Unification scale vs. electroweak-triplet mass in the SU(5) + 24_F model at three loops

It was shown recently that the original SU(5) theory of Georgi and Glashow, augmented with an adjoint fermionic multiplet 24_F, can be made compatible both with neutrino masses and gauge coupling unification. In particular, the model predicts that either electroweak-triplet states are light, within the reach of the Large Hadron Collider (LHC), or proton decay will become accessible at the next generation of megaton-scale facilities. In this paper, we present the computation of the correlation function between the electroweak-triplet masses and the unification scale at the next-to-next-to-leading-order (NNLO). Such an accuracy on the theory side is necessary in order to settle the convergence of the perturbative expansion and to match the experimental precision on the determination of the electroweak gauge couplings at the Z-boson mass scale.