Conformal window from conformal expansion

We study the conformal window of asymptotically free gauge theories containing ${N}_{f}$ flavors fermion matter transforming to vector and two-index representations $SO(N),SU(N)$ $Sp(2N)$ groups. For $SO(N)$ we also consider spinorial representation. determine critical number ${N}_{f}^{\mathrm{cr}}$, corresponding lower end window, by using conjectured condition on anomalous dimension bilinear at an infrared fixed point, ${\ensuremath{\gamma}}_{\overline{\ensuremath{\psi}}\ensuremath{\psi},\mathrm{IR}}=1$ or equivalently ${\ensuremath{\gamma}}_{\overline{\ensuremath{\psi}}\ensuremath{\psi},\mathrm{IR}}(2\ensuremath{-}{\ensuremath{\gamma}}_{\overline{\ensuremath{\psi}}\ensuremath{\psi},\mathrm{IR}})=1$. To compute ${\ensuremath{\gamma}}_{\overline{\ensuremath{\psi}}\ensuremath{\psi},\mathrm{IR}}$ employ (scheme-independent) Banks-Zaks expansion up 4th order in ${\mathrm{\ensuremath{\Delta}}}_{{N}_{f}}={N}_{f}^{\mathrm{AF}}\ensuremath{-}{N}_{f}$ with ${N}_{f}^{\mathrm{AF}}$ onset loss asymptotic freedom, where show that latter provides a better performance along this expansion. quantify uncertainties our analysis, which potentially originate from nonperturbative effects, propose two distinct approaches assuming large behavior separately, either convergent divergent asymptotic. In former case, take difference Pad\'e approximants definitions condition, whereas case truncation error associated singularity Borel plane is taken into account. Our results are further compared other analytical methods as well lattice available literature. particular, find $SU(2)$ six $SU(3)$ ten fundamental likely edge consistent recent results. predict $Sp(4)$ antisymmetric fermions have numbers flavors, approximately five, respectively.