Impact of the pion mass on nonpower expansion for QCD observables

Abstract

A new set of functions, which form a basis of the massive nonpower expansion for physical observables, is presented in the framework of the analytic approach to QCD at the four-loop level. The effects due to the $π$ meson mass are taken into account by employing the dispersion relation for the Adler function. The nonvanishing pion mass substantially modifies the functional expansion at low energies. Specifically, the spacelike functions are affected by the mass of the $π$ meson in the infrared domain below few GeV, whereas the timelike functions acquire characteristic plateaulike behavior below the two-pion threshold. At the same time, all the appealing features of the massless nonpower expansion persist in the considered case of the nonvanishing pion mass.