Renormalization of the pseudoscalar operator at four loops in QCD

We present the renormalization constant of the pseudoscalar operator defined with a non-anticommuting ${\gamma }_5$ in dimensional regularization up to four-loop order in perturbative Quantum Chromodynamics (QCD). Furthermore, by virtue of renormalization-group invariance of the relation between the scalar and the pseudoscalar operator, we predict the $\overline{\mathrm{M}\mathrm{S}}$ factor of the renormalization constant for the latter at five-loop order in QCD.