Gluon propagator in fractional analytic perturbation theory

We consider the gluon propagator in the Landau gauge at low spacelike momenta and with the dressing function Z(Q2) at the two-loop order. We incorporate the nonperturbative effects by making the (noninteger) powers of the QCD coupling in the dressing function Z(Q2) analytic (holomorphic) via the fractional analytic perturbation theory (FAPT) model, and simultaneously introducing the gluon dynamical mass in the propagator as motivated by the previous analyses of the Dyson-Schwinger equations. The obtained propagator has behavior compatible with the unquenched lattice data (Nf=2+1) at low spacelike momenta 0.4GeV<Q≲10GeV. We conclude that the removal of the unphysical Landau singularities of the powers of the coupling via the (F)APT prescription, in conjunction with the introduction of the dynamical mass M≈0.62GeV of the gluon, leads to an acceptable behavior of the propagator in the infrared regime.