On equivalence of gluon-loop exchange in the inelastic processes in perturbative QCD to pion exchange in ɸ³ theory

¹ Odessa National Polytechnic University, Shevchenko av. 1, 65044 Odessa, Ukraine
² Jozef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
³ Bielefeld University, Universitatsstrasse 25, 33615 Bielefeld, Germany

^a e-mail: sharph@ukr.net
^b e-mail: andrii.tykhonov@ijs.si
^c e-mail: siiis@te.net.ua

Published online: 26 November 2013

Abstract

We consider the hadron–hadron inelastic scattering in the framework of QCD perturbation theory. It is shown that in QCD, due to conservation of color, the tree-level diagrams of inelastic scattering are prohibited and one has to deal with the diagrams with loops. We examine the simplest type of such diagrams, where the diagram can be split into blocks, so that the integration over four-momenta of virtual particles in each block can be done independently. It is shown that for these diagrams the squared absolute value of scattering amplitude has a maximum point, similar to that observed earlier in ɸ³ model, if one takes into account the relations between the arguments of scattering amplitude, imposed by the energy-momentum conservation law. This enables to apply the Laplace’s method for the calculation of cross section of hadron–hadron inelastic scattering. It is shown that the diagrams of gluon-loop exchange in QCD are equivalent to the diagrams of pion exchange in ɸ³ theory, whereby the new mechanism of cross section growth, discovered earlier in ɸ³ theory, takes place also in the perturbative QCD. The latter may explain the origin of experimentally-observed growth of cross section of hadron–hadron inelastic scattering as function of energy of colliding hadrons. The discovered mechanism can’t emerge in any Regge-based model due to the premises on the particle kinematics, made in these models.