Evaluations of low-energy physical quantities in QCD with IR freezing of the coupling

Abstract: MSbar-like schemes in QCD have in general the running coupling which contains Landau singularities, i.e., singularities outside the timelike semi-axis, at low squared momenta. As a consequence, evaluation of the spacelike quantities, such as current correlators, in terms of (powers of) such a coupling then results in quantities which contradict the basic principles of Quantum Field Theories. On the other hand, in those QCD frameworks where the running coupling remains finite at low squared momenta (IR freezing), the coupling usually does not have Landau singularities in the complex plane of the squared momenta. I argue that in such QCD frameworks the spacelike quantities should not be evaluated as a power series, but rather as a series in derivatives of the coupling with respect to the logarithm of the squared momenta. Such series show considerably better convergence properties. Moreover, Pade-related resummations of such logarithmic derivative series give convergent series, thus eliminating the practical problem of series divergence due to renormalons.