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Boris Ermolaev (PhTI , Petersburg)
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Parametrization of the QCD coupling in hard processes and evolution equations.
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We examine the parametrization of the QCD coupling in the Bethe-Salpeter
equations for the hard and Regge processes and determine the argument of
alpha_s of the factorized gluon. Our analysis shows that for the hard
processes alpha_s = alpha_s(k^2_T/(1- beta)) where k^2_T and beta are the
longitudinal and transverse moment of the soft parton. On the other hand,
in the Regge processes alpha_s = alpha_s(k^2_T}/beta). We have also shown
that the well-known parametrization alpha_s = alpha_s(k^2_T) in the DGLAP
equations stands only if the lowest integration limit, mu^2, over k^2_T
(the starting point of the Q^2 -evolution) obeys the relation mu >>
Lambda_{QCD} exp {(\pi/2)}, otherwise the coupling should be replaced by
the more complicated expression.