Parametrization of the QCD coupling in the Evolution Equations

Abstract

We examine the parametrization of the QCD coupling in the Evolution Equations, including DGLAP. Our conclusion is that the well-known parametrization, where the argument of the coupling is k 2 ⊥ /β or just k 2 ⊥ , stands only if the lowest integration limit in the transverse momentum space (the starting point µ 2 of the Q 2 -evolution) obeys the relation µ ≫ ΛQCD exp (π/2), otherwise the coupling should be replaced by the more complicated expression presented in Eq. ( 37).