of the dimensional reduction, which is similar to the dimensional reduction 3+1 D rightarrow 3 D of the high temperature gauge theory. It is demonstrated that being supplemented by the exchange by virtual 3+1 D gluons this 2D model gives rise to the hermitian version of the effective action of Lipatov for the interaction between the ordinary and the reggeized gluons.
Highlights
The d√escription of the hadron-hadron scatteri√ng at large energies s compared to the momentum transfer t is dominated by the amplitudes with the so-called multi-Regge kinematics [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
The integration over x± is effectively reduced to the integration over the intervals of lengths 1/Λ because we describe the high energy scattering in the center of inertia reference frame, and the scattered particles have such a large energy that during the collision the fields A±, Aa have not time to change. 1/Λ is of the uncertainty relation assumes
In order to use the above actions for the calculation of the leading contribution to the scattering amplitude of the i-the sector in the multi-Regge kinematics we should calculate the correlator of Eq (20) in the center of inertia reference frame of the two colliding hadrons
Summary
The d√escription of the hadron-hadron scatteri√ng at large energies s compared to the momentum transfer t is dominated by the amplitudes with the so-called multi-Regge kinematics [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. The effective theory of Lipatov should be able to reproduce the basic features of this approach as well as of the other formalisms related to the resummation of leading logarithms and to the description of the processes with the multi-Regge kinematics associated with the small-x physics. The light cone coordinates of the original version of Lipatov theory correspond to the direction of motion of the colliding hadrons in their center of inertia reference frame. Using the Eikonal approximation for the multi-gluon ejection/absorbtion by the high energy particles, we are able to express in this effective theory the contribution to the scattering amplitude through the propagator of the reggeon.
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