Five-dimensional CFTs from the ε -expansion

We look for UV fixed points of non-Abelian $SU({n}_{c})$ gauge theories in $4+2\ensuremath{\epsilon}$ dimensions with ${n}_{f}$ Dirac fermions in the fundamental representation, using the available five-loop $\overline{\mathrm{MS}}$ $\ensuremath{\beta}$-function and employing Pad\'e-Borel resummation techniques and Pad\'e approximants to the series expansion in $\ensuremath{\epsilon}$. We find evidence for a five-dimensional UV fixed point for $SU(2)$ theories with ${n}_{f}\ensuremath{\le}4$ and pure $SU({n}_{c})$ theories for ${n}_{c}\ensuremath{\le}4$. We also compute the anomalous dimensions $\ensuremath{\gamma}$ and ${\ensuremath{\gamma}}_{g}$ of respectively the fermion mass bilinear and the gauge kinetic term operator at the UV fixed point.